Talk:Single transferable vote

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Archive 1

NP hard[edit]

Can you please summarise what NP-hard means. This is a wholly inappropriate use of jargon - one needs to read another whole article to deduce what it means. I am a politics student, and have studied politics as a personal interest for many years, but have never come across the application of NP-hard <or even any explanation of what it meant> in relation to STV.

If someone could explain that a bit better, I'd be v. grateful. (RM21 00:13, 14 July 2006 (UTC))
  • I think the NP hard statements are a little over the top. Yes, I accept that it is possible to construct a situation where it is difficult to compute and that is what the proof does. But what is suggested here is that STV tactical voting is always NP-hard. That is the equivalent of saying that finding a prime factor of a large number is hard: yes it is for some, but not for 1000000000000000000000000000000000000000000000000000 or indeed any even number. Take for example the Knockiveagh 21 May 1997 election [1] (about 2/3 of the way down the page that is linked from a related page). It seems obvious to me that if the SDLP first preferences had been evenly split 805/804 rather than 946/661 then the party would have won two seats rather than one. Many parties try to manage their votes in this way especially in systems where full preferences are not expressed, and many voters are happy to follow guidance (as they are in SNTV where balancing the votes is even more important). --Henrygb 17:46, 10 July 2005 (UTC)
  • Tactical voting is always NP-hard, however NP-hard problems are not always unsolvable. This is particularly true in the small districts of only 4 or 5 representatives common to many of the STV systems. Also, it is quite possible that erroneous assumptions about the viability of their strategy are being used by election campaigns. Also, tactical voting is easier in systems not using Meek's method, as stated in the article. Was Knockiveagh using that method in 97? Scott Ritchie 22:53, 10 July 2005 (UTC)
Trying to balance first preference votes between candidates from the same party is a standard vote management technique in many systems where there are substantial numbers of incomplete preferences. Getting it to work is sometimes difficult because some voters will not take instruction, but the mathematics of it are relatively simple:
If at the final stage there are three remaining candidates all under quota, two of which are from your party and one from another, and your two candidates have more than twice as votes between them as the other candidate, then if your candidates' support is evenly shared you will win both seats. If not then you may not. There is more likely to be balanced support in the final round if there is balanced support in the first round.
To stop that you would need a system which reduces the quota as votes drop off - does Meek's method do that? As far as I am aware, Meek's method is used in New Zealand and not in the other countries listed. If so, the article should make that clear. It is certainly not used in Northern Ireland, the Republic of Ireland or Malta. I don't know about Australia. --Henrygb 00:29, 11 July 2005 (UTC)
Meek's method does reduce quota as votes are exhausted.--TreyHarris 00:44, 11 July 2005 (UTC)
Indeed. I found this [2] --Henrygb 01:21, 11 July 2005 (UTC)

BTW, NP-complete problems always have many easy solutions, far far more than factoring, which is why NP-complete problems are not used for cryptography. Yes, the NP-hard part should be toned down. Its easy to imagine asituation where a significant amount of information proved that a specific voting strategy was optimal. JeffBurdges 22:27, 26 November 2005 (UTC)

Could you describe one - for a layman?--Red Deathy 08:43, 28 November 2005 (UTC)
On Karp's_21_NP-complete_problems, it says "many of the problems can be solved if restricted to special cases, or can be solved within any fixed percentage of the optimal result". A good example is the traveling salesman problem where many solutions are easy to find, just not all of them. Anyway, it might be true that "tactical voting in STV elections is vastly more difficult than with other commonly-used election methods", but just being NP-hard really does not support this claim at all. JeffBurdges 15:23, 29 November 2005 (UTC)
The best naive explination is: Some problems are hard and some are easy, but all problems have sub-problems inside them, as well as supper-problems containing them, and you can obviously glue problems together if you like. Said this way, it seem natural that "most" hard problems have big easy sub-problems. JeffBurdges 23:02, 29 November 2005 (UTC)
Ta, that's helpful, but (and sorry to be a pain) you say Its easy to imagine asituation where a significant amount of information proved that a specific voting strategy was optimal could you describe one? It'll help relate this discussion to the article and provide some cues for proper editing. --Red Deathy 09:18, 30 November 2005 (UTC)

A question: is Meek's Method of counting NP-Hard itself? It looks as if it could be: it uses approximation methods, gets highly complicated with extra candidates and seats, and even with computer counting in New Zealand, it led to weeks of delay in announcing the results. In that case tactical voting will be at least as hard. --Henrygb 12:18, 31 January 2006 (UTC)

No, definitely not. There's a difference between sounding complicated and taking an amount of time that grows exponentially, and there's a difference between that and the theoretical notion known as "NP-hard".
What "NP-hard" means is that if you find a way to solve it in a polynomial amount of time in any possible situation -- note that this can be any polynomial, even an unreasonably large one like n1000000 -- then you solve a huge theoretical problem in CS at the same time. It has almost nothing to do with how long the votes actually take to count in real life, especially since many situations can be easy and yet the general problem can still be NP-hard. Or, the problem can be completely infeasible to solve but not be NP-hard because it doesn't have the theoretical properties.
Of course, we know that applying STV isn't completely infeasible. We have clear rules that tell us just how to do it, and people even manage to do it without the aid of computers in many situations. If the election results take a week to return, that's not theoretical computer science getting in your way, it's bureaucracy.
I'd say that computer science concepts that sound more relevant than they are and are so prone to be misinterpreted do not belong in this article. rspeer / ɹəədsɹ 04:31, 14 July 2006 (UTC)


We'd do really well with some good pictures of actual STV ballots to show what voting is like. An Australian ballot demonstrating group voting tickets, for instance, would round out a section nicely. Also, replacing that MS Paint picture that's in there currently would be nice :) (unsigned 21:18, 28 May 2005 User:Scott Ritchie)

I am not sure about ballot papers: these really belong in the preference voting page; even group tickets are a form of preference voting. --Henrygb 22:13, 31 May 2005 (UTC)
Why not have them here as well? Nothing prohibits us from using the same image in multiple articles (the one there is used that way already), and they certainly add information about what STV is like, and since afterall this is meant to be an encylopedic article on STV, that can only help make it better. Scott Ritchie 00:02, 1 Jun 2005 (UTC)
The article is fairly long as it is. And there is plenty more on preferential voting (e.g. the potential for confirming vote buying) which could also go here. But I don't really care. --Henrygb 19:55, 2 Jun 2005 (UTC)
I added one for the Aussie system. It's not a real ballot I don't think but it gets the idea across. Felix the Cassowary 03:56, 12 July 2005 (UTC)

First preference and party preference[edit]

The proportionality section is getting a little apologetic again, saying that it is impossible to determine whether first preferences reflect party preferences, and saying this twice. It is in fact easier to measure for STV than for any one candidate per party system or SNTV since the proportion of people who transfer from a candidate of one party to a candidate of a different party when they could have gone to a candidate of the same party can be measured. It might be sensible to look at early transfers to avoid donkey vote effects. In Malta a quick clance suggests this seems to be about 1%, in Northern Ireland perhaps about 15-20%, at least for distinctive parties - the smaller non-sectarian parties seem to swap votes more. --Henrygb 22:10, 8 Jun 2005 (UTC)

  • A measure of party loyalty, however, is still not a measure of party preferences. For instance, it could be the case that the first five candidates on my ballot represent moderates from another party. More importantly, you need a mechanism for distinguishing between early defectors (say, one who ranks only one or two candidates for a party before choosing another) and late defectors (say, one who ranks all but one candidate from the same party before picking candidates from another) - do you count them both equally as members of the same party, or both equally as defectors? Scott Ritchie 23:08, 8 Jun 2005 (UTC)

Article could really use some expansion on the Irish bits[edit]

This article could benefit a great deal from some review of the history of STV in the Republic of Ireland and Northern Ireland. The articles on Ireland, Gerrymandering, and The Troubles hint that STV might have come about as a solution to some of the serious problems caused by the old voting system that may have lead to the Irish civil rights movement, such as disenfranchisement via gerrymandering. I don't know anything about the history myself, however, but Wikipedia could certainly use some review of this topic (either here or in the related Irish articles). I'm going to tag this article for expansion. Scott Ritchie 06:53, 11 July 2005 (UTC)

The only slight problem with this is that STV there started with the Irish elections, 1921. It continued in the Free State/Eire/Republic despite the desire of leading politicians to end it. It was stopped in Northern Ireland (late 1920s?) because too many Labour or other non-sectarian representatives were being elected. Then came local gerrymandering (most notably in Derry/Londonderry). In Northern Ireland it came back into local government in 1973 where it has remained. It is a matter of opinion whether electoral areas are still carefully drawn: see for example Belfast [3] and compare unionist/loyalist Court with nationalist/republican Lower Falls next door. Meanwhile in the Republic the average number of winners in a constituency is below 4. --Henrygb 19:51, 11 July 2005 (UTC)
And even Derry/Londonderry carries a curious result in 1973: the United Loyalists and the Alliance Party between them won a majority of the first preferences, but the SDLP, Nationalists, and Republican Clubs won a majority of the seats under STV.[4] --Henrygb 00:17, 12 July 2005 (UTC)
How's that curious? Why would STV have preferences if that sort of thing was forbidden, or to be considered odd? It happens all the time, because STV isn't proportional on first preferences, but proportional on the balance of preferences. (A controversial case of it happened in the last Australian Senate election for Victoria, but that was due to an oddity of the Australian system allowing Parties to allocate preferences if the voter lets them—and it probably won't happen again.) Felix the Cassowary 02:13, 12 July 2005 (UTC)
Very late in the day comments, but here's my 2c. It probably looks odd to those familiar with the parties and the likely transfer patterns. STV in practice can throw up anomalies because although it's aiming for reasonable proportionality within a single constituency, multiple constituencies together can create anomalies. In an individual constituency there is always a near quota of votes left over at the end of the count so one party can get a smaller % of seats than its vote even with heavy internal transfers. See for instance this Tasmanian example (scroll down a bit to the diagrams) where the Liberals had 31.4% of first preferences, 31.7% on the final count and 20% of seats. Note also that Labor had 47.2% of first preferences, 50% of the final count and 60% of seats.
(Irish observers will be surprised to see the parties nominating so many candidates which would be electoral suicide in Irish elections but this is a consequence of the specific local rules - a voter must cast at least 5 preferences for their vote to be valid and candidates from the same party are grouped together. Running 5 candidates minimises the leakage as many voters will just vote for a single party - especially voters who wouldn't turn out under non-compulsory voting.)
If this effect is repeated in multiple constituencies then the anomalies start to stack up and magnify. Differential levels of turnout in difference constituencies can also create problems in comparing the overall popular vote to the seat result. One of the most notorious cases was the Maltese general election, 1981. In a country with a very strong two party system and very heavy internal rates of transfers one party got the most votes but another the most seats. This provoked an opposition boycott and a constitutional crisis which was resolved by introducing an emergency top-up method so in future elections the party with the most first preferences is guaranteed a majority of seats. This kicked in to the Nationalists' benefit in 1987 & 2008, and Labour's in 1996. Timrollpickering (talk) 11:05, 17 May 2011 (UTC)
As for the disparity between Court and Lower Falls this isn't due to the original drawing of those areas but rather a combination of the failure to redraw since and differential turnout. The current ward boundaries & DEA combinations were drawn up about twenty years ago and were never intended to last as long as they have; however restructuring of local government in Northern Ireland has been repeatedly deferred by a combination of the problems with getting lasting devolution and more recently the lack of political will (on multiple sides) for it. Consequently the ward boundaries have not yet been subject to a review despite population shifts that have seen Court decline comparative to Lower Falls. There's also the issue of differential turnout with the Falls traditionally having a much higher turnout than Court, but very few electoral systems take this into account and the boundaries are based on the registered electorate only. Timrollpickering (talk) 11:05, 17 May 2011 (UTC)

Wasted votes[edit]

I am not convinced that we can say something like "the number of wasted votes must by necessity be less than a quota". Two examples, the first plausible, the second not:

  • A one seat STV election where 60% of the first preferences go to one candidate: the quota is marginally over 50% of the votes, but the wasted votes are the 40% going to the other candidates plus the 20% of the total votes which the winner won but did not need to win on the first round, making virtually 60%.
  • A ten seat STV election with eleven candidates: 1000 voters give a full preference listing for the first 10 candidates in various orders with the candidate Z in last place every time, while 1 voter puts the candidate Z first. The quota will be 1001/11+1=92, but the number of wasted votes will be 980 (those of the 1000 which would not have made any difference to the result if they had not been cast) plus 1 for the first preference for candidate Z.

Clearly you could define wasted votes so as to ignore unnecessary votes for winning candidates, but taking that as your definition would justify an STV system which did not transfer surpluses, leading to fewer wasted votes. --Henrygb 22:45, 28 July 2005 (UTC)

    • Hmm, I see what you're saying. I will note that in your second example, the candidates are winning not because they fulill quotas, but because all other candidates were eliminated. It is still true, however, that the number of remaining excess votes (a subset of wasted votes) will always be less than one quota. Scott Ritchie 23:29, 28 July 2005 (UTC)
      • I had imagined that in the second case, the surpluses would shuffle round the first 10 candidates until they each had 92 or more; if there had only been 20 votes for them together and 1 for Candidate Z then the surpluses would shuffle round until the first 10 each had 2 votes (or the quota if a smaller fraction). But it doesn't really matter. --Henrygb 19:55, 29 July 2005 (UTC)

The New Example[edit]

I don't want to knock other people's hard work - but I don't find thenew example that easy to follow - IMNSHO the pictures are distracting and the star votes aren't that clear. I do think a simple numerical table suffices. Maybve I'm just being a miserable old git. Sorry. --Red Deathy 12:31, July 29, 2005 (UTC)

  • I cleared out some of the unnecessary pictures, so it should look a little smoother now. Also, the stars were just an arbitrary character I picked - perhaps something larger and easier to color-differentiate would be better. I do think the added visibility of seeing which votes are transfering is helpful, however - I did this demonstration live with toothpicks, and found that people grasped it a lot better when there was a visible movement of certain toothpicks from one pile to another. The colored stars are an attempt to illustrate that sort of movement - something we can't get with numbers. Scott Ritchie 10:50, 30 July 2005 (UTC)
  • My only complaint is that the stars in the example are too hard to distinguish. All of the reddish-orange colors look about the same. Even if they don't match the pictures, some of them should be changed to different colors like green, purple, or black. I also suggest a more visible vote marker, like ♦, except I'm not sure if entities like that show up in everybody's browser. Maybe even just a bold x. RSpeer 06:59, August 15, 2005 (UTC)
    • You're definately right about this. I went and changed the stars to x's and made the colors more visible. My concern, however, is with people who are color-blind in various ways - perhaps we can find one to comment on the current colors, altering them with dashes of red and blue if need be. Scott Ritchie 21:37, 16 August 2005 (UTC)
      • First impressions: The new one is hard to read even with the x's. At first I thought there was an error, because it said "20 voters" and I only saw 6. It does not come easily that the x's represent multiple voters with the same votes. If numbers after x's and colons were used, such as "4x:", "2x:", "8x:", etc., it would be more clear -- 11:17, 30 September 2005 (UTC)
  • I think there's also a problem with it. Look at round 2. Chocolate's been elected and we're looking for 2 more winners. We only have 14 votes that are still not yet locked in. The droop quota at round two is floor((14/3)+1) == 5. This means that strawberry wins in round 2, followed by an elimination of pear in round 3, and a win for orange in round 4. Correct me if I'm wrong please. :) --06:58, 11 December 2009 (UTC) —Preceding unsigned comment added by (talk)
  • To avoid ambiguity in Round 1, can we please have a different number of surplus votes for chocolate compared to the quota? Currently they are both six which makes the explanation slightly ambiguous. And in Round 2 could we please have different values for number of surplus votes compared to total number of transferable votes (currently both are six). I know this is not easy to design and still have the equations give neat integer solutions. Sqgl (talk) 10:51, 26 August 2013 (UTC)

"number of surplus votes/total number of transferable votes (that have the second preference)*number of second preferences of the given candidate" wouldn't this be clearer as (number of second preferences of the given candidate * number of surplus votes) /total number of transferable votes [that have the second preference] — Preceding unsigned comment added by (talk) 19:54, 4 June 2014 (UTC)

US dates[edit]

Lo all - I've shoved the list of US cities that used STV off to a specific list page, though useful; I don't think it belonged in the article.

If anyone could scare up some dates to put on that page I'd be chuffed to bits.--Red Deathy 07:48, 28 September 2005 (UTC)

I don't have the dates right now, but I can tell you where to find them. See the chapter by Leon Weaver in Electoral Laws and their Political Consequences (eds. Grofman and Lijphart 1986).

Also, now that the use of STV around the world has its own page, I think it would better to put the 22 cities in that page and not have a separate page.

Malta Encore[edit]

Nevertheless, failures to produce partisan proportionality exactly analogous to the party affiliations of top choice candidates as occurs in list PR elections can be controversial. For example, in Malta in 1981 the party winning more than half the top preferences won less than half the seats, resulting in a constitutional crisis: see below.

My problem here is linking the first sentence to the second - in essence the Malta situation was STV behaving like a party list system, with simple droop quotas - if you'd used D'Hondt or any of the others with the same constituency boundaries you'd have got much the same result. OK, list constituencies use bigger electorates (because counting is much simpler) but the fact is that it isn't an explicitly STV problem, and I think that needs to be got across. --Red Deathy 12:43, 29 September 2005 (UTC)

You cannot have it both ways. Either it is impossible to judge how proportional STV is (then don't call it PR) or there are examples of controversy. If Malta had for example open list PR, then the natural response would be larger constituencies or even a national constituency. But STV makes larger constituencies harder as described at the end of the section Single_Transferable_Vote#District_size. Having 100-200 candidates from a single party would be hard even in Malta. --Henrygb 17:05, 29 September 2005 (UTC)
I'm not trying to have it both ways, I'm suggesting there is a problem of phraseology there, in that you are taking an example where STV behaves as a list system (effectively) where the weakness demonstrated would be one that any list system could suffer with equal constituency sizes. i.e. the controversy is not related to STV per se but constituency use. Yes, STV does favour smaller constituencies for reasons of complicatedness, and as you say, that is covered elsewhere in the article. OK, how about this - The practicalities of counting votes means relatively small constituencies are used in STV (see below). This means that where voting behaviour would be analogous to that in list PR elections can be controversial due to large remainders. or something along those lines but less cumbersome.--Red Deathy 07:20, 30 September 2005 (UTC)
When STV does not behave like a list system on some criterion, it is difficult to judge how proportional it is and you are left with personal belief. When it does, you say that it has the same flaws. But the fact is that anomalies in STV raise questions about STV and need to be pointed out. The US presidential election, 2000 had the same anomaly, and that raised questions about the electoral college even though other systems could produce the same problem. I simply think it is unreasonable to try to hid anomalies in apologetics.--Henrygb 19:39, 30 September 2005 (UTC)
My point is the anamoly - constituency sizes - is already adequately covered in the article, and that the pararaph as stands is not entirely accurate or clear, i.e. is badly phrased. I agree the Malta case needs examining, but I'm looking for a better way to explaining it. The Electoral Cllege issue is very different to STV's, there's not even the semblance of equality of votes in that system (deliberately so). third party re-prahsing suggestions welcome.--Red Deathy 09:47, 1 October 2005 (UTC)
My purpose is to say there have been cases of STV elections where the party with majority support has lost, and more frequently other cases where more popular parties have won fewer seats than less popular parties, and that this has led to controversy. I don't mind other paragraphs in the same or different sections saying this can happen with other systems too, or that sometimes STV does quite well, but I do mind what I see as POV apologetics in the same paragraph trying to hide or obscure the fact that STV does not always deliver what people expect from PR.--Henrygb 19:58, 1 October 2005 (UTC)

OK, how about: The practicalities of STV means relatively small constituencies are used compared to list-pr systems. This can mean that whilst the result in each constituency is proportional to the votes cast, the overall result can be disproptional. The Most striking example is in Malta in 1981 the party winning more than half the votes won less than half the seats, resulting in a constitutional crisis: see below. Now, I hope you're not accusing me of being POV here, I am genuinely trying to reach an accurate statement based on the evidence of the data you link to, to explain Malta without reference to constiuency sizes and remainders strikes me as misleading - we need to show how the anomolous result occurred. now, please, I'm trying to work towards an acceptable rewording, stating what changes I'd like to work toward, I'd appreciate some comments back rather than being accused of appologetics. I prefer to work this way than to make changes which get swicthed back and forth. .--Red Deathy 10:34, 2 October 2005 (UTC)

Your edit was reverted by Scott Ritchie [5] with the comment "Revert user:Red Deathy's undiscussed changes to previous version. Calling maltese results disproportional implies a POV interpretation of proportionality)". I think "undiscussed" may be pushing it a bit. --Henrygb 00:14, 4 October 2005 (UTC)
Whoops, sorry, didn't see this. A lot of edits came in that day (including some hefty vandalism). I'll comment tomorrow when I have more time. Scott Ritchie 04:08, 4 October 2005 (UTC)

Just to get in my reply to Scott first: 1) I'm sure we can all agree that 'proportionality' is tendential rather than binary (perhaps a point worth making somewhere). 2) Any deviation from strict proprtionality that affects the global outcome of the election is significant. 3) I think Henry is right to maintain that Malta is an example of a significant deviation from proprtionality, and this needs to be emphasised. 4) I also think that the behaviour in that election is effectively STV as an open-list system, so not analogous to a list-system. 5) That we need to explain teh Malta case rather than simply mention it (at the least we should reference teh fuller description below)--Red Deathy 11:36, 4 October 2005 (UTC)

Ok, I decided to be bold and just made a pretty huge edit to the proportionality section. I tried to keep everything in there intact, though I did rearrange things a lot and removed the Irish example. I think it's better now, while still conveying the same meaning, though it is possible I changed something pretty drastically. What do you think? Scott Ritchie 08:48, 15 December 2005 (UTC)

"Choice of Votes transferred" section[edit]

I removed the following text that creeped in after being on the front page:

Choice of votes transferred[edit]

A difficulty exists with the STV during the choice of which votes are to be transferred to other candidates after a particular candidate (candidate A) has been elected. For example suppose a candidate requires 1000 votes to be elected, and 2000 voters give their first preference to candidate A. If these 2000 voters are broken into two groups Ab and Ac depending on their second preference (Candidate B - Ab and Candidate C - Ac) and Ab has say 1200 members and Ac has 800 members. The difficulty now exists on the choice of which 1000 votes to transfer. If all votes transferred are in Ab then Candidate B has an advantage. If all votes in Ac are transferred then Candidate C has an advantage. In fact, this can often happen during the counting process if votes from particular regions of a constituency are counted before those of another constituency and the second preference in the first constituency is on average different from that in the second.

One might counter that it could be done proportionally. In this case, since 60% of Candidates A's voters were Ab and 40% Ac, then 60% of the transferred votes would go to Candidate B and 40% to Candidate C.

This is already covered in the article to some degree, and if expanded on should be in the counting single transferable votes article - all STV methods in use today either transfer them fractionally (such as Meek's method), or randomly (and therefore effectively fractionally). Scott Ritchie 23:44, 3 October 2005 (UTC)

I thought this section was quite good. If anything, I would have added to it, to say that the selection of which votes to transfer is an opportunity for election mischief and a disadvantage of STV. The examples used in the article are relatively simple (Ab and Ac), but in a more life-like complex example (Abdf, Abf, Aceg, Aeg, Age, ...) the transferral process is bound to disadvantage someone, even if done with perfectly honest intent. Bill Taylor 00:10, 4 October 2005

I see what you're saying, however we should probably mention something like this in a summary sentence then link to a relevant section in the Counting Single Transferable Votes article - it's somewhat of a minor point (and one that varies significantly per method since things like Meek's handle it differently), and the article is possibly too long and technical already. Scott Ritchie 21:17, 11 October 2005 (UTC)
The question arises in the example, where chocolate's surplus is transferred. The example has been contrived to have a natural solution, but the issue would still bear mentioning. G Colyer 22:07, 30 November 2005 (UTC)

Trimming the article[edit]

I have a wee proposal - the article is getting a bit ragged - again - I suggest that we hive off |Issues and |Use Around the World to their own seperate articles - as we did with counting?

I think something needs to be done....--Red Deathy 15:32, 14 October 2005 (UTC)

I don't think you can remove Issues and stay NPOV. But Counting could be shrunk as here is another article, Vacancies could also largely move to that article. Other paragraphs which I personally feel have low useful info/length ratios (as of 22:54, 16 October 2005 (UTC)) are the first and second of Issues, the second of Proportionality, the second, third and fourth of Tactical voting, the third and fourth of Effects on factions and candidates, and the third of Voting system criteria. --Henrygb 22:54, 16 October 2005 (UTC)
I don't think you can remove Issues and stay NPOV - I don't think that's necessarilly true, if we leave what would be a short factual description of what STV is - perhaps trimming the remaining article carefully for contentious phrasings - and then flag up the link to the issues which could then themselves be improved considerably as a coherent article-in-themselves. The Voting and History sections, which would essentially be all that remains - are fairly balanced in themselves. It's just my feeling is that people will be more receptive to a series of short articles than to what appears to be one epic article. Anyway, I'll leave trying the look of anything till the back of this week, and we'll see how it goes...--Red Deathy 07:23, 17 October 2005 (UTC)
My personal view is that calling STV "proportional representation" verges on POV - it often produces non-proportional results and it is not designed to be a party-based system anyway; semi-proportional would be a better description. Move that out with Issues and I would be less concerned. I am not sure I would agree about a series of short articles being better. --Henrygb 08:51, 17 October 2005 (UTC)
STV is widely viewed as proportional representation, however. In New York, for instance, the system of STV was literally referred to as "proportional representation", rather than as simply STV or some other name for the voting system. You'll find similar usage in texts about Irish history as well. "Proportional representation" does not simply mean party-proportional, both in common usage and among voting theorists. STV does provide Droop proportionality (anyone meeting the droop quota will obtain a seat), which is a term relevant to PR and probably deserving of an article. Scott Ritchie 01:05, 21 October 2005 (UTC)
A note of caution: I'm not sure the previous hiving off of Counting Single Transferable Votes has worked too well; that article is still a mess, nobody is fixing it, and the section here is not really a summary of it. Having said that, Tactical Voting could well be moved there (possibly the page would be renamed to something like "technical details of STV"?) since the issues of tactics interplay with the counting method. In fact, all of Voting should be moved there and summarised here (keeping the example here, though we need better examples there).
Issues could get a subarticle each, but of course need to be at least summarised in the main article. (Vancancies could have a one-sentence summary, others possibly longer). STV around the world can easily be separated out, possibly taking History with it (USA and Canada sections are largely historical anyway). In summary, I agree that some sections have grown more than others, giving a lopsided feel to the article; subarticles could fix this, provided they are split into logical units, as self-contained as possible, and all signposted from this main article. Sounds like hard work. Joestynes 15:15, 17 October 2005 (UTC)

OK - Use of STV around the world seems to be an uncontroversial move, so I'll do that now, and we can see how it looks and think about if anything else needs trimming/moving. Everything can be easilly reverted so no harm should be done. --Red Deathy 07:11, 19 October 2005 (UTC)

Let's be careful not to overtrim the article, however. A very large amount of the "text" calculated as putting the article over the 32k warning level is simple markup language and comments (the example table, in particular, takes up more characters than several sections). Taking the current version of the article and copy/pasting the readable words into Office tells me that the current word count is about 35,000 characters in 5500 words, many of which are in the references/external links section. Unless it grows further, that should be condensed enough for now. Scott Ritchie 01:05, 21 October 2005 (UTC)
Yes, I think having moved use around teh world to a sensible sub artiucle, I think it looks more balanced, and about 5K words isn't too much. obviously, you can never stop trimming and condensing - so long as you can find simpler ways of saying the same thing. But I think further changes would need to be re-wordings rather than straight-up moves. --Red Deathy 08:08, 21 October 2005 (UTC)
On second thought, the cutting out of the use of STV around the world has been a bit abrupt - there was some interesting content in there. Perhaps it should be summarized in mainarticle format for the history section, rather than merely linked as a See Also? Perhaps we should even move the content there to History of STV, and include some of the juicier relevant bits in the main article's history section. At the very least, we should have a couple of sentences saying that STV is used in various places. Scott Ritchie 19:32, 22 October 2005 (UTC)

Meek details[edit]

This statement is correct: (1) Meek's method also dynamically adjusts the quota during the counting process of the election, lowering it slightly to take account newly exhausted votes. In Meek's method, initially different ballots that express the same preferences after particular candidates are eliminated are weighted exactly the same - there is no penalty for ballots arriving at a candidate in an earlier round than others.

These two statements are incorrect. I deleted (2) and RedDeathy reinserted it as (3). (2) Meek's version contained the innovation that electors could rank preferences equally, but this option has not been used. (3) Meek also considered a varient [sic] on his system which would have allowed for equal preferences to be expressed.

When one talks about "equal preferences" they generally mean that one could give multiple candidates the same rank on a ballot. E.g. rank two candidates first, one candidate second, and three candidates third. Some STV methods can account for this, but Meek STV cannot. Further, Brian Meek did not discuss this in either of his two Voting Matters articles.

RedDeathy, could you please explain why you wrote (2) and (3)?

jeff 14:24, 6 December 2005 (UTC)

Lo Jeff, I inserted the following comment in the text: [!--(Meek also considered an alternative formulation in which voters would be allowed to indicate equal preference for some candidates instead of a strict ordering; we have not implemented this alternative.) See reference 1 Hill 1987 --] --Red Deathy 14:06, 7 December 2005 (UTC)


I've just made a few changes to the article. Basically I felt that the article was front-loaded with too much complex detail, too early on, and this made in inaccessable. So I've tried to make it so that it begins with a run down of the basics, then proceeds in later sections to go into details about ballot design and surplus transfer methods, etc. I've also put back in a brief guide to the basic mechanics of the count. I think this is too important to be entirely spun off to another article. I've also added some information here and there and made minor aesthetic changes.

Iota 18:28, 23 March 2006 (UTC)

The basic mechanics were there and were rather clear, until some changes seemed to completely reorder the article. Unfortunately, it seems to be in pretty bad shape now compared to when it hit the front page. Right now the lead section has fallen apart as well. Scott Ritchie 08:00, 28 April 2006 (UTC)


Why is the title of this article capitalized? →bjornthegreat t|c 04:51, 1 June 2006 (UTC)

Why are so many instances of the phrase "single transferable vote" capitalized? That is like capitalizing "runoff voting" or "underground irrigation system". It is incorrect, according to Wp:manual_of_style#Capital_letters. It is not a proper noun. -Pgan002 02:42, 3 February 2007 (UTC)

I just came to this talk page with the same point. Can anyone make the case that each word in this article's title should remain capitalized? -Phoenixrod 19:46, 20 February 2007 (UTC)

Dead images[edit]

Where are they on the commons? That is the reason they were deleted. gren グレン 06:22, 16 August 2006 (UTC)

Current use[edit]

There remains no summary of current usage of STV in the article (pretty pathetic for a featured article). Instead, since the splitting off of content to History and use of the Single Transferable Vote, there is only a summary of the early history (only up to the end of the 19th century).

Someone needs to summarise the remainder of the content in the article I've linked to, and append to the section "History and current use" in this article.

In the meantime, I do not think this article should keep its featured status - for an article on STV it offers scant example of how it works in practice in places such as the Republic of Ireland (where it is used for presidential, local council, national parliament and European parliament elections - not to mention popular Irish usage for secret ballot votes in random groups, classrooms, organisations, etc.)

zoney talk 13:57, 17 August 2006 (UTC)

The article is already on the big side (perhaps too big) - the subject is now explored in three articles (Counting & History and use) - I think it reads better that way. This article is general, exploring the theoretical side with the practical put soemwhere else. Utlimately, if there is enough material, you could have STV in Country X articles, if you think there is sufficient scope...As it is, this article is pretty exchaustive.--Red Deathy 14:26, 17 August 2006 (UTC)

If it is getting too big, it needs other sections split off, and summaries of those sections provided. The article should give a *summary* of STV in country X - otherwise it is not comprehensive (especially if it doesn't properly act as parent article to its daughter articles). zoney talk 09:32, 18 August 2006 (UTC)
It lists the types of STV available, and cites where they are used (including citations about which systems are used in ireland) the focus is on the types of STV rather than on the places it is used. Real world examples should be (and are) scattered throughout the text to illustrate problems and benefits. Given that teh detailed work will be in the Politics of Somewheria page...--Red Deathy 16:14, 4 September 2006 (UTC)

Tactical voting[edit]

The "tactical voting" section is written with POV, and also has various impotant mistakes. I'd like some help cleaning it up.

I'm going to go through the current version and make comments.

The single transferable vote eliminates much of the reason for tactical voting.

This is not just POV, it's puffery. STV is less succeptible to tactical voting than what system, under what conditions?

Voters are "safe" ranking candidates they fear may not be elected, because their votes will be transferred after they are eliminated.

This is inaccurate, since it can easily cause a candidate to be eliminated for lack of first-round support.

Similarly, voters are also "safe" voting for a candidate they believe will receive overwhelming support, because their votes will then get reallocated to their next preference, though with less than the value of a full vote.

This can be accurate under the assumption that the voters for that candidate have similar preferences to the voter, but inaccurate otherwise. If two candidates can be elected out of (Perfect_Candidate, Far_Right, Far_Left) and everyone wants Perfect_Candidate to win, a tactical voter will vote for Far_Right or Far_Left first, since otherwise the voter is essentially losing a large fraction (in this case around 1/2) of his/her vote.

Tactical voting is chiefly accomplished in STV by making assumptions about the other voters.

This is true not just of STV but any votng system which depends on more than one vote. It should be stated more generally or dropped.

A preferred popular candidate can be assumed to win and thus ranked lower on a tactical voter's ballot, allowing the voter to give more weight in transfers to his second-choice candidates (and, implicitly, giving fellow supporters of the popular candidate less weight.) This is particularly effective in the older STV systems still used in many countries that prevent elected candidates from receiving additional votes, as in that case none of the tactical vote is diluted on the already winning candidate. Under such old systems, a voter may even rank a non-preferred candidate that is assumed to lose first in order to increase the chances of his vote arriving late. This method of tactical voting is much less effective in the New Zealand STV system using Meek's method, however, as votes receive the same fractional weighting regardless of when they arrive at the successful candidate.

This is one sentence about manipulatability and three of apologetics for STV, raising my concerns about POV.

Though still theoretically possible, figuring out how to successfully vote tactically in modern STV systems by exploiting the non-monotonicity in this way can be computationally difficult.

I don't believe that this is correct. Yes, it's NP-hard, but in most cases at least one tactical decision is obvious, even to the common voter. In fact, with less than (say) 10 viable candidates, the problem is almost trival. Further, tactical voting instructions can be determined centrally (as by a political party), which in addition to reducing the problem of computational difficulty (since, if needed, mainframe time can be used). This raises a question about division of power, especially if parties use tactical voting advice to advance secondary concerns not shared by all of their members.

This makes tactical voting in STV elections vastly more difficult than with other commonly-used election methods.

This should be dropped or referenced. There's no reason to assume a priori that other systems' manipulatablities are in NP \ NPC.

As a consequence, the difficulty of tactical voting in STV elections increases sharply as the number of voters, candidates, and winners increase. This gives an incentive for larger electoral districts other than their increased proportionality, since particularly small electoral districts may have few enough candidates to make tactical voting feasible.

I don't believe this is correct. The difficulty of tactical voting should be independant of the number of voters, although it depends strongly on the number of viable candidates and winners.

Of special note is that voters have a real incentive to list their preferences honestly in STV, as it is the best strategy for securing representation if tactical voting is either impractical or impossible.

This is true with almost all serious methods. It should be removed or generalized.

This is frequently the case in large electoral districts, as successful tactical voting (when possible) requires both nearly perfect information about how others are voting and the computation of a virtually unsolvable math problem.

This is (1) blatantly incorrect, see above, and (2) redundant. Little information is needed to achieve some effect with tactical voting, and the computational difficulties are quite easy with small numbers of candidates. It's true that (near-)perfect information is needed to have perfect tactical voting, but that's a much higher bar that has little practical relevance.

I don't want to come off as a critic of STV: I prefer it to most methods currently in use, in fact. However the article (or at least this section) comes off as advocacy more than encyclopedia. CRGreathouse (talk | contribs) 01:03, 21 August 2006 (UTC)

I’m thinking of rewriting this section (the one with POV notice) allong the following lines:

The single transferable vote eliminates much of the reason for tactical voting. Voters are "safe" ranking candidates they fear may not be elected, because their votes will be transferred after they are eliminated. Similarly, voters are also "safe" voting for a candidate they believe will receive overwhelming support, because their votes will then get reallocated to their next preference, though with less than the value of a full vote. However, the Gibbard-Satterthwaite theorem states that tactical voting is possible in any deterministic voting system where any candidate can win, and that STV is no exception.

Remove this paragraph – this is relevant to single winner methods/ bloc vote not proportional methods. The potential and effectiveness of tactical voting under all proportional systems is related to the size of districts in which proportionality is determined – tactical voting can generally only effect the outcome in 1 seat per district. The larger the districts the less effective it is.

Tactical voting is chiefly accomplished in STV by making assumptions about the other voters. A preferred popular candidate can be assumed to win and thus ranked lower on a tactical voter's ballot, allowing the voter to give more weight in transfers to his second-choice candidates (and, implicitly, giving fellow supporters of the popular candidate less weight.) This is particularly effective in the older STV systems still used in many countries that prevent elected candidates from receiving additional votes, as in that case none of the tactical vote is diluted on the already winning candidate. Under such old systems, a voter may even rank a non-preferred candidate that is assumed to lose first in order to increase the chances of his vote arriving late. This method of tactical voting is much less effective in the New Zealand STV system using Meek's method, however, as votes receive the same fractional weighting regardless of when they arrive at the successful candidate.

This frequently mentioned method of tactical voting applies only to systems that use the simple Gregorian transfer method (only votes from the last parcel transferred to an elected candidate are considered for transfer). This tactic could, in theory, work for systems like Cambridge, Massachusetts STV, Irish Republic Handcounting and the Newland-Britton family of systems (Newland-Britton Northern Ireland, ERS97). This tactic would be completely ineffective for inclusive Gregorian transfer (Australian Senate), weighted inclusive Gregorian transfer (BC-STV), Meek and Warren.

Provide example of how this form of tactical voting could work, add statement that if all voters vote for candidates they don’t believe will win in the hope that their votes will transfer and have greater weight in determining the outcome, the candidates who nobody believed could win WILL win. This strategy doesn’t work if everybody tries to use it. Provide real world example of attempt to use this strategy

Though still theoretically possible, figuring out how to successfully vote tactically in modern STV systems by exploiting the non-monotonicity in this way can be computationally difficult. It is NP-hard to determine whether there exists an insincere ballot preference that will elect a preferred candidate, even in an election for a single seat.[1] This makes tactical voting in STV elections vastly more difficult than with other commonly-used election methods. Importantly, this resistance to manipulation is inherent to STV and does not depend on hopeful extraneous assumptions, such as the presumed difficulty of learning the preferences of other voters. Furthermore, it is also NP-hard to determine when an STV election has violated the monotonicity criterion, greatly reducing the likelihood that the electorate will know if even accidental tactical voting has occurred. As a consequence, the difficulty of tactical voting in STV elections increases sharply as the number of voters, candidates, and winners increase. This gives an incentive for larger electoral districts other than their increased proportionality, since particularly small electoral districts may have few enough candidates to make tactical voting feasible.

Providing an explanation of this form of tactical voting in terms of monotonicity (or the lack of it) or NP-hardness makes the explanation difficult to understand and overly technical. The commonest form of tactical voting (organised by parties, for example Sinn Fein in Belfast West for the last NI Assembly elections which involves non-monotonicity) is what could better be described as vote splitting or vote equalisation.


Three parties A, B and C present the following candidates- A1, A2, B, C1 and C2. 1000 votes, 3 seats

All B voters prefer party C to party A. All C voters prefer party B to party A. All A voters prefer party B to party C.

Party A has 410 votes, Party B has 190 votes and party C has 400 votes.

A1 210

A2 200

B 190

C1 250

C2 150

C2 is eliminated first and the winning set is A1, B and C1.

If party C’s votes are split equally between its two candidates for example:

A1 210

A2 200

B 190

C1 200

C2 200

B is eliminated first and the winning set is A1, C1 and C2.

Describe with an example the form of tactically voting mentioned above, provide real world example, provide commentary on the problems with organising this sort of thing – it requires good information about voting intentions, cooperation of the voters, lots of organising, can go wrong if you don’t get it exactly right, the vote distribution between parties makes this sort of thing possible in only a minority of constutuencies.

Of special note is that voters have a real incentive to list their preferences honestly in STV, as it is the best strategy for securing representation if tactical voting is either impractical or impossible. This is frequently the case in large electoral districts, as successful tactical voting (when possible) requires both nearly perfect information about how others are voting and the computation of a virtually unsolvable math problem. Since tactical voting in STV works by effectively substituting one's own alternate preferences for transfers with other supporters of the same candidate, the effectiveness of tactical voting is greatly reduced when other supporters of preferred candidates have similar second-choice preferences. Although there is no way to completely prevent tactical voting by hiding support for preferred candidates, the tactical voter carries the significant danger of his assumptions about the popularity of his preferred candidate being wrong, risking his most preferred candidate losing because of his miscast tactical vote. This contrasts heavily with non-proportional, plurality-based systems, where there is both tremendous incentive and ability to vote tactically in order to avoid the spoiler effect.

Get rid of this paragraph – non-proportional systems generally provide greater incentives for tactical voting than proportional systems because the use of tactical voting generally can only effect one seat per district using proprtional methods.

Dgamble997 4 Sept 2006

Is you example actually about tactical voting - it's relevent but not tactical. Surely if you have people who support a party strongly enough to pursue voting to maximise its representation they are actually expressing their true preference. It would be tactical voting if they expressed a first preference for B in order to ensure, that, say, A is knocked out entirely or to ensure both C's win.--Red Deathy 16:02, 4 September 2006 (UTC)
I think the example is tactical voting, though not one of the more extreme versions. Regardless, I'm fine with Dgamble's suggestions in general. I think there should be some mention of Gibbard-Satterthwaite, and I don't like the line "Tactical voting is chiefly accomplished in STV by making assumptions about the other voters." because it's insufficiently general, but these are more quibbles than anything else. CRGreathouse (t | c) 16:12, 4 September 2006 (UTC)
I've always considered tactical voting to be voting differently to how you would sincerely vote in order to alter the result of an election. Voters spliting their votes equally between two candidates of a party when they would normally favour one candidate of that party in order to increase the party representation is IMHO a form of tactical voting.

Vote management strategy is one of the few (possibly only) potentially effective forms of tactical voting in STV. See article

Vote management is described on page 10

Dgamble997 5th Sept 2006

Precisely, my point was that for someone to be sufficiently committed to a party to vote in a managed way probably is expressing their true preference (they might not care about which candidate so long as it's their party, or if they did and still followed instructions, that suggests their preference is the party first) - I think calling it vote management might be more useful than tactical voting--Red Deathy 07:40, 6 September 2006 (UTC)
But there are two other clear versions of tactical voting seemingly unique to STV
  • one is "first preferences for candidates who will be eliminated in the middle of the count" which works for non-Meek methods even when you really support a popular candidate first but want your transfers to count as much as possible
  • another is the Australian group voting tickets (also used in Fiji) where parties tactically swap preferences for tactical rather than ideological reasons.
--Henrygb 09:09, 6 September 2006 (UTC)
Several good points. It is worth noting that group voting ticket and voting for a canadidate certain to be eliminated only work for certain STV systems. Group ticket voting only works if you have above and below the line voting and "first preferences for candidates who will be eliminated in the middle of the count" only works for single Gregorian transfer - not for Meek, Warren, BC-STV (inclusive weighted Gregorian transfer) or Australian Senate rules (inclusive Gregorian transfer). I'll bear all these points in mind.

Dgamble997 8th Sept 2006

New section completed. I've only been on wikipedia 2 weeks so the layout and references could possibly be done better.

Dgamble997 10th Sept 2006


  1. ^ Bartholdi, John J. III and Orlin, James B (2003). "Single Transferable Vote Resists Strategic Voting".

unspoilt votes[edit]

Could anyone explain what is meant by "unspoilt votes"? Or what would be spoilt votes? Martinwilke1980 18:04, 25 August 2006 (UTC)

A spoilt vote is an invalid one (perhaps deliberately so). So not voting for anyone, or doing something else so that made the vote not be counted. --Henrygb 21:14, 25 August 2006 (UTC)
Technically, I think it should say "spoilt ballots", rather than "votes", but I could be wrong. Mdotley 21:14, 14 September 2006 (UTC)
Spoint Ballots and Voters are slightly different. I am taking an A level in Government and Politics, and we have been told that a voter can spoil his or her ballot paper (a spoilt ballot), for instance by marking the box with a tick rather than a cross (if that is what should be marked), however the vote may be counted (if the candidates all agree) - as it is clear who the voter wanted to win. Therefore it is a spoilt ballot but not a spoilt vote, and spoilt votes are what we are referring to in this context. Woodgreener 21:18, 6 January 2007 (UTC)
It is not up to the candidates; it is up to the rules as interpreted by the returning officer and possibly the election court (i.e. after a petition by a candidate). In UK elections where crosses are required, a a ballot paper with a tick instead of a cross would not count as a spoilt ballot for that reason. --Henrygb 00:02, 7 January 2007 (UTC)

I was an observer at an election count for Wicklow, in Ireland, during the 19 70's Three members to be returned. The process for dealing with ballot papers that had not been filed in exactly as specified by the rules, that is arabic numerals, 1, 2, 3 and so forth was they were picked out as "doubtful ballots" and then examined by an official called the "adjudicator." He was legally qualified, In this case a Barrister of the Kings Inns, Dublin. He invited representatives of the candidates (and me) to witness the adjudication process which consisted of him looking at each paper in turn and either deciding whether or not the INTENTION was clear or ruling the ballot spoiled. On each case he listened to the views of the candidates representatives, having made clear it was his decision alone, in the end, and that his decision was not final but could be disputed in the courts. (He asked me to give my opinion also on each paper). In practice the decision in each case was clear and in fact agreed by everyone. So for example, ballot papers showing a single "X" were regarded as showing a first preference only. Ballot papers with a single tick were also accepted as a single preference only. Amid some amusement the ballot paper where all the candidates had a preference indicated against them, but shown in ROMAN numerals was accepted as valid. I realise this comment counts as "original research" but I hope you find it helpful, and that being on the talk page and not the article, makes that ok (ish) Daithidebarra (talk) — Preceding undated comment added 16:23, 15 May 2015 (UTC)

The Voting Series[edit]

This page should be part of the voting series with the voting tag {{{voting}}} however, due to pictures and diagrams in the article, i struggled to place it correctly. Could someone please add the tag as best they can? Woodgreener 21:00, 6 January 2007 (UTC)

Oscar nominees[edit]

The Academy of Motion Picture Arts and Sciences employs a preferential ballot for the selection of the five nominees in each of the various award categories. I believe that the counting system is a form of STV although they do not actually call it that. Here is an article I found that describes the process:

Perhaps somebody more knowledgeable than I could confirm that the process described in the article is STV? The article describes the setting of a Droop quota, and any film that gets enough votes to meet that quota is considered ‘nominated’. Then, the article says, "The stacks of votes belonging to films that have clinched a nomination are immediately set aside. Then the remaining ballots are resorted into the existing piles based on the voters' second-choice films." --Citefixer1965 00:27, 27 January 2007 (UTC)

Not quite. Apparently, you are only allowed to rank five choices (maybe at most five, maybe exactly five, the article is unclear). True STV should allow (if not require) you to rank all candidates. Since there are thousands eligible for, say, best supporting actor, that won't really be feasible until the ballots are cast online. The limit is set at five presumably is because that's the number of winners [winners, that is, of the "honour of just being nominated"]. The use of five as the limit is essentially arbitrary; there's no particular reason they don't limit it to 8 or 10 or 15 rankings, which would more closely approach true STV. jnestorius(talk) 01:44, 27 January 2007 (UTC)
Reading on, I see you also need to get at least one first-preference to be successful. In true STV, you can get zero first preferences and still be elected simply by receiving transferred votes from the surplus of previously-elected candidates. jnestorius(talk) 01:49, 27 January 2007 (UTC)
Still interesting enough to add to History and use of the Single Transferable Vote#NGOs. Thanks! jnestorius(talk) 02:45, 27 January 2007 (UTC)
It looks STV without transfers of surpluses (but with transfers from those eliminated jumping over those already elected). It would be interesting to know if quotas reduce in later rounds. Without transfers of surpluses, those with no first preferences will be eliminated anyway. --Henrygb 00:02, 14 February 2007 (UTC)
I think it does redistribute surpluses: point six of the exposition says "We haven't even gotten into the scenario in which a film receives considerably more votes than it needs, in which case it secures a nomination and all of its ballots are redistributed into other piles, with the second or third or fourth choices counting as a fraction of a vote." jnestorius(talk) 15:41, 14 February 2007 (UTC)
You are probably right - I only got as far as: and it'll move to "A History of Violence" only if "Cinderella Man" is either out of the running or it has already secured a nomination and no longer needs his help --Henrygb 23:16, 14 February 2007 (UTC)

Photograph of a best-actor nomination ballot here: [6]. --Citefixer1965 08:42, 19 February 2007 (UTC)

I found an article in Variety from 1993 that gives more information. The article says that fractional surpluses are redistibuted if the candidate’s tally is more than 20% over the quota. --Citefixer1965 17:49, 19 February 2007 (UTC)
That bit is very odd.
Another check kicks in when a nominee receives more than 20% of the quota from first-place votes. A system had to be instituted to keep from discarding all of those ballots, which would skew the count on the remaining potential slate. The proportion over 20% is then calculated to a percentage that reflects the required quota. So, if Clint Eastwood were to receive 75 top choices -- 50% above the necessary level -- the individual votes would be revalued to 0.7 and the second-place votes, which would have otherwise not been counted, are given a value of 0.3.

The trigger criterion seems arbitrary but the example gives a correct transfer ration for ordinary STV. Perhaps the journalist has simply misunderstood the process? Really we need a quote from the horse's mouth, rather than a hack with a deadline who's never seen the system before. jnestorius(talk) 01:10, 20 February 2007 (UTC)

Choosing Later Candidates[edit]

Are candidates who were eliminated in early rounds restored when choosing later candidates? I had thought so, but the description suggests they are not. Example:

99 people favor A > B > C > D > E > F > G 1 person favors E > F > G > A > B > C > D 1 person favors F > G > E > A > B > C > D 1 person favors G > E > F > A > B > C > D

B, C, D get no first place votes, so are immediately eliminated. It ends up choosing A, E, F, G, far from a proportional representation. Had B, C, D been restored after A's election, they would have been picked, even with the downscaled votes. Or am I misundertanding? 19:33, 13 February 2007 (UTC)

You are misunderstanding. (Assuming there is more than one winner) A's surplus is distributed before any eliminations, since the surplus is big enough to affect the final result. I once saw an election where someone started with 0 votes, received 0.01 of a vote in a surplus transfer, and then was eliminated. --Henrygb 23:55, 13 February 2007 (UTC)

There are a number of problems listed which are actually about the limits of any form of proportional system - for example "malapportionment". These are all reasonable discussions - including the fact that most people that use STV deliberately sacrifice strict proportionality to keep districts (constituencies) etc small.

Finding the winners section[edit]

This section was marked as "repetition" but I think I have found a good solution. Essentially, the same information was being presented three times. The ordered list of steps is clearest so I have retained it. Hence I have removed the tag. Endorphin78 11:16, 27 May 2007 (UTC)

Creating a new sub-page[edit]

Lo All, well, I noticed taht the article was too long and all but unreadable - the issues section was a rambling rag-bag thatstill needs serious editting - but my main thought is that we need to keep the main page simple, we've already forked off a couple of times for history and counting - the topic is so big we need a lot of pages, and users can navigate them by category if need be. Basically, I picked out key sentences from the paragraphs I moved so as to form the basis of a precised section here, while moving the bulk of the text elsewhere. The struggle is on to regain featured article status!--Red Deathy 07:28, 31 May 2007 (UTC)

Should the main article be about, what it is (i.e. the basic idea of selecting multiple candidates in order of preference), the history, and where it is used. Things like implications & counting etc should be (is?) as separate article. --Nate1481(talk/contribs) 13:54, 31 May 2007 (UTC)


This section is unclear: "two tables below (the first is a numerical representation, the second is pictorial)". Ask someone who has never seen this page what this means, regarding the tables shown. Also, why does chocolate appear twice in the first table? DBrnstn 14:46, 18 August 2007 (UTC)

Unrelated: are "Write-in candidates" typically allowed? If not, this blocks write-in campaigns. If so, this can change (and possibly thwart) the dynamics, if voters write-in their first choice as their second, third, and fourth choice also. (Orange, orange, orange, orange.) Perhaps "write-ins may not duplicate prior choices." DBrnstn 14:46, 18 August 2007 (UTC)

STV Action[edit]

I am the Webmaster of STV Action ( I would STV Action tobe added to the list of proponent groups in this article. I thought it best not to add this link myself after reading the Conflict of Interest Policy WP:COI. John Cross 21:39, 25 August 2007 (UTC)

Getting back to featured article status[edit]

So, what needs to be done to get this page back to featured article status? I think we should make that a high priority, and also get Instant Runoff Voting to featured status. Perhaps a peer review is in order for that latter objective. Captain Zyrain 17:41, 9 October 2007 (UTC)

London Mayoral Elections[edit]

Can anyone, with more knowledge on this subject than me, determine whether the London Mayoral Elections (2008) used STV. I remember choosing a first and second choice candidate? C.harrison1988 (talk) 03:33, 28 June 2008 (UTC)

London Mayoral Elections use a limited form of preferential voting called the Supplementary Vote, which differs from STV in two key ways: (1) Voters are only allowed to express two preferences. (2) Candidates who do not come first or second in the first round are eliminated even if it is still possible for them to win after second preferences are counted. Duncan Keith (talk) 06:04, 28 June 2008 (UTC)

Unclear - allocated value[edit]

In comparing "paper-based" to "value-based" counting methods, the definition of "value" is unclear. An example showing the difference would be helpful. -- Beland (talk) 02:52, 5 January 2009 (UTC)

I've removed the text in question entirely, I'll paste it here:
There are two basic forms of counting an STV election: one is based on the number of ballot papers allocated to a candidate; the other, more accurate system, is based on the value of the vote as it progresses throughout the count. This variance is important in the calculation of a candidate's surplus. The paper-based formula (the surplus divided by the number of ballot papers) undermines proportionality and the "one vote, same value" principle due to some votes increasing in value at the expense of other votes. The value-based formula (the value of the vote divided by the surplus) avoids these shortcomings, ensuring proportionality and maintaining the "one vote, same value" principle.
It seems like this is an attempt at explaining the difference between Meek's method, the Gregory method, and the old "pick a few random ballots for the winner out of the hat and count them" method. In any event they're better explained just 2 sections down in the article, after the example at the Differing Counting Methods section. Scott Ritchie (talk) 04:12, 21 January 2010 (UTC)

Current Use[edit]

Now it reads " remained in approximately two cities, including one in Massachusetts." Approximately two? Could it be one or three? What other(s) retain STV? Irv (talk) 04:58, 26 November 2009 (UTC)

Failed Definition[edit]

A definition of an acronym must be complete. To give the words which the letters of the acronym represent does in no way explain the acronym appropriately. We are left with a three word phrase without a clear meaning. This needs to be addressed first and foremost. - KitchM (talk) 16:24, 31 January 2010 (UTC)

Do you have more specific suggestions for improvement? Gabbe (talk) 23:21, 31 January 2010 (UTC)

Question about the example[edit]

Text from the article:

Round 2: Chocolate's surplus votes transfer in equal proportions to Strawberry and Sweets according to the Chocolate voters' second choice preferences. However, even with the transfer of this surplus no candidate has reached the quota. Therefore Pear, who has the fewest votes, is eliminated.

Why is it split equally? 2/3 of the party that wanted chocolate wanted strawberries. Shouldn't the vote be split 5/3 instead of 4/4?

An explanation would be appreciated. —Preceding unsigned comment added by (talk) 23:12, 16 August 2010 (UTC)

I fixed it, whoever wrote "equal proportions" was simply wrong or confusing. The correct ratio is 4 and 2, since there were 8 strawberry and 4 sweet votes. I'll note the graphic was right the whole time. Scott Ritchie (talk) 20:11, 17 August 2010 (UTC)

The example was useful for me, but it didn't explain how things work when voters declare third or fourth choices. --Shay Guy (talk) 20:50, 27 June 2011 (UTC)


Did Thomas Hare and Carl Andrae invent STV independently of each other, or did one copy it from the other? Are we certain that Hare was the (only) originator? (talk) 17:35, 26 August 2010 (UTC) Update: it's my understanding now that the two men invented it independently, and that Andrae has a reasonably good claim to have invented it first. (talk) 22:27, 31 August 2010 (UTC)

Edit on the issues section[edit]

I am making these comments as Edits because I find the Discussion on this subject wholly off-topic.

It is elementary that STV procedures can be affected by strategic voting. The procedure can give a minority party a majority in the Legislature. (The party is a minority party in the sense that it commands strictly less than 50 percent of first preferences and is beaten in pairwise comparison by another party, which itself is an all round winner (in pairwise comparisons with all other parties)) Further, such an all round winning party can, under any STV procedure, be left with no representation in the Legislature at all.

All this can be shown with 3 member constituencies and 3 parties putting lists forward.

Further every STV procedure can deliver a set of members in the Legislature, which set is weakly Pareto inoptimal (ie there is another set of candidate-members which all voters prefer under sincere voting).

This can be seen very simply by considering a 3 member constituency with 4 party lists. Three of the parties, a, b and c have about the same level of support which is overwhelmingly larger than z's, the fourth party, with it's small amount of first preference support. .

The three largest parties' voters vote cyclically, viz, aPbPc, bPcPa, and cPaPb.

Because of the small amount of support for z, the member set under any STV system must be 1/3 'a' party candidates, 1/3 bs and 1/3 c's.

Now z is the second worst alternative for all these voters. Thus when these voters exhibit risk aversion the set of members all from z is weak Pareto superior to the equal mix of a, b and c members.

This result may need a little explication in view of the weak state of the theory of coalitions to be found elsewhere

The result can be justified in three ways. Either equal 3 way voting in the Legislature results in a lottery (probably the best outcome given our assumptions here) or some coalition emerges which is the result of 3 party bargaining and in which the outcome is an admix of distinctive policies of the parties party to the coalition or z is better than the convex combination of the policies advocated by the parties a b and c. Members always vote 'sincerely' in the sense that they advocate their best alternative throughout. The lottery option is justified by the balance between the parties. In contrast, should the three popular parties comprise a pair with opposed preferences, xPaPy and yPaPx and a middle ground party putting 'a' top (with a fourth party, z, as above) in every constituency, then the member set under any STV procedure is equal numbers from the x, a and y parties. Now despite the FPTP equality 'a' is an all round winner against x and y in the Legislature and the electorate. Should z be in second place in the ordering of all the x, a and y parties supporters then it would be z that would win in the Legislature and the country. (Given, of course, that the Legislature uses pairwise comparison methods rather than the wholly inadequate 'Aye' and 'Nay' method used in the British Parliament(a method producing results worse than some Arrow has described as threatening sanity)!)

No clear pattern emerges. With singleton all round winners Pareto inoptimality can occur. Equally the key is NOT 4 parties nor 3 member constituencies. For if xPaPy and yPaPx for half each of all voters, with little variability in any of the 2 member constituencies, then the member set is equal numbers of x and y members. If all voters are risk averse so that 'a' as a certainty is preferred to the lotteries on x and y and on x, a and y, then the member set is weak Pareto inoptimal under sincere member voting.

The ease with which this last result can be generated should act as a note of caution in respect of even numbered member constituencies. Trivially they are prone to all the problems described in the first two paragraphs above.

The interesting thing is that the above points to a serious difficulty when STV uses constituency - wide rather than jurisdiction - wide voting.

With 6 -member constituencies and two opposed preference parties forming their core and constituency based voting, parties with as much support as 8 percent of the popular vote can find themselves unrepresented, whilst in 100 seat jurisdiction-wide voting two such parties would get....8 seats each. If they are alternatives, having extreme parties talk in Legislatures may be better than suffering their street expressions of opinion.

All the above shows how STV just does not solve the difficulties I raised with voting systems in a series of papers in Theory and Decision and resolved in the context of majority decision making in Synthese a decade ago. Dr. I. D. A. MacIntyre (Do please re-assign this contribution to where you think it best belongs. (Obviously I think here))

will edit this in the near future if anyopne wants to provide suggestgions please do so. — Preceding unsigned comment added by Digmores (talkcontribs) 22:54, 10 January 2011 (UTC)

Surplus votes[edit]

The surplus needs definition. I've been following today's Irish election count and came here to understand the system. The article fails to make it clear how the surplus is calculated and apportioned. If the surplus is shared in proportion to all the second preference votes, how come there are no fractional votes in second and subsequent counts? I think I understand it, but that's from working through the example, definitely not from the description given. Bazj (talk) 19:53, 26 February 2011 (UTC)

I agree with your point, but the problem is that (as the article says) "There are variations in applying these STV rules, such as in how to transfer surplus votes from winning candidates and whether to transfer votes to already elected candidates."
From personal experience, the most proportional system is to transfer a fractional vote once a winning candidate has been elected with each vote having the value [(Total Votes - Quota)/ Total Votes], but I don't have a ref for that. When I was at Edinburgh University, however, they used a system for student elections in which the full value was transferred - no fractions at all. I'm not sure how to handle the different examples. --rpeh •TCE 20:30, 26 February 2011 (UTC)

The difference is not that difficult to understand if you have witnessed an election count.

Assume the simplest case, someone has just been elected on the first stage (or count) well over the quota, and so with a comfortable surplus. So the candidate has a big pile of votes, all first preferences for them. All of the value "one vote" Calculate the size of the surplus - subtract quota from total. This will be a whole number of votes. Take the votes and sort them for their second preferences. That means you have a series of piles, or parcels of votes, each consisting of the second preferences for a particular candidate. Count the totals of second preferences. Then transfer the surplus by EITHER


Divide the size of the surplus by the total vote for the candidate. Do this to whatever number of decimal places is specified. In Northern Ireland its done to two places, for Irish republic Seanad Elections to Panel seats its done to three decimal places. This gives you the new values for each paper. Now transfer the papers to the candidates and total up.


Work out how may votes are going to be transferred to each candidate. So say surplus a 1000 votes and half the second preferences for the candidate go to someone else then that someone else gets, 500 votes. Pick 500 papers out of the bundle of second preferences for that candidate and physically transfer.

This is inferior to the fractional method, but easier to do when counting manually. It is the system in use for elections to the Dail. Theoretically inferior, in practice it works.

So how does that info get into wikipedia?

Daithidebarra (talk) — Preceding undated comment added 16:44, 15 May 2015 (UTC)


Wasn't this what the referendum in the United Kingdom in May 2011 was about? ACEOREVIVED (talk) 23:43, 5 May 2011 (UTC)

Nope, the referendum is on whether or not to introduce the Alternative vote. It's similar to STV in that you rank candidates, but there's only one candidate per seat in AV. rpeh •TCE 08:57, 6 May 2011 (UTC)


In what way is Hare-Clark different from conventional STV? (talk) 12:39, 17 May 2011 (UTC)

Voting every day, any time you want.[edit]

Vote at any time. On any issue. Every voter can vote themselves or delegate their vote to other voter - whether individual or conglomerate (party list etc). Revoke your vote delegation at any time, either permanently or for a specific issue where you want to vote yourself. The ballot is secret but your vote's use is open, for you.

Amount of nation-wide votes delegated to them gets a delegate a proportional weight to their vote they cast through the system themselves or delegate further. This changes constantly, thus the will of voters is constantly represented truly, with no distortions, at any point in time. No more waiting 4 years to overturn the corrupt government/president.

Governments are formed by a majority of votes. Anti-oscillation device is that to overturn a decision/gov't, 80% majority is needed in first 3 months; 65% after a year; 50% + 1 vote after 4 years.

Simple. Just. No vasted votes, no gov't cheating the voters. Instant true representation of the populace's will.

There isn't really a good reason why we should not do this. It's time we have just and true voting system already. WillNess (talk) 09:04, 15 August 2011 (UTC)

If you can find this in a published work, its own Wikipedia article is a possibility. —Quantling (talk | contribs) 20:04, 19 August 2011 (UTC)
Proxy voting#Delegated voting has something very similar, as it turns out - almost exactly the same, sans the "any time" part. I read about this somewhere on John McCarthy's web pages more than a few years ago, but when I later tried to find it there, I couldn't. Don't know exactly what happened.
There's also an idea of each voter earmarking their taxes, to decide in which way they'd be used. Some would "donate" to defense, others to welfare, that's how the budget would get formed automatically. Of course there too it must be made retractable, changeable at any point in time. The really massive use of computers/connectivity can really change the way we do democracy/self-governing.
The immediacy of votes I saw e.g. in one of Stanislaw Lem's humorous Star Diaries, where a President of some planet would get his approval ratings continuously - with a twist where when they'd get lower than a certain limit, he'd be automatically killed. No-one wanted to be a President there, naturally. :) WillNess (talk) 23:33, 19 August 2011 (UTC)


An entire article on voting but not one metion of the word transparency??? Single Point of Failure - when the vote gets disconnected from the name, and the magnet for being hi-jacked by the status quo. 100% Transparency is wasted on Facebook where it doesn't matter but not applied where it really matters, voting, i.e. John Alfred Smith votes for Bill# 3402, Elizibeth Jane Thompson votes against Bill# 3402. — Preceding unsigned comment added by (talk) 19:46, 23 February 2012 (UTC)

Are your hypothetical John and Elizabeth members of the legislature (at any level, including Congress) or are they "just" voters? If they are members of a legislature, their voting records should be available. I'm not sure that has anything to do with this article anyway. STV is generally a method by which the public elects officials, not a method for voting on legislation within a legislative body. (There may be exceptions to that, but it is generally true.) Neutron (talk) 21:15, 23 February 2012 (UTC)

Is STV really proportional?[edit]

It depends on how many members are elected per constituency, if the number is maximum six (this is the situation in most countries adopt this method) it's much less proportional than pary-list or MMP which usually have at most 5% threshold. — Preceding unsigned comment added by (talk) 14:25, 7 June 2012 (UTC)

Look at the Irish General Election of 2011. Fine Fail with 36% of the vote get 46% of the seats. Finna Fail with 17.5% of votes get 12% of seats. This seems to be for two main reasons - constituency sizes range from 3-5 members ie 25-16% needed to get elected - and nature of prefential cross-party voting.

Arguably there is a choice between smaller sized constituencies which are less proportional and larger constituencies which are more proportional - but less 'local'.

Check Wikipedia link to Irish 2011 election (link not working) (Coachtripfan (talk) 08:58, 15 August 2013 (UTC))

=STV is a proportional system. Any system becomes less proportional with a fewer number of seats, but that is separate from the system choice. So while not every application of STV is as proportional as what it could be, the system of STV itself provides proportional representation within the restrictions of that district magnitudeRRichie (talk) 15:12, 17 August 2013 (UTC)

If your focus is on party share of the vote - then STV may not be always proportional as later preferences from other candidates from other parties may be factor. Look at Sligo-North Leitrim in 2011, Sinn Fein got 13% and Finna Fail 22% yet SF got a seat and FF didn't. That is because SF attracted a lot more later preference votes from Indpendent candidates than FF. (Coachtripfan (talk) 10:49, 4 September 2013 (UTC))

@Coachtripfan on the contrary, your example shows that the majority of people preferred SF over FF. Focussing on the number of people who gave their *primary* vote is ignoring the way preferential voting works. The primary vote does not tell you which party people hate the least. Sqgl (talk) 13:42, 4 September 2013 (UTC)

Preferential voting takes account of people's second, third preference - but shouldn't the only prefence that matter be what people really want ie first prerence? 'the primary vote does not tell you which party peopel hate the least'. Exactly, voting should be about which party you positively want not which you hate least down to hate most. Most democracies with PR do not of course have STV. (Coachtripfan (talk) 20:14, 9 September 2013 (UTC))

I would say: the term proportional is not really applicable for preferential voting methods. I.e. STV is proportional to an interpretation of all the votes where you count the first preferences of some voters and the second preferences of some other voters and the third preferences of again other voters and so on. However, this is obviously something very different than the "normal" proportional, because most (arbitrary strange) apportionments can be described as proportional to such an interpretation of n-th preferences, where n varies with every voter. Thus, STV is just something different than a proportional system. It is not really "proportional" or "not proportional", but just different. However, this is my opinion. Most advocates of STV like to call it "proportional". If one of them is here: Could you please explain to what exactly the result of an STV election is proportional? (You're welcome to assume a unique not small (maybe 100 seat) constituency) Thx. Arno Nymus (talk) 23:16, 9 September 2013 (UTC)
As additional question: Does someone has a good and clear definition of a proportional system? I think the intuitive definition ("for each party/group the ratio of the seats is roughly the same as the ratio of the votes"; the article proportional representation does not give a clear definition, too) is not sufficient (What does "roughly the same" mean, where are the limits of that?) to really answer the question "Is the voting system X a proportional voting system?" Arno Nymus (talk) 18:38, 11 September 2013 (UTC)
Proportionality refers to like-minded voters electing seats in proportion to their share of the vote. By this definition, STV is fully proportional. The district magnitude is not tied to the system choice. STV is proportional within whatever district magnitude is provided.RRichie (talk) 18:25, 12 September 2013 (UTC)
  • Ok, since the number of seats for a party/candidate have to be an integer (no "half seats"), there can't be a seat distribution that is (exactly) proportional for most vote distributions. Hence, the "roughly the same" above. That was the reason, why I asked what exactly the definition is. It's the question about the limits of "proportional". Maybe something like "Whenever the number of ideal claims of seats (i.e. number of votes divided by Hare quota) is an integer for ALL parties, the seat distribution must allocate these ideal claims. In all other cases, the result must lye within the bounds these ideal results pretend". But, ok, let's skip that definition question.
  • Now, for one choice votes ("I vote for X!"), the meaning of "the seat distrubution is proportional to the vote distribution" is clear, since every vote belongs to a single party/candidate.
  • On the other hand, for ranked choices votes ("My first preference is X, my second is Y, third is Z...") this is not so easy. So, my question is, to which candidate (or) party belongs a ranked choices vote when checking a ranked voting system for proportionality? Arno Nymus (talk) 21:18, 17 September 2013 (UTC)
There is no right answer to this. Some analysts persist to do based on first choices, but others make a good case for doing it based on the what you have after the transfers are done. The fact that the latter can be true shows just how STV delivers proportionality while giving voters a freer range of choice among candidates than most PR systems.RRichie (talk) 22:41, 19 September 2013 (UTC)
I thought about it and only taking what you have after the transfers are done in account would also give some terribly stupid system the predicate "proportional" (when the transfers are terribly stupid). E. g. propose the "most hated voting system" (MHV) that makes STV on the reversed votes, i.e. it starts with the last choices of each vote and redistributes to the second to last choice if necessary and so on. The result would be as proportionally to "what you have after the (MHV) transfers" as STV is proportionally to "what you have after the (STV) transfers" (the only difference would be that the MHV transfers are much more stupid than the STV ones). I don't think that MHV could be considered "proportional", but I also can't think of a definition for which STV is proportional and MHV is not. Any ideas on this? Arno Nymus (talk) 01:02, 24 September 2013 (UTC)

Suppose N is the number of voters. Suppose M is the number of seats. Suppose there are at least M candidates. Suppose the Droop quota is given by N/(M+1). Then Droop proportionality says that, for every natural number m with 0 < mM and for every set of (at least m) candidates, the following must be true:

If strictly more than m Droop quotas of voters strictly prefer every candidate of this set to every other candidate, then at least m candidates of this set must be elected.

The single transferable vote is proportional in so far as it satisfies Droop proportionality. Markus Schulze 12:51, 25 September 2013 (UTC)

In this extent AV or even FPTP are proportional too. — Preceding unsigned comment added by (talk) 11:08, 24 February 2014 (UTC)
In single-winner elections, Droop proportionality is identical to mutual majority. AV satisfies this criterion, but FPTP doesn't. Markus Schulze 20:53, 4 October 2014 (UTC)

Small example to show proportionality[edit]

Here's a real and small example STV poll I created awhile ago, 20 voters, ranked ballot on favorite fruit, and counted for 3 winners, counting two ways as: 25% droop quota or 33.33% Hare quota. I allowed tied rankings, which were counted as an equally divided vote. The counts below are rounded to 0.1 votes. To simplify the summary below, I hid about 8 candidates who were removed by bottom-up elimination and never gained more than 1.0 votes. I also eliminated a 3-way tie with 1.2 votes in one step in the first round show.

In the final round of the Droop count, there was a last-place tie between Banana and Pineapple, requiring a tie-breaking method. The Hare quota worked out better to avoid ties. In the Droop quota, 74% of voters picked one of the 3-winners (25%,25%,24% support each). In the Hare quota, 82.5% of the voters picked one of the 3 winners (17.5%,30%,32.5% support each). You could say Droop "wasted" 24% of the votes, and Hare wasted 17.5%, on the 4th candidate who can't win.

Anyway, this example shows me STV found the 3 strong candidates among mutually exclusive voter bases, although not necessarily the "strongest candidates". Proportionality assures a WIDE set of voters are represented, and any voter who is a part of a united quota faction is guaranteed at least one winner. I like the Hare quota better, but political elections probably prefer the Droop quota which gives more power to bloc ranking by larger coalitions. Tom Ruen (talk) 00:29, 10 September 2013 (UTC)

Droop quota: with 20 votes, 3 seats, (25%=5 votes)

  1. Cherry=4.0 Banana=3.2 Apple=3.0 Mango=2.2 Strawberry=2.2 Pineapple=2.0 (Apricot=1.2 Nectarine=1.2 Raspberry=1.2)
    • Eliminate set {Apricot, Nectarine, Raspberry}
  2. Strawberry=4.3 Cherry=4.0 Banana=3.3 Apple=3.0 Pineapple=3.0 (Mango=2.3)
    • Eliminate Mango
  3. Strawberry=5.0 Pineapple=4.3 Cherry=4.0 Banana=3.7 (Apple=3.0)
    • Eliminate Apple
  4. Cherry=5.0 Strawberry=5.0 (Banana=4.8 Pineapple=4.8) [NOTA=0.3]
    • Winners: Cherry (25% Droop), Strawberry (25% Droop), (Banana or Pineapple)

Hare quota: with 20 votes, 3 seats, (33.33%=6.7 votes)

  1. Cherry=4.0 Banana=3.2 Apple=3.0 Mango=2.2 Strawberry=2.2 Pineapple=2.0 (Apricot=1.2 Nectarine=1.2 Raspberry=1.2)
    • Eliminate set {Apricot, Nectarine, Raspberry}
  2. Strawberry=4.3 Cherry=4.0 Banana=3.3 Apple=3.0 Pineapple=3.0 (Mango=2.3)
    • Eliminate Mango
  3. Strawberry=5.5 Cherry=4.0 Pineapple=4.0 Banana=3.5 (Apple=3.0)
    • Eliminate Apple
  4. Strawberry=6.5 (32.5%), Cherry=6.0 (30%), Pineapple=4.0 (20%), (Banana=3.5 (17.5%))
    • Eliminate Banana
    • Winners: Cherry=6.7 (33.3%) Strawberry=6.7 (33.3%) Pineapple=6.1 (30.5%) [NOTA=0.5 (2.5%)]

Tom Ruen (talk) 00:29, 10 September 2013 (UTC)

Thx for presenting an example so that I can try to understand. Without the ballots, it's a little bit difficult to see the values. Also the redistribution of votes that exceed the quote is here somehow hidden. And I think that allowing equally divided votes doesn't make it easier to see. But I'll try.
However, it seems to me that at the last (or prelast) step (of hare) there are the following votes:
  • cherry: 6 (4 first preferences and 2 second preferences)
  • strawberry: 6.5 (2 first, 4 second, 0.5 from an equally divided 1th through 6th-preference)
  • Pineapple: 4 (2 first, 2 second)
So, are these votes (8 first preferences and 8 second preferences and 0.5 equally divided 1h through 6th) to which the seats are proportional? Arno Nymus (talk) 20:44, 10 September 2013 (UTC)

Complexity/Transparency/Size 'gerrymandering'[edit]

It is a complex system - not to fill in a ballet paper of course but the counting and allocation of seats. Transfers, surplus votes, meek rules. Much the same results could be given in an open-list PR multi-member system.

Well, infact STV may be less proprotional than an open-list as people can vote between parties and the share of seats a party gets may differ from the share of first preference vote. Just look at Ireland's results under STV.

There is also the issues of size. A 3 seater, requires a party/candidate to get 25% of the vote, a 9 seater, 10%. The bigger the connstituency the more proportional - but more remote an MP is to constituents.

If you have STV then surely all seats have to be the same size, or very similar. You can't have some constituencies returning 3 MPs but others 8 or 9. That is 'size gerrymandering'(Coachtripfan (talk) 15:58, 17 July 2013 (UTC))

Not sure what your point is, but much of what you suggest is wrong. For example, you can have unequal constituency sizes, just as is common in other proportional and non-proportional systems that rely on multi-seat districts. Compared to list systems, STV is likely to be more proportional when district magnitude is low because it reduces wasted votes. List systems also can seem "opaque" when you get into the fine points of allocating seats. And so on. (talk) 14:46, 19 July 2013 (UTC)

If constituency size varies from say 3 members to 9 - then that leads to a wide variation ie 25% or 10% needed to get elected. True, other multi-member systems may have this. It is less proportional than Mixed Member Systems that allow minor parties to get elected. A party with 10% spread throughout a country would not get elected under STV. It is also more complex than MMS in allocating seats. Regional Top Up

Then there's also the issue of 'above the line' voting - ie voting for a party ie essentailly closed list or 'below the line' ie voting for individual candidates. Australian State elections allow both. 95% or so vote for the party list! STV versus Open List complexities

(Coachtripfan (talk) 08:26, 15 August 2013 (UTC))


I put a POV tag on this article because it reads like an advocate's brief. It includes criticism of the system only by way of showing that all criticisms have been answered. To judge by this article, there is no good reason why any sensible people shouldn't adopt STV, yet it has been rejected (or, at least, not adopted) by democratic polities the world over. Are we to surmise that only entrenched interest prevents the universal adoption of STV? That's the logical conclusion to be drawn from this article, yet the article doesn't say it, which makes me suspect that the facts wouldn't support such an argument. Surely there are some intelligent arguments against STV that have not been handily disposed of? Let's have an article that reflects the actual state of debate on this issue. J. D. Crutchfield | Talk 19:34, 4 March 2015 (UTC)

Hope you don't mind my answering here. You are probably right that this article has been written mainly by people who think STV is in its way the best of all possible voting systems. So obviously it should have its shortcomings described clearly. But in the opposite direction I think it's lacklustre in its advocacy of STV: the case for STV could be argued more clearly. The trouble is that that would involve a pretty major rewrite, and I'd be grateful for guidance as to how one goes about that - is there a way of posting a draft rewrite for comment rather than taking the drastic step of just substituting it for the present article?
On your comment about the limited adoption of STV, I'd say yes, it is largely vested interests that prevent it: reform of voting systems normally comes up against huge inertia, because those in power are obviously those who do well under the existing system. As example, STV came near to being adopted in the UK during a period (roughly 1914 to 1930) of political upheaval when Labour was replacing the Liberal party; once politics had settled back to the 2-party system that FPTP encourages, those two parties prevented further consideration of alternative voting systems for 50 years. Dmollison (talk) 16:03, 28 March 2015 (UTC)
Dmollison: There is a "namespace" for drafts (WP:DRAFTS) as an alternative to the sandbox. One place to put questions is at the Teahouse WP:Teahouse - if you search the questions page there (WP:Teahouse/Questions) for "draft" you will find others with similar problems. To encourage comments on your draft take a look at WP:CANVASS. The alternative approach is WP:BOLD which is what I have done in the past. The article certainly is in need of a re-write. --BalCoder (talk) 08:27, 2 April 2015 (UTC)
Jdcrutch: You dispute the neutrality of the article although you seem to be unfamiliar with "the actual state of debate". You may feel that there must be arguments (intelligent or not) against STV ("Surely there are...") but if you can't identify one I am surprised you feel able to make such a bold edit. When you say the article shows "that all criticisms have been answered" perhaps you could give us an example of what you are talking about. Concerning casual vacancies, for example, the article simply lists various ways the problem has been handled. What do you expect? Unless you can justify your claim of bias you should remove the POV box. --BalCoder (talk) 08:27, 2 April 2015 (UTC)
@BalCoder: I come to the article as one more-or-less unfamiliar with the topic, seeking a balanced exposition of it. That's how I presume most readers come to any Wikipedia article. What I get instead is a description of a perfect system, with which nobody who has it seems to be dissatisfied, yet which most of the world has nevertheless failed to adopt. Every other voting system has pros and cons, but the only thing wrong with this one, as far as the article is concerned, is that voters may not be smart enough to recognize its superiority. ("A frequent concern is its complexity compared with plurality voting methods.") But even that quibble has been disposed of, thanks to computers. The article has clearly been written by true believers, and I don't need to know the skeptics' counter-arguments to see that and object to it.J. D. Crutchfield | Talk 14:03, 2 April 2015 (UTC)
Hyperbole. Noting that computers faciltate counting can hardly be described as partial. The article mostly just describes what STV is and how it works. None of the cons listed by the Electoral Reform Society is discussed but neither are any of the pros ("wasted votes" is at least mentioned). The article is not at all biased, it just needs drastically improving. Instead of a POV box a "multiple issues" one such as at the top of the Counting single transferable votes page would be more useful. I don't understand what WP:DRIVEBYTAGGING is but I suspect this is it. --BalCoder (talk) 17:42, 7 April 2015 (UTC)
Name-calling. The article Wikipedia:Tagging pages for problems, which is where the shortcut WP:DRIVEBYTAGGING leads, makes it quite clear (to anybody who bothers to read it) what drive-by tagging is, and how it can be avoided. It says,
When it comes to confusing or ambiguous tags, such as {{npov}} or {{dead end}}, you should explain yourself on the talk page and/or in an edit summary.
I did exactly what the article suggests, and more: I have returned several times to defend my action in good faith. If the scholarship is truly unanimous in favor of STV, as the present article would seem to suggest, then there should at least be reliable, impartial sources saying so. I rather suspect that there is a continuing debate, which somebody has probably summarized in a reliable secondary source. Citations to such an article might add the balance needed, and justify the removal of the POV tag. If an opponent won't step up to edit the article, even an advocate of STV, if she or he is frank and well-informed, should be able to supply the proper balance, because he or she will have considered the arguments for and against, each in the best possible light, and chosen between them. Meanwhile, the POV tag leaves the article unaltered, but stands as a warning to readers who might not otherwise read with the necessary skepticism. J. D. Crutchfield | Talk 18:54, 7 April 2015 (UTC)

Seems to me that some of the main issues with STV (monotonicity, transparency, proportionality, forming working majorities, "nursing the constituency", etc) are for the most part well-sourced and already mentioned in the "Issues" section; however they are buried within a mountain of info that attempts to refute each problem. IMO the article is not so much biased, as it is confusingly written. It might be appropriate to rename this section "Effects," and rewrite the section to make it much more cut-and-dry. I think that would be a better solution than having "Advocacy" and "Issues" sections. We could do like First-past-the-post voting and have an Effects section AND a Criticism section, but that doesn't seem quite right to me either. There is certainly enough research on STV to make this article look just like that (also C-class rated) one. <> Alt lys er svunnet hen (talk) 02:16, 5 May 2015 (UTC)

Here's a couple sources I found on the issues btw... [1] [2] <> Alt lys er svunnet hen (talk) 02:20, 5 May 2015 (UTC)
Monotonicity is the primary issue with STV, due to the fact that with enough candidates, and with candidates with very strong second-or-third order choices, the order of elimination becomes important, and as the number of candidates and availability of information about voting preferences increases, the chance of running into a monotonicity violation increases. It's simple to vote, complex to tally, like most preferential or evaluative systems, which isn't really a problem, more a logistical issue. It's also not very proportional on a national level, as it relies on electorate boundary-setting, but this is an issue of perspective rather than a mathematical flaw: STV represents electorates proportionally, while for example list systems represent party affiliations proportionally throughout the nation. So STV is a good system for those who like local representation, wheras those who want party proportionality (for instance, to fairly represent smaller parties) will probably want to look towards list systems as their preferred way to vote. Also, it should be noted somewhere (or perhaps Disambigged?) that STV is sometimes used as a name for IRV single-winner elections, as New Zealand calls all of its IRV elections (such as for Wellington Mayor) Single Transferrable Vote. --54x (talk) 03:51, 25 September 2015 (UTC)

Confusion over dates, 1840 or 1855?[edit]

In the article on STV it states that the original concept was not used in a "real election" until introduced in 1855 by Carl Andrae, a Danish politician.

Yet in another Wikipedia article on Thomas Wright Hill, it states that STV was used in an election in Adelaide, South Australia in 1840. Presumably this qualifies as a "real election". If so, there would appear to be some confusion over when STV was first used in a public election.

Here is the exact quotation from the article on Thomas Wright Hill.

"Thomas Wright Hill (24 April 1763 in Kidderminster – 13 June 1851 in Tottenham) was a mathematician and schoolmaster. He is credited as inventing the single transferable vote in 1819. His son, Rowland Hill, famous as the originator of the modern postal system, introduced STV in 1840 into the world's first public election, for the Adelaide City Council, in which the principle of proportional representation was applied."

Romper Levis (talk) 10:15, 10 August 2015 (UTC)

As far as I know, Carl Andrae and Thomas Hare were the first ones who proposed a form of the single transferable vote that could be used for secret ballots. Older forms of the single transferable vote presumed open voting. Markus Schulze 07:28, 13 August 2015 (UTC)

Pruning and proposed re-write[edit]

As discussed on this Talk page last year (see under POV above), I would like to propose a general re-write. Trying to be as transparent and cooperative with others as possible, I'll do this in stages, beginning with some pruning. If anyone else would like to help, let me know.

I've started by simply deleting the section on `Determining ultimate preferences'. This is/was about the special case of electing one individual, i.e. Instant Runoff / Alternative Vote; if it belongs anywhere it should be on the Instant runoff voting page. However, it is also over-specialised, possibly only of Australian interest, and has no citations, so I think it needs radical improvement if it is to be resurrected anywhere on Wikipedia.

Dmollison (talk) 15:10, 22 October 2016 (UTC)

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Couple USA things[edit]

Two things that could be added.

  • The local uses of STV in the US include |Park board and library board elections in Minneapolis, Minnesota - but didnt figure out how to add to chart
  • Congressman Don Beyer has introduced the Fair Representation Act, HR 3057, this year to enact STV for U.S. House elections - see

RRichie (talk) 00:04, 2 July 2017 (UTC)

  1. ^ [7]
  2. ^ [8]