Talk:Borda count

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Note: this is content moved from the Jean-Charles de Borda page. Does not represent my opinion at all -- RobLa

Invented by Ramon Llull! "With the 2001 discovery of his lost manuscripts Ars notandi, Ars eleccionis, and Alia ars eleccionis, Llull is given credit for discovering the Borda count and Condorcet criterion, which Jean-Charles de Borda and Marquis de Condorcet independently discovered centuries later."[8] —Preceding unsigned comment added by (talk) 07:00, 26 April 2011 (UTC)

Voting is something that has been used for a very long time, so obviously it is the best way right. Wrong, simple voting can be modified and made a lot better. Written sources attest the existence of voting procedures all through the middle Ages. Confusion in choosing the right system was common, nobody really knew what was best for them. In 1130, for example, the ambiguity of voting led to the election of two Popes, an event that created a rift within the Catholic Church.

In June of 1770 a French mathematician named Jean-Charles de Borda (1733-1799), who was a member of the French Academy of Sciences, proposed a new method of voting. He noted irregularies in the qualifications of members being elected to the Academy. He suggested that voters rank the candidates, and in turn assigning the candidates points on how they prefer them. For example, in a 3-candidate election, the first ranked on a ballot received 2 points, the second obtained 1, and the third ranked got 0 points. The candidate with the most points won.

There are many ups and downs of each way of voting, but at the time, The Borda Method was the most appealing. But mathematicians found the answer; they have bad and good news for the voting population. The bad news is Borda's count 2,1,0 is not ideal; it can still lead to distorted results. The good news: within the point method, the Borda count is by far the best. Moreover, our voting rule 1,0,0 is the worst; it gives the least amount of information about what voters want and can yield results that speak against the people's will.

This becomes clear from the following examples. In 1970 the centre-right candidate Buckley won the New York senate election even though more than 60% of the votes went for either of the two centre-left candidates. A less obvious but even more disturbing case is the recent Bush-Gore race. If those voting for Nader could have made Gore their second choice (which is a reasonable assumption), the democrats would have won without trouble, as the popular vote suggests.

But there are more complicated systems. The run-off method, for example, uses the 1,0,0 point rule in combination with several rounds of vote. Only a more than 50% support makes the winner. Otherwise the last candidate is dropped and the vote is repeated. An alternative is to exclude all but the first two candidates and vote a second time. This system, however, has its flaws too. The first version takes too long to be efficient in a national election, whereas the second can bring weird outcomes. In the 26 November 2000 election for the Romanian Presidency, this method led to a run-off between a left wing extremist and a right wing one. The centre vote had been split among several candidates.

The only simple and efficient method that in most cases expresses the will of the majority is the Borda count. Ranking the candidates and assigning a balanced rule of points, as in the 3,2,1 example, would make our elections fairer. We only need to implement this rule. Its time has arrived.


The Atlantic Baptist Convention uses a variant that I'm pretty sure is equivalent: the rankings are reversed (1=top choice) and the winner has the least total. (I've been looking for a name for this method for a couple of years, thanks =) 01:17, 18 Jun 2004 (UTC)

A (1=top, 2=second)... point count, with least points for the winner is only equivalent to Borda if all candidates must be ranked. In contrast Borda counts can allow (or force) limitations to rankings, like top-three only. (Your ABC variant could also allow limited ranking if all unranked candidates are given a some maximum point score rather than zero)
The paragraphs above ARE certainly biased in evaluating Borda. Borda can reward strategic dishonest ranking. Borda is a simple and good method if you want to assume sincere voting and you don't care about simple majority rule. --Tom Ruen 01:33, Jun 18, 2004 (UTC)
ANY voting method has the opportunities for strategic dishonest ranking. One simply needs to look at the mathematical analysis of the method to see this. Simple majority rule is accomplished only by running two candidates for a position. And even that is a special case of Borda count where n=2. There is no way to design a voting method that completely prevents dishonest voters from creating manipulative effects. Take a look at Arrow's Theorem for proof of that. --Fahrenheit451 17:40, 5 Mar 2005 (UTC)
I believe that what he is referring to is the fact that Borda is one of the few methods that fails the majority criterion, which is that the first choice of a majority should be elected. This is why he recommends Borda "if you don't care about simple majority rule", because there is the possibility that a simple majority will not get its choice.
Arrow's theorem is irrelevant to this discussion; it says that no voting method can satisfy a certain three properties, but there are many other properties to consider.
RSpeer 19:09, Mar 26, 2005 (UTC)

The whole article reads like a POV apologetic: "Borda is wonderful, and it is has any minor flaws then every other system has them too." A better article would be "This is how Borda works, this is its biases (towards candidates who are lots of people's second choice but few first choice), these are its curiosities, here is where it is used." --Audiovideo 14:11, 21 Mar 2005 (UTC)

Pro-Borda POV[edit]

The section on strategic voting was written with an extremely pro-Borda POV, making unfounded attacks on other voting systems, and unjustified declarations that Borda would solve all the world's problems.

The terminology used was taken from Donald Saari's very POV book, "Chaotic Elections", in which he constructs mathematical models specifically designed for analyzing positional election methods, concludes (correctly) that Borda is the fairest positional election method, but then he tries to apply this model to other ranked methods, and uses the fact that it doesn't fit to conclude that Borda is better than any other election method. He glosses over the strategic flaws in Borda, which are more obvious than the ones he attacks in Approval and Condorcet.

I suspect that the section was written either by a Saari supporter, or someone who has been taken in by his book without looking at the argument critically. I've tried to NPOV the section; let me know if I swung it too far the other way.

An interesting note: Saari and other Borda supporters tend to advocate Instant Borda Runoff when confronted with strategic flaws in Borda, but they claim, approximately, that Instant Borda Runoff is simply a "tallying method" on top of Borda that cleans it up in real-world situations, and allows its excellence to shine through. Yet Instant Borda Runoff turns out to be a Condorcet method, and Saari at least spends chapters on discrediting Condorcet. (My personal opinion is that IBR is indeed better than Borda, but if you're going to do Condorcet, you can do it much more easily than with a boatload of Borda counts.)

RSpeer 17:59, Mar 25, 2005 (UTC)

Anti-Borda POV and misinformation[edit]

The statements I wrote about other voting systems in relation to Borda are true. Never did I state that Borda would solve all the world's problems as Rspeer falsely alleges. [Personal attack removed]. IBR is NOT a combination or irv and borda count. That is false information and I am removing that. --Fahrenheit451 02:04, 26 Mar 2005 (UTC)

Rspeer seems have the idea that comparing one voting system to another is bad, when it is entirely legitimate as they are in the same body of data. [Personal attack]. The comparison was restored. IBR is most definitely only a tallying method. [Personal attack]. All true statements have been restored. Rspeer strategic nomination points have been retained with correction of his grammar.--Fahrenheit451 02:44, 26 Mar 2005 (UTC)

[Personal attack], as instant borda runoff is just a term to describe a tallying procedure where the lowest scoring candidate is eliminated ALONG with his points, unlike irv which transfers them to another candidate. The tallying procedures are entirely different as ibr never transfers votes to another candidate. The purpose is to break asymmetric ties and ascertain the strongest candidate overall. --Fahrenheit451 02:56, 26 Mar 2005 (UTC)

I will respond to your points later, but in order to participate meaningfully in this discussion you should refrain from personal attacks, as Wikipedia policy dictates. RSpeer 07:18, Mar 26, 2005 (UTC)

Response to Fahrenheit451[edit]

Summary of points:

  • IBR has exactly the same relation to Borda as IRV has to Plurality.

That is a falsehood. IRV ranks candidates and transfers votes. Plurality neither ranks or transfers votes. IBR eliminates and retallies with no vote transference. It is strictly a tallying procedure as a straight tally can be done without ibr. There is no equation whatsoever.-- 22:42, 26 Mar 2005 (UTC)

  • I certainly don't think comparing methods is bad; in fact, I am trying to open up objective comparisons between Borda and other methods that the previous article shut out.

Yes? You did not do that in your edit. -- 21:19, 26 Mar 2005 (UTC)

  • In one personal attack, you said that I resented the rigor of Saari's research. (Other observers of this debacle will have to look in the history for confirmation; I stand by the doctrine of removing personal attacks.) I have no issue with the parts of "Chaotic Elections" that are rigorous; the part I take issue with is the opinion, and I do not resent it, I disagree with it.

Exactly which opinions do you disagree with. You did not specify. -- 21:19, 26 Mar 2005 (UTC)

On Instant Borda Runoff[edit]

First of all, I didn't even add the section on Instant Borda Runoff comparing it to IRV. Your original version said:

Instant Borda Runoff, or IBR, as mentioned in a previous section, provides the advantages of the Borda count with the counter-manipulation features of an instant runoff tally.

Just because the words "instant" and "runoff" are used does not imply ibr is in any way related to irv, which is called in other countries, alternative vote, Hare method, etc. -- 21:19, 26 Mar 2005 (UTC)

Additionally, I shouldn't even have to defend this point if I were really anti-Borda. Instant Borda Runoff is a fairly good voting method based on Borda, and if my purpose were to attack Borda, I could do so more easily without pointing out that many of the problems are fixed by IBR.

IBR is Not a voting method, it is a tallying method that uses a Borda count ballot. Tallying and ballots are two different bodies of data. -- 21:19, 26 Mar 2005 (UTC)

But IBR, as I understand it, does exactly the same thing with Borda that IRV does with plurality. In the IBR that I know of, the candidate with the fewest points is dropped - along with his points, yes - and then the points for other candidates are recalculated based on ballots that are missing that candidate and where the points go up to n-1 instead of n. Since the distribution of points changes, I don't see why you wouldn't call this a "transfer", though it is indeed more subtle than IRV's transfer. (And if the distribution of points didn't change, then there would be no point to the runoff.)

Not true. In plurality voting, you get one choice. In irv, you rank candidates, where the rankings are considered seperate ballots. The initial tally eliminates the candidate with the least number of votes and transfers them proportionally to the remaining candidates. The instant runoff is an integral part of irv. Borda count can exist completely independent of ibr. Again, ibr is a tallying method and nothing more than a tallying method.-- 21:19, 26 Mar 2005 (UTC)

The same method describes IRV when you take "points" to mean the number of first-place votes. Candidates are dropped along with their points, and then you recalculate the points based on ballots without that candidate.

No. In irv, votes are transfered. Votes are never transfered in Borda count or when using the ibr talling procedure. -- 21:19, 26 Mar 2005 (UTC)

This is not a point I am adamant about, but I feel that the clearest and most correct way to describe IBR is a combination of IRV and Borda, since (as your article stated) it combines features of both.

No it does not. IBR is strictly a tallying procedure. Call it successive Baldwin elimination if you will. Forget the instant and runoff words if it helps. But it is still only an alternate tallying procedure for the Borda count. -- 21:19, 26 Mar 2005 (UTC)

Now, I may have misunderstood what you mean by Instant Borda Runoff - the section that describes it in terms of Baldwin elimination is not especially clear. However, this is what most people mean by Instant Borda Runoff, including Saari.

Yes. We agree.-- 21:19, 26 Mar 2005 (UTC)

Responses to responses[edit]

It would be far easier to tell what point you were making if you formed a response as a coherent whole, instead of interspersing your sentences with mine. I get the feeling that you are generally quibbling over semantics in my response to you, instead of supporting your own argument.

I have asked below for you to explain what the difference is between a "tallying procedure" and an "election method", because I have never heard a "tallying procedure" used to describe something that can change the outcome of the election.

"Successive Baldwin elimination" is a term that should be eliminated completely from the article, due to its obscurity. The mechanism should be described, not just named.

The distinction you are drawing between IRV and IBR seems to be ideological, rather than mathematical. If you envision the changes in scores that occur in IRV as "transfers of votes", that's okay, but that visual model is not part of the method. I also can't tell why you are so adamant on divorcing Instant Borda Runoff from Instant Runoff Voting; you are getting hung up on implementation details while the "instant runoff" mechanism remains the same. It's even in the title of each.

IRV and IBR and two different methods entirely.--Fahrenheit451 01:24, 27 Mar 2005 (UTC)

I will generalize both by describing "Instant Positional Runoff", which works like this:

  • Decide on a way to assign scores positionally to votes. This way might be plurality (first place gets 1, all other places get 0), or it might be Borda (first place gets n-1, second place gets n-2, etc, last place gets 0).
  • Add up the positional scores.
  • Drop the candidate with the lowest score from all the ballots
  • If one candidate remains, that candidate wins.
  • Otherwise, re-assign the scores, based on the new ballots, and repeat.

O.K. You have legitimatized it by rigorous definition.--Fahrenheit451 01:25, 27 Mar 2005 (UTC)

If you plug in Plurality as the positional method to Instant Positional Runoff, you get IRV. If you plug in Borda, you get IBR, as described by Saari on page 103 of "Chaotic Elections".

Now you would be correct. --Fahrenheit451 01:24, 27 Mar 2005 (UTC)

RSpeer 21:45, Mar 26, 2005 (UTC)

On comparing methods[edit]

I believe that the state of the election method articles on Wikipedia does not include enough comparison between methods. Often, methods are discussed entirely within their own framework, without giving the mathematical criteria necessary to compare methods. This is true of other articles besides the Borda Count one.

I am with you 100% on that point.-- 21:19, 26 Mar 2005 (UTC)

However, I do not consider a valid comparison to be "method A is less manipulable than method B" or "method A is fairer than method B", because those are subjective, and in fact they shut out objective comparisons. A valid comparision is "method A satisfies the monotonicity criterion while method B does not." Of course there is subjectivity in defining criteria, as it is easy to find criteria that one's favorite voting method satisfies and others don't; the best you can do is go with criteria that supporters of different voting methods agree on, and to describe in what voting situations those criteria are useful.

We agree again.-- 21:19, 26 Mar 2005 (UTC)

Your current edit shuts out objective comparison with its first sentence:

The Borda count does not encourage tactical voting to the degree that plurality voting, approval voting or instant-runoff voting does.

O.K. I believe my statement is true, but without a mathematical demonstration, I can only summarize in words. What to do? -- 21:19, 26 Mar 2005 (UTC)

because it is not possible to define a measurable "degree" of tactical voting. There are simply different tactics that each method is susceptible to.

Not true. Actually it is possible to measure degrees of tactical vulnerability by enumerating paradoxical opportunities in the method. -- 21:19, 26 Mar 2005 (UTC)

Responses to responses[edit]

The only valid way to compare voting methods is with well-defined criteria. Use these criteria (Category: Voting method criteria) to show in which areas your voting method does better. Without criteria, you are left with nothing but competing ideologies.

I assume that "enumerating paradoxical opportunities" is something you do within Saari's positional models; he certainly likes the word "paradox". If that's the case, then it is only applicable for comparing positional methods, which is not useful because there are no other ranked positional methods on Wikipedia.

If you mean you want to count the number of situations where a voter, given certain information, can get an advantage by voting dishonestly: that doesn't work. You can't just enumerate them, because some situations are more likely than others, and you don't know what information voters will have. Determining the likelihood of strategic voting is a really hard problem, and it depends entirely on your model of how people vote. Supporters of different voting methods have come up with different models that each support their favorite method, just like Saari's model supports Borda.

RSpeer 22:17, Mar 26, 2005 (UTC)

On rigor[edit]

I am certain that Donald Saari has done some impressive and rigorous things in his career, and indeed he begins "Chaotic Elections" with some mathematically rigorous definitions, but the point he wants readers to take away from the book - that Borda is the best voting method - is not rigorous because it is an opinion, and I disagree with the reasoning he uses to convince his readers of that opinion, which generally involves taking mathematical models he defined for positional methods, and then applying them to non-positional methods in ways that he hopes will give unflattering results.

I would not presume Don Saari has ulterior motives for his endorsement of the Borda count. You are assuming that he is attempting to propagandize Borda count and there is not evidence to prove any such thing. -- 21:19, 26 Mar 2005 (UTC)

For example, I will paraphrase his treatment of Approval voting like this: "The ballots cast in an approval election could come from voter preferences spanning all these segments of my positional-ranking triangle diagram" (fact). "Isn't that horrible?" (opinion).

True, but it is clear what the fact is and what the opinion is. -- 21:19, 26 Mar 2005 (UTC)

Responses to responses[edit]

I don't know what Saari's motive is - I'd guess it's that he spent a lot of time making a model of positional methods, so he wants positional methods to be relevant.

To put it another way, he wants to educate the public about ranked methods, which is a noble goal. However, the only machinery he has to do so is his positional model, so the only method he can advocate with the backing of his mathematics is the Borda Count.

I will emphasize again that what I take issue with is his criticisms of other methods, including Approval and Condorcet, using a model that does not apply to them. He does this in such a way that the reader is likely to come out convinced that he is absolutely right. I was temporarily convinced after reading the book, at which point my math advisor (who gave me the book, wanting me to look at it critically, and got me interested in studying voting methods) had to talk me back to the real world, making similar arguments to the ones I am making now.

Saari criticizes Approval, essentially, by saying that a certain Approval result could correspond to any of a number of different Borda results. If you put this the other way, a certain Borda result could correspond to any of a number of different Approval results. This is not illustrating a flaw in either; it is illustrating that they are thoroughly unrelated methods.

He criticizes Condorcet by rearranging the preferences on Condorcet ballots until he has some imaginary "cyclical ballots", which do not correspond to the wishes of any voter. He also forces his model on Condorcet and calls the resulting mess "Condorcet noise". (You could just as well analyze Borda with a Condorcet graph, and call it "positional noise" interfering with the result of Condorcet.)

Finally, to show that either he's not really convinced of his criticism of Condorcet, or he didn't think it through fully, he proposes Instant Borda Runoff, which happens to always choose the Condorcet winner when one exists.

On POV[edit]

Your original article was clearly biased in favor of Borda, and this has been confirmed by User:Audiovideo long before I made the edit. Your revert has restored almost all of that original article, so it is still POV, and I will mark the page as such.

One other user considers the article to be biased and you say that confirms your opinion as true? I object to that and consider your action to be unjustified. -- 21:19, 26 Mar 2005 (UTC)

Forgot to login on replies. The ip address of is mine. --Fahrenheit451 21:22, 26 Mar 2005 (UTC)

Look up at the comments above: the general consensus was that the page was POV. Anyway, my action was to put the pov template on the page, which says "The neutrality of this article is disputed". It certainly is - we're disputing it right now. Am I unjustified? RSpeer 22:17, Mar 26, 2005 (UTC)

To move forward[edit]

This page will need to have the pro-Borda POV removed, and be put into a form that is as neutral as possible while enabling comparisons to other voting methods. It should do this by following the outline of Wikipedia:WikiProject Voting Systems, which this page deviates from in the later sections. For example, the teaming effect (clone candidates help each other) should go in the "Effect on factions and candidates" section.

The information on the page is rather jumbled; for example, technical details like Baldwin elimination are described high up on the page. In places, Baldwin elimination is suggested as a tie-breaking technique; most voting method pages do not go into such detail on tie-breakers.

I don't know that is even relevant, as tie breaking procedures are important aspects of any voting system.--Fahrenheit451 21:38, 26 Mar 2005 (UTC)

The page will need to be extensively rewritten.

Why? And who are you to demand that?--Fahrenheit451 21:38, 26 Mar 2005 (UTC)

For now, I will respond to specific statements that have been added in User:Fahrenheit451's recent series of edits, so that they can be corrected or clarified when the page is revised:

Unlike approval voting, all candidates are ranked on their merits, and in contentious elections, does not tactically revert to plurality voting.

This statement belongs, if anywhere, in the criticisms section of the Approval voting article.

I disagree and object. Why? --Fahrenheit451 21:38, 26 Mar 2005 (UTC)

In the paragraph where I describe the teaming effect:

then adding more of these candidates to the ballot increases the odds of one of this group winning. That is, the method is not cloneproof, a characteristic which it shares with almost all other voting methods.

Changing "each" to "one of this group" was correct. Sorry about my sloppy wording. However, you should explain which voting methods you are considering when you say that vulnerability to clones is "a characteristic which it shares with almost all other voting methods." The most widely-used voting methods (plurality, two-round runoffs, and maybe IRV) are indeed vulnerable in the opposite direction, having the spoiler effect. Approval and well-designed Condorcet methods, however, are cloneproof.

The only Condorcet type method I know of that is cloneproof is Schwartz Cloneproof Sequential Elimination. Approval voting is Not cloneproof. --Fahrenheit451 21:38, 26 Mar 2005 (UTC)

Wrong. Approval voting is cloneproof.
It should be noted that any paradoxes which can be found in the Borda count are also present in all other positional methods, and usually in greater number.

This is misleading. It makes it sound like Borda triumphs over a large number of other voting methods, because you're glossing over the fact that only two positional methods are seriously proposed: Plurality and Borda. And Plurality doesn't have ranking paradoxes, because people don't actually vote on ranked ballots in plurality elections.

There are other positional methods like vote for two, vote for three. The winner of a plurality election is the result of plurality ranking paradoxes. --Fahrenheit451 21:38, 26 Mar 2005 (UTC)

"Paradoxes" is a vague word anyway, and it should be avoided unless an example is given.

No, just look it up in the dictionary. --Fahrenheit451 21:38, 26 Mar 2005 (UTC)

Finally, I do not understand the distinction you are maintaining between an "election method" and a "tallying procedure". To me, a "tallying procedure" is like whether you calculate Single Transferrable Vote by writing down numbers on paper, putting rankings into a computer, or moving ballots between bins; that is, they are different mechanical ways to compute the same result. Instant Borda Runoff, however, gives different results than plain Borda, so I would say it is a different election method, not a tallying procedure.

Not true. IBR will likely produce the same winner as a straight Borda tally, unless there are some significant condorcet components in the tally. An election method is all of the procedures used to determine a winner or winners in an election, the tallying procedure being only one part of the overall method. --Fahrenheit451 21:38, 26 Mar 2005 (UTC)

RSpeer 19:43, Mar 26, 2005 (UTC)


Your one-shot rebuttals are not useful to the debate or the article; they will cause this debate to devolve into a bunch of quibbling threads with very little to do with the overall article. But since it seems you want me to respond to each one, here are my responses:

Looking up "paradoxes" in the dictionary will not give you something that you can enumerate over an election method.

I suppose it needs a specialized definition, which I have not seen offered anywhere.--Fahrenheit451 23:57, 26 Mar 2005 (UTC)

You ask why I want to put a criticism of Approval in the Approval article, instead of the Borda Count article. I ask why you would possibly not want information to be put under the appropriate topic. Someone looking up the Borda count is not looking for criticisms of Approval.

Only as a comparison to another voting method. I would say that it is not essential content, but interesting.--Fahrenheit451 23:57, 26 Mar 2005 (UTC)

  • Should every election method page have this criticism of Approval? There's no reason for this to go specifically on the Borda Count page, is what I'm saying. RSpeer 00:56, Mar 27, 2005 (UTC)

Point well taken. --Fahrenheit451 01:31, 27 Mar 2005 (UTC)

You ask who I am to demand that the article be changed -- I'm a Wikipedia editor, and I'm not demanding that the article be changed, I'm stating my intent to change it. That's what Wikipedia editors do with articles that are messy and POV. I'm also outlining my plan to revise the article in case someone wants to help me. As it is, I probably won't get around to it for a while, especially since you're likely to revert most of what I do.

There is nothing "messy" about the Borda count article as it currently stands.--Fahrenheit451 23:57, 26 Mar 2005 (UTC)

  • This gets to the real reason I suspect you are opposed to changes to the article: you wrote it and you're protective of it. That doesn't work on Wikipedia. Sorry, but it is messy, and I'm sure an outside observer would agree.

We very much disagree on that. It is your opinion. I am sure you could find someone who would side with you on that and I could find one who would side with me.--Fahrenheit451 01:31, 27 Mar 2005 (UTC)

"Vote for two" and "vote for three" are not seriously proposed by election reformers, so they are easy straw men to shoot down. Supporters of other methods don't compare their methods to clearly inferior methods like "vote for two" and "vote for three"; why waste time comparing Borda to them?

That was an example. A more useful comparison would be irv.--Fahrenheit451 23:57, 26 Mar 2005 (UTC)

  • IRV is not a positional method. RSpeer 00:56, Mar 27, 2005 (UTC)

True. Why did you mention that?--Fahrenheit451 01:31, 27 Mar 2005 (UTC)

  • Because we were talking about positional methods. The statement I was responding to was: It should be noted that any paradoxes which can be found in the Borda count are also present in all other positional methods, and usually in greater number.

Approval is cloneproof. Voters vote the same way on all clone candidates (if a significant number of voters approved of one and disapproved of another, they wouldn't be clone candidates), so clones get the same number of total votes. The team of clones wins if and only if one of them would have won independently.

I was looking at AP from the standpoint that a voter would not fully apprise themself of all the candidates and would vote for their known favorites, clones or not. I understand your reasoning however.--Fahrenheit451 23:57, 26 Mar 2005 (UTC)

"Likely" is not the same as "always". In fact, most election methods are "likely" to give the same result in the same situation, but they do not always do so, and that is why they are different methods. This is also why IBR is a different method from Borda, just like IRV is different from Plurality, and one Condorcet method is different from another. In fact, even Cloneproof SSD is considered a different method from SSD, even though they only differ in the tie-breaking procedure.

I am beginning to suspect that you are using your nonstandard "tallying procedure" terminology to obstruct revision to this article. You still haven't defined what the distinction is, and why you need to make that distinction. Why is it so important to you that IBR is described as a "tallying procedure" instead of an "election method"?

One could define a different tallying procedure linked to a standard balloting procedure as a similar election method. I fail to see that this is any benefit to the understanding of someone reading the Borda count article. I suppose you could endulge yourself and do so. Eccentricity is no crime.--Fahrenheit451 23:57, 26 Mar 2005 (UTC)

  • The benefit is that the reader doesn't have to encounter the term "tallying procedure" and wonder what you mean by it, when in fact you mean "election method". Less new terminology is a good thing. RSpeer 00:56, Mar 27, 2005 (UTC)

RSpeer 22:45, Mar 26, 2005 (UTC)


I am beginning to believe that you don't know what "neutral point of view" means, because your recent edits have not been using it.

I don't think you do.--Fahrenheit451 08:27, 2 Apr 2005 (UTC)

An important clarification is that the neutral point of view is not just about balancing positive statements with negative, but qualifying statements based on who claims them.

I don't agree with you at all on that. Neutral is staying with documentable facts and not employing pr either way.--Fahrenheit451 08:27, 2 Apr 2005 (UTC)

That said, I don't know anyone who claims that strategic nomination decreases with more voters. That's nonsense. The result is the same regardless of the number of voters. Look at the other side of strategic nomination, the spoiler effect, and how it affects elections with hundreds of millions of people.

Show me an article that documents that if you want to convince me.--Fahrenheit451 08:27, 2 Apr 2005 (UTC)

And at some point you removed the NPOV notice without addressing my complaints. I've been giving you a chance to fix this article, (personal attack).

The article evidently was not fixed to your liking.--Fahrenheit451 08:27, 2 Apr 2005 (UTC)

Note that the fact that I'm only reverting this one statement doesn't mean it's the only objectionable one, just that I haven't had time to check the validity of the others.

RSpeer 08:11, Apr 2, 2005 (UTC)

I see you are back to your old stuff Rspeer. You should read the article by Arkadii Slinko on the external links. I also do not appreciate you personal attack in your comment on deletion.--Fahrenheit451 08:18, 2 Apr 2005 (UTC)

For the benefit of outsiders, I removed a provably false statement in support of the Borda count, and used the edit comment "please don't lie".

For the benefit of outsiders, RSpeer's last statement is a falsehood. I based my statement on an article in the links by Arkadii Slinko. Clearly, RSpeer refuses to read and understand it. --Fahrenheit451 21:34, 2 Apr 2005 (UTC)

Fahrenheit451, you agreed to have an outside opinion, so here goes. RSpeer 15:31, Apr 2, 2005 (UTC)

Please don't lie RSpeer, I stated, "Show me an article that documents that if you want to convince me." as above. I don't care about an opinion, I want to see the facts. --Fahrenheit451 21:34, 2 Apr 2005 (UTC)

Statement for Third Opinion[edit]

I believe that Fahrenheit451 is using this article to push his POV in favor of the Borda Count. Per discussion above, (removed personal attack) Wikipedia:Neutral Point of View (removed personal attack).

Please don't lie RSpeer. It appears to me that RSpeer wants to make destructive critical remarks about me editing but does nothing to be helpful. --Fahrenheit451 21:42, 2 Apr 2005 (UTC)

He also disagrees that this page needs cleanup; I say that because of all the incremental edits, the page is a mess. (removed personal attack), and defends the page against edits by anyone but him.

RSpeer 15:31, Apr 2, 2005 (UTC)

Please don't lie again, RSpeer. Others have edited this page since I started editing it as well. RSpeer uses a generality that the page needs "cleanup" but has not taken responsibility to do so, i.e exactly what should be changed, other than the one sentence he disagrees with.--Fahrenheit451 21:42, 2 Apr 2005 (UTC)

  • This is wrong. I gave an extensive plan for cleanup of the page, and you disagreed with every point with terse justification, and claimed that it needed no cleanup at all. If you look up at the rest of this discussion page, you will see that I do not disagree with one comment, I disagree with Fahrenheit451's entire writing style. RSpeer 09:12, Apr 3, 2005 (UTC)

Wikipedia:Check your facts needs to be applied here. I read the Slinko article and the math and reasoning look correct to me. The statement under contention with RSpeer was based on that article. He evidently refuses to read it. --Fahrenheit451 22:01, 2 Apr 2005 (UTC)

  • The statement is about voters' strategy, not strategic nomination, which is what you were talking about. You can include this statement when describing positive aspects of Borda, but you can't use it to try and nullify the negative aspect that is strategic nomination, becaues it isn't about strategic nomination. And there's a difference between "refusing to read it" and having fewer free hours in the day than you to argue this. RSpeer 09:59, Apr 3, 2005 (UTC)

Request for Comment[edit]

I'm still finding my way around the dispute resolution process. It looks like I'm supposed to make it a Request for Comment first before using mediation, which sounds like a difficult process. RSpeer 14:26, Apr 5, 2005 (UTC)

I opine that in the edit RSpeer did today he removed some important and neutral information. I am restoring that information within his restructuring.--Fahrenheit451 00:45, 9 Apr 2005 (UTC)

New version of page[edit]

I hope the new version of the page is an acceptable compromise. Maybe we don't need an RfC after all.

I don't think that the "Quota Borda System" should be included in this article. It's a very different voting method, being a multiple-winner method - such methods have their own section on Voting system. It also only has 36 google hits. I'm not sure it's significant enough for someone to be looking for information on it on Wikipedia.

RSpeer 06:00, Apr 9, 2005 (UTC)

I agree. One of us should create a new article and move the entry to that page, citing it in the Borda count article.--Fahrenheit451 16:03, 9 Apr 2005 (UTC)

Created qbs article and moved entry there.--Fahrenheit451 16:34, 9 Apr 2005 (UTC)

reversion to (removed personal attack)[edit]

I thought we had come to a good, stable version of the page, Fahrenheit451, and I was prepared to let this debate end amicably. (removed personal attack). I'll split my points up into sections, so you can respond to each individually as you prefer, so please respond after my signature instead of in the middle of my comments. RSpeer 03:49, Apr 12, 2005 (UTC)

Baldwin elimination[edit]

It will take a damn good reference for you to convince me that Baldwin elimination has anything to do with the Borda count, because there are 0 Google hits for "baldwin elimination" "borda count" -wikipedia. I suspect that using Baldwin elimination as a tie-breaker is your own original research. RSpeer 03:49, Apr 12, 2005 (UTC)

Two links found without much time spent. here is it called a recursive elimination method: here it is refered to as Borda elimination: I guess it could be called Borda elimination. It is obvious it can be used to break ties and that is hardly original research.--Fahrenheit451 17:26, 12 Apr 2005 (UTC)

Those pages are describing variants of Instant Borda Runoff, and do not mention breaking ties.

You failed to use your signature on the above comment of yours. Please do so. Those pages do not mention Instant Borda Runoff, either.--Fahrenheit451 17:56, 12 Apr 2005 (UTC)

Regardless of whether it is "obvious" that it can be used to break ties, it is not obvious that it should. As far as I can tell, you are the only person who is proposing this kind of tie-breaker. Therefore it does not belong on Wikipedia.

Most election method pages don't mention tie-breakers, unless it is crucial to a property of the method (like Cloneproof Schwartz Sequential Dropping, where the "cloneproof" part comes from the tie-breaker). This is because you don't need complicated rules for a tie-breaker. You can determine randomly, or you can designate someone as casting a tie-breaking vote, and that resolves any tie in any method.

RSpeer 17:38, Apr 12, 2005 (UTC)

I never stated or implied that complicated rules were needed for tie breaking, you said the contrary for some reason. Borda or Baldwin elimination is a simple method.--Fahrenheit451 17:56, 12 Apr 2005 (UTC)

Transfers of votes[edit]

You have not provided an explanation for why you think IRV transfers votes and IBR doesn't, and even if that were true why it would be relevant. That claim sounds a lot like claims made by the IRV supporters, who use ill-defined catch-phrases like "one person, one vote" and "don't divide your forces" and say that only IRV satisfies them. RSpeer 03:49, Apr 12, 2005 (UTC)

IRV is based on the single transferable vote, where votes from a candidate eliminated after a round are transfered and distributed to the remaining candidates. IBR eliminates the candidate and the votes. They are not transfered and distributed to other candidates. It is relevant because ibr and irv and two entirely different procedures. I am surprised that you ask this. Your comparison of my statements to false irv public relations lines is baseless.--Fahrenheit451 17:26, 12 Apr 2005 (UTC)

Let me deliberately caricature this argument. Remove it as a personal attack if you will, but I am trying to make a point to you.

  • You add a statement to the article saying "The Borda count is not emfoozable."
  • I say, "What does that mean?"
  • You say, "That means that it cannot be emfoozled, obviously."
  • I say, "Even if that meant something, why should it go in the article?"
  • You respond as if I had argued that the Borda count is not emfoozable, with a heated response affirming that of course it is emfoozable, and ignoring my question of why this belongs in the article.

You may believe there's something inherently wrong about "transfers" and therefore frame IBR to deny that it's doing "transfers", but that's all meaningless. There are no "transfers" in IBR or IRV, there are only numbers and lists of candidates that change from one round to another. You have not explained why this distinction needs to be made, and why anyone should care.

RSpeer 17:53, Apr 12, 2005 (UTC)

There are transfers of votes upon elimination in IRV. That is a verifiable fact. There are no transfers of votes in IBR upon elimination and that is a verifiable fact. This distinction needs to be made because they are two different bodies of data. Sensible people do care about differences and care about facts. --Fahrenheit451 18:10, 12 Apr 2005 (UTC)

These are not facts, (removed personal attack) (this was an attack on your argument, not you. RSpeer), until you define what you mean by "transfer", preferrably with a mathematical basis. Any consistent definition of "transfer" I can think of encompasses both IRV and IBR.

I can see why IRV looks more like "transfers", in a fuzzy and ill-defined way. The points in IRV can be imagined as discrete entities that move from one candidate to another, while in each round of IBR, all the scores change and you can't trace the changes back to the candidate that was eliminated. Is this what you're doing? Why do you believe this is a valid way of comparing voting systems?

This sentence makes no sense: This distinction needs to be made because they are two different bodies of data. Clearly the distinction does not need to be made, because so many thorough descriptions of the Borda count don't feel the need to make it, and I'd be surprised if you showed me one that does. (Please, one that actually does, not one that talks about a vaguely similar thing.)

RSpeer 21:57, Apr 12, 2005 (UTC)

You need to clear up the word "transfer" in a good dictionary. For you and I to communicate well, we need to have the same definitions of words. That is the crux of our present disagreements and I think we will continue to have disputes in this area until that happens. There is no further purpose in debating this matter, otherwise. --Fahrenheit451 22:56, 12 Apr 2005 (UTC)

I agree that there is no further purpose in debating this matter. Can we come to a consensus to leave the IBR section as it is, and remove the npov tag?

If you agree, go ahead and remove npov. It seems to me that we have consensus on the vast majority of the page, and this debate isn't going anywhere useful, so we might as well have consensus on all of it. Right?

RSpeer 23:14, Apr 12, 2005 (UTC)

Our dispute is not about neutrality, but rather about factuality. I see nothing objectionable about the page as it presently is. Be advised that you made internal links on some topics that do not yet have articles. I am removing the npov template as you suggest. --Fahrenheit451 23:30, Apr 12, 2005 (UTC)

Okay. I'm glad we could resolve this dispute.

The redlinks are intentional, because I believe those articles (positional voting method and consistency criterion) should exist.

RSpeer 23:41, Apr 12, 2005 (UTC)

Forgot to log in. I moved links to new article on borda fixed point.--Fahrenheit451 19:44, 23 Apr 2005 (UTC)

Criteria for Nanson[edit]

Fahrenheit451, you added Nanson's method to the Voting system page saying that it passed certain criteria, and also listed them here. Do you have a source or a proof for these criteria?

I have made some correction to the Nanson section per ----Fahrenheit451

I am most suspicious of the statement that Nanson's method satisfies the participation criterion. I can't find a source that says specifically whether Nanson passes or fails, but Participation criterion says that "most" Condorcet methods fail. says that all Condorcet methods fail, but also gives no source or proof.

That is a vanity page with little mathematical rigor.---Fahrenheit451

I'd also want a proof for the defensive strategy criteria; however, I think those just shouldn't be referenced in articles at all, because it's unclear what they say and what constitutes a proof or a counterexample for them. User:MarkusSchulze says that they're not well-defined at all. RSpeer 21:02, May 1, 2005 (UTC)

I just removed them in my last edit and agree with User:MarkusSchulze.

Here is the link on the independence of clones for Nanson's method: ---Fahrenheit451

The participation criterion and the Condorcet criterion are incompatible. This has been proven by Moulin (Hervé Moulin, "Condorcet's Principle Implies the No Show Paradox," Journal of Economic Theory, vol. 45, pp. 53--64, 1988). See here!
By the way: Also the consistency criterion and the Condorcet criterion are incompatible.
By the way: Blake Cretney's website says that Nanson also violates independence of clones and monotonicity. Markus Schulze

I am convinced on monotonicity, but not independence of clones. Need to investigate further. ---Fahrenheit451

Edit war with RSpeer is back on[edit]

Very interesting that you deleted the first three links. The first is the deBorda Institute, the only Borda count organization in the world and the other two are published and peer-reviewed. If you want a war I think you are getting one.--Fahrenheit451 02:40, 16 May 2005 (UTC)

I'm not hiding my full name, but I prefer to go by RSpeer in Wikipedia discussions, so I'm changing your heading.

There are too many pro-Borda links here, especially given the lack of opposing links. You will not find that many positive links on any other voting system article. So I picked a few to delete. The deBorda one was probably the wrong one. I apologize for editing rashly - I'm not going to defend that particular edit.

I don't want an edit war with you. It was nice to temporarily be on the same side as you about Hermitage's links, but you started going too far, making edits that served no purpose except to attack or thwart Hermitage. I was also trying to show that my goals for the voting systems pages don't just apply to new users: Hermitage complained that the external links for Borda are excessively slanted, and he was right, so I started doing something about it. The only thing that makes this an "edit war" with you is that the links were added by you, and you are protective of them. - RSpeer

I am not against you. I am glad to see that there are other folks who care about voting methods and selecting the methods that are appropriate to the needs of a circumstance. If you want to do that as part of your career, I wish you great success in that. It is a skill that is badly needed. I hope you understand that. The links I have posted are published peer-reviewed articles. Yes, most of them present favorable conclusions about the BC, but some of them prove that the BC has vulnerabilities. The voting systems page links usually go to websites that have general information or research articles on voting systems in general. We need to impose standards for links which I think should be advocacy organizations for a particular method and primary, published and peer-reviewed research on the method or comparing the method to others. Otherwise, we open the door to anyone putting up a stupid pro or con vanity site into the links and just adding clutter to the article. I am as protective of this article as you are of what you edit, but like you, I am willing and grateful for others to responsibly edit. They usually do a good job. Usually. You are perhaps aware that theoretical vulnerabilities are not the same as what occurs in practice. The BC is used in real elections and I have not found complaints from any parties involved with them. Hermitage's concluding comment in his BC article, which is not pub'd and peer-rv'd, contradicts actual experience with this method. It is simply shoddy scholarship. I have respect and regard for the academic process. Occasionally it censors a radical innovation, but more often it weeds out slipshod scholarship and overt bias. I welcome any con BC articles that are published and peer-reviewed to be added to the links.--Fahrenheit451 13:42, 16 May 2005 (UTC)

I may seem inconsistent to you in who I side with. This is because I'm not siding with editors, but with edits. The edits that you make to all other articles besides Borda count are reasonable and helpful, and I commend you for spending so much time on the project. It's just this one page where you're unreasonably protective.

RSpeer 06:09, May 16, 2005 (UTC)

I recommend that Hermitage do some further research into the BC and rewrite his article, citing published and peer-reviewed sources, then have his advisor read it through critically and rewrite if necessary. I think he is capable of producing something much better than the current article. --Fahrenheit451 14:32, 16 May 2005 (UTC)

Clone Independence[edit]

The latter criteria should receive some commentary: No clone candidates have ever been or are likely to be identified, so the ICC non-compliance should be viewed only from a theoretical perspective for actual candidates. However, for referenda, the ICC could have real relevance, as clone multi-option proposals could easily be crafted.

A source is needed for the notion that "no clone candidates ... are likely to be identified." Since Borda rewards nominations of similar candidates, it doesn't even seem relevant whether clones can be "identified" after the fact.

ICC non-compliance should be viewed only from a theoretical perspective for actual candidates also needs a source, else it's just POV. I don't think it is good advice. Why are referenda proposals "easily crafted" while candidate nominations aren't? KVenzke 04:05, Jun 12, 2005 (UTC)

ICC itself is POV as there is no evidence for "clone candidates". Clone proposals would be easy to create. ICC is Tideman's theory, and for candidates has no evidence of existence. I favor removing the ICC statement in the article entirely, but it is evidently a sacred cow to some theorists.--Fahrenheit451 18:22, 12 Jun 2005 (UTC)

ICC is not a "theory," and it's not limited to Tideman. This article even has a link to an article on clone manipulability. If you don't like that article, then also Woodall discusses it in "Properties of Election Rules," Voting Matters Issue 3, Dec 1994. Whether a method satisfies or fails a criterion is just a fact; you don't have to accept that it's an important fact. KVenzke 21:24, Jun 13, 2005 (UTC)

Please show me some clone candidates and you will answer your own question. Hint: They do not exist.--Fahrenheit451 19:11, 12 Jun 2005 (UTC)

Here are some clone candidates:

 40% A>B>C
 40% B>A>C
 20% C>B>A

A and B are clone candidates.

A clone is a copy or duplicate of something else. The theoretical example you have provided shows that A and B have some positional correlation. That is all. There is no demonstration of "clones" there.--Fahrenheit451 16:02, 13 Jun 2005 (UTC)

Except that this is the definition of "clone." KVenzke 21:24, Jun 13, 2005 (UTC)

No, that may be Tideman's definition of a clone, but not a dictionary definition. I view his definition as nonsense.--Fahrenheit451 23:50, 13 Jun 2005 (UTC)

So you just criticize the use of the term clone? Or are you saying you don't understand Tideman's definition? KVenzke 15:25, Jun 14, 2005 (UTC)

Voting theory is not an experimental science, it is theoretical math. If you insist on discussing only the results of real elections, then the topic you are discussing is electoral reform, not voting theory. RSpeer 04:43, Jun 13, 2005 (UTC)

For a voting theory to be relevant, it must reflect reality, or even predict heretofore unobserved phenomena which can be confirmed. ICC does neither on the subject of candidates. ICC is Junk Science.--Fahrenheit451 16:02, 13 Jun 2005 (UTC)

You haven't explained why you have this belief. It's quite obvious that you can use e.g. FPP's failure of ICC to predict that factions won't run multiple candidates under FPP. KVenzke 21:24, Jun 13, 2005 (UTC)

No, you deduce that without any reference whatsoever to Tideman's "clones". --Fahrenheit451 23:50, 13 Jun 2005 (UTC)

Ok, so I guess you really do just criticize the use of the term clone. (You don't deny that the idea is useful; you suggest here that it's so obvious it doesn't need to be mentioned.) Unfortunately this term "clone" has caught on; outside of the EM mailing list, I don't know of any term used besides "clone." KVenzke 15:25, Jun 14, 2005 (UTC)

It should be Independence of correlated pairs. In real life those correlated pairs may be identical or very similar alternatives, and properly they would be proposals or objects. Extending that criterion to people is quite a stretch. This sums up my objections to the term and its use. Hope this clears things up.--Fahrenheit451 17:34, 14 Jun 2005 (UTC)

So all of this was because you thought the term "clones" referred to people? Then it is just a misunderstanding. Clones can be any sort of options, and in voting theory you don't care whether the options are people, proposals, or flavors of ice cream.

The term "candidate" is often used to mean any kind of option that can be voted for, which is perhaps awkward terminology, but it shouldn't be taken to mean that a statement about "candidates" applies only to people. The terminology doesn't distinguish whether the candidates are people or not, because there's no reason to. The algorithm still works the same way.

So "clones" are pretty much the same as what you mean when you say "correlated pairs". But "correlated pairs" is not standard terminology, and in fact it's not general enough, because they don't just have to come in pairs. You could have a set of 3 or 5 or 100 clones. RSpeer 20:20, Jun 14, 2005 (UTC)

Taken down to the minimum unit it would be pairs, which are subsets of a correlated set. The smallest non-empty set would contain two elements. O.K. so it should properly be called independence of correlated elements. This clones stuff is very misleading and is a poor choice of noun.--Fahrenheit451 21:10, 14 Jun 2005 (UTC)

However, some methods would satisfy "Independence of Pairs (as in two candidates)" but do not satisfy "Independence of Clones (as in any number of candidates)." For example, MinMax methods can misbehave when you replace a single candidate with three candidates, all in a cycle. But it can't misbehave when you just replace one candidate at a time with two candidates. KVenzke 05:11, Jun 15, 2005 (UTC)

Criticizing ICC in the article text is off-topic[edit]

I've removed the criticism of ICC from the text of this article, not actually because it is F451's own opinion (that is a long hard battle to fight), but because it's off-topic. If that criticism belonged here, it would belong on every voting system article.

Fahrenheit451, the proper way for you to add this commentary to Wikipedia would be to make your case on the Talk:Strategic nomination page, get a consensus for it, and add it to the strategic nomination article. RSpeer 05:02, Jun 13, 2005 (UTC)

Inconsistent and arbitrary use of criteria in method evaluation[edit]

Hermitage reverted an edit I made by removing the Smith Criteria from the Borda count article. Several points here: There is no consensus on which criteria to evaluate a method by. The evaluation of methods with criteria is arbitrary and inconsistent. As Borda is not a Condorcet method, it would never be Smith compliant, thus stating it fails Smith is redundant and unnecessary. Therefore, User:Hermitage's revert was unjustified. I am again removing that criteria.--Fahrenheit451 00:06, 15 Jun 2005 (UTC)

I agree with removing Smith, since the failure is implied by failing Condorcet. I also agree with removing IIA, since virtually every method fails that. I don't know why you say, in the summary, that IIA is only for Condorcet methods. I guess the "local" version, LIIA, is only for Condorcet methods. KVenzke 05:14, Jun 15, 2005 (UTC)

You are right on all counts, but I added it back because it is one of the main criteria used in wikipedia articles for method evaluation. I would like to remove it, but we need a consensus to do so.--Fahrenheit451 14:31, 15 Jun 2005 (UTC)

See Talk:Voting_system/Included_methods_and_criteria --Hermitage 06:41, 14 July 2005 (UTC)

tactical voting section[edit]

Discussion of tactical voting is important to an understanding of the Borda method. For example, Dennis Mueller (who has many favorable things to say about Borda) writes "The Borda count's Achilles' heel is commonly felt to be its vulnerability to strategic behavior (Pattanaik 1974; M. Sen, 1984)." Opinions may differ on the severity of Borda's vulnerability, but certainly the issue should be represented significantly within the article.

F451 advocates the Borda count, and such is obviously his right, but his pro-Borda opinions should not cause him to edit the tactical voting section down to a tiny stub.

The following sentence was written by RSpeer on 23:10, 8 April 2005:

Voters in a Borda count election can usually see the potential for voting strategically: if there are only two candidates with a reasonable chance of winning, they will want to rank the candidate of those two they prefer first, and the other candidate last, to maximize the difference in points they contribute to the total.

F451 removed it on 00:39, 7 June 2005, with the summary "removed POV paragraph". On 08:32, 12 July 2005, I modestly expanded the tactical voting section, and included a re-worded version of RSpeer's example, as follows:

"For example, if there are two candidates whom a voter considers to be the most likely to win, the voter can maximize the power of his or her vote by ranking the more-preferred of the two candidates in first place, and ranking the less-preferred of the two candidates in last place, thus potentially employing both the compromising and burying strategies at once. If many voters employ such strategies, then the result will no longer reflect the sincere preferences of the electorate."

F451 considers this to be "POV". I disagree. First of all, it is factually correct. Second of all, it illustrates a relevant aspect of the Borda method. In my opinion, the tactical voting section of this article should be further expanded at some point, but I think that the current version is good considering its brevity. If F451 can come up with a factually correct statement that he feels gives more 'balance' to the section, I will welcome it. --Hermitage 07:09, 14 July 2005 (UTC)

Hmm. I don't like RSpeer's "can usually" phrasing, but otherwise it's not bad. I don't find Hermitage's wording to be as clear, with wording like "maximize the power." It should say something to the effect of (or at least, implying): When there are two front-runners (say A and B), and some weak candidates (say C) that no one likes, the voters have a dilemma. Suppose my sincere preference order is A>B>C. I can best help A defeat B by voting A>C>B instead. But if other voters do the same thing, then C will win, which no one wants. But on the other hand if I vote sincerely as A>B>C, I could very well be handing the election to B when A could have won. KVenzke 14:57, July 14, 2005 (UTC)
How about this:
For example, if there are two candidates whom a voter considers to be the most likely to win, the voter can maximize their impact on the contest between these candidates by ranking the candidate whom they like more in first place, and ranking the candidate whom they like less in last place.
for the re-phrasing of the initial idea? I got rid of the "maximize the power" phrase.
However we phrase that part, I still like the other supporting/expanding ideas that I added:
If neither candidate is their sincere first or last choice, the voter is employing both the compromising and burying strategies at once. If many voters employ such strategies, then the result will no longer reflect the sincere preferences of the electorate.
The first part ties the example into the preceding definitions. The second part begins to explore the possible consequences of tactical voting. --Hermitage 21:39, 14 July 2005 (UTC)

which criteria to include?[edit]

Over the course of a month or so, a group of voting methods-interested wikipedia editors (including F541) tried to reach a consensus on which criteria to consistently include in voting methods articles, on the following page: Talk:Voting system/Included methods and criteria. A majority of participating editors agreed that summability should not be one of these criteria, on the grounds that it is only failed by one method on wikipedia (instant runoff voting), and that it would be excessive to list it on all other method pages. (In the same way that it would be excessive to list the Pareto criterion on all method pages, when nearly every voting method (approval voting is the exception that I'm aware of) passes it.)

Recently, F451 re-added the summability criterion to this page on the grounds that it is listed on the Schulze method page. My counter-argument was that the criteria listed on the Schulze method page goes far beyond the standard criteria list, making that page something of an exception to the rule. My reasoning is that if the Schulze method page is used as a justification for adding the summability criterion to this page, then by the same token a whole slew of other criteria should be added as well, such as mutual majority, pareto, local IIA, Woodall's plurality, minimal defense, reversal symmetry, invulnerability to burying, etc. (There are 30 criteria currently listed on the Schulze method page.)

So, I think that the summability criterion should not be included in this page unless anyone can offer a better justification. --Hermitage 05:24, 26 July 2005 (UTC)

More pro-condorcet POV from you again Hermitage. Rather than remove all the criteria from Schulze method that was not agreed to be consistent from article to article, you suggest it all be added to other pages as well. So there is a double standard, one for Schulze method and one for Borda count and a few others. That's POV and not o.k. here on wikipedia. --Fahrenheit451 00:52, 27 July 2005 (UTC)
My heavens F451, you certainly like to accuse people of "POV"! Yes, the Schulze method page has not been affected by the talk:Voting system/Included methods and criteria discussion. It might be nice to gain greater consistency. I would be open to adding more criteria from the Schulze page to the other method pages (for example: mutualy majority, Pareto, Smith, Schwartz, Woodall's plurality, and invulnerabilty to burying), and I would also be open to deleting criteria from the Schulze page (for example: strategy free criterion, generalized strategy free criterion, strong and weak defensive strategy criteria, minimal defense, favorite betrayal criterion, summability). Note that there is no extreme pro-Condorcet slant here, as many of the Mike Ossipoff criteria that I am willing to delete were designed specifically to support WV Condorcet.
Maybe we could go back to the talk:Voting system/Included methods and criteria page, and agree on both a long list and a short list of criteria. The long list could look more like the Schulze method page, and the short list could be the one that we've agreed on so far. Then, it would be at editors' discretion at a page-by-page basis to choose between the long and short lists.
Anyway, consistency aside, I just don't see any justification for adding the summability criterion to the Borda page, when it is apparently unpublished, not very well defined, and when every method on wikipedia except IRV passes it. --Hermitage 01:15, 27 July 2005 (UTC)
O.K. Then remove summability from the Schulze method page. Let's be consistent. And consistency is not weasel wording "agree on a long and short list". Let's just be consistent. No arbitrary "editor's discretion". --Fahrenheit451 01:23, 27 July 2005 (UTC)
What do you mean by "weasel wording"? I think that the two list solution is viable.
As I mentioned, I am open to the removal of summability from the Schulze method page. --Hermitage 01:27, 27 July 2005 (UTC)

Long and short list is just another POV arbitrary. Ya, so go ahead Hermitage. You removed summability from the Borda count page, go ahead and remove it from the Schulze method page. Are you afraid of something?--Fahrenheit451 01:55, 27 July 2005 (UTC)

What an odd question, reminiscent of a schoolyard taunt. I will give others a chance to respond to the discussion on the Schulze method page before I remove summability from that page. Ideally, I would like to delete it along with several other Mike Ossipoff criteria; a sizable deletion that deserves some discussion. There was no need to discuss before reverting the addition of summability to the Borda page, because such discussion had already taken place. If you remove summability from any page other than the IRV page, I will not revert your edit. --Hermitage 03:23, 27 July 2005 (UTC)

I added summability back to the bc article and will continue to add it as it is an important criteria, see talk:summability_criterion and it is clearly arbitrarily removed from methods that anti-borda editors, like Hermitage, remove just out of sptie and hatred.--Fahrenheit451 17:18, 9 August 2005 (UTC)

As long as a criterion has an article, it isn't POV to mention in the article of an election method whether this election method satisfies this criterion. Markus Schulze 9 Aug 2005

I agree with Markus, adding content such as which criteria it satisfies isn't POV as it adds encyclopedic information. This applies even if it may be relatively obvious or implied from other information, such as with the strong and weak defensive strategy criterion; see Wikipedia:State the obvious. Scott Ritchie 21:08, 9 August 2005 (UTC)

Treatment of truncation[edit]

Another way, called the modified Borda count, is to assign the points up to k-1, where k is the number of candidates ranked on a ballot. For example, in the modified Borda count, a ballot that ranks candidate A first and candidate B second, leaving everyone else unranked, would give 2 points to A and 1 point to B. This variant would not satisfy the Plurality criterion.

It's true, that this doesn't satisfy Plurality. Incidentally, this isn't the variation I had in mind when I edited Plurality criterion, though. I'll give an example to illustrate:

51 A
50 B>C

In the variant that satisfies Plurality, A receives 102 points, B receives 100, and C receives 50.

Using the quoted method, A receives 51 points, B receives 100, and C receives 50.

The method I had in mind was to give A 102 points, but then B and C would split the 51 points that could have gone to one of them. Then B receives 100+25.5 points, and C receives 50+25.5. KVenzke 20:48, August 10, 2005 (UTC)

The third way is to employ a uniformly truncated ballot obliging the voter to rank a certain number of candidates, while not ranking the remainder, who all receive 0 points. This variant would satisfy the Plurality criterion.

In my opinion, this (as well as strictly-ranked Borda) violates the "spirit" of the Plurality criterion, since a voter might be compelled to rank randomly when he would prefer to just truncate. Then a candidate could win due to these random rankings. KVenzke 20:06, August 29, 2005 (UTC)

Strategic voting section[edit]

I'm sorry, F451, but your edit to replace the strategic voting problem in Borda with a link is seriously poor style.

I don't think you are sorry about anything. I think it is proper editing. Please show me the wikipedia policy against it.
  • Wiki articles don't say things like "For more information, see:" in the text. The reader knows that clicking on a link gives more information.
O.K. Then why not just remove that phrase?
  • There is no rule against duplicating information; in fact, it's quite common to include information from another page when it's relevant to the topic. This is much nicer to the reader than sticking the information behind a link, which requires effort (and, currently, about a minute of waiting time on average) to load. An example of this is that numerous articles about voting give brief statements of Arrow's impossibility theorem, rather than just mentioning it and making the reader click a link to find out what it means.
The latency time for me is about 10 seconds.
  • I don't understand what your motivation is for removing this section, unless it's to hide a common criticism of Borda from the reader. Can you give me an explanation? It's getting harder to assume good faith.
Your motivation is clearly that you hate Borda count. I moved the paragraph because you stated the explanation in the tactical voting article was in the abstract. It is long passed the point where I assume good faith from you.--Fahrenheit451 20:46, 16 September 2005 (UTC)

RSpeer 15:44, 16 September 2005 (UTC)

And you clearly love the Borda count (or at least as much as I "hate" it), but I thought we put aside this difference long ago and started working on generally improving the voting system articles. I'm disappointed that we have to start fighting again.

You've dodged the most important question: why should the reader have to click through a link at all to read pertinent information about the Borda count? It's not POV to describe a common criticism of something, and in fact including relevant criticisms is an important component of NPOV.

No, I replied that the latency time for me is about 10 seconds. There is no burden clicking the mouse once.

As a somewhat tangential issue, the current state of that section is very clunky just in writing style. I'd fix it, but you probably wouldn't like my version.

Probably not. You predicted accurately.

I'd just like to put the mention of the particular voting strategy back. We can even still describe how the strategic problem is mitigated by truncated ballots, which is something I didn't know before (but don't you mean uniformly truncated and not voter-truncated?) Right now, though, it's not even clear what vulnerability truncated ballots are reducing.

Strategic manipulation. Uniform truncation definitely makes it more difficult to manipulate, but so does voter truncation possibly to a lesser extent. In both cases, information is denied to the manipulators to predict with accuracy the ballot profiles. That is based on Conitzer's and Sandholm's research.

No matter what else you want to respond to, I'd like you to respond to this: how does removing the description of this particular voting strategy improve the article?

Because it is put into the tactical voting article where lengthy descriptions belong.--Fahrenheit451 17:50, 17 September 2005 (UTC)

RSpeer 05:05, 17 September 2005 (UTC)

Of course it doesn't. There's nothing wrong with the section as written before. F451, try to fix an article or a section that is actually bad, rather than lowering the quality of a section that is pretty good. If you have some correct and useful infomation, go ahead and add it. Otherwise, you're just wasting your own time and the time of others. You must have something better to do, eh? If you like Borda so much, go ahead and form a Borda advocacy group. Pass out fliers, harangue your local politicians... whatever. There are better venues for your Borda-love than making poorly-thought-out changes to the wikipedia. If you think that people revert your edits because you're some kind of noble minority of one standing up against groupthink, that's just goofy self-aggrandisement, and you should get over yourself. People revert your edits because they're not well thought out. They are often innacurate, misleading, or vague, and they sometimes delete content that is accurate and meaningful. Of course you have a few good contributions to make to the discussion, but your edits go well beyond that point. Anyway, that's my opinion. Thanks for reading it. --Hermitage 07:47, 17 September 2005 (UTC)
It always is your opinion and you are welcome I have read it. I am a wikipedia editor and I shall edit. And incidentally, you are badly mistaken about truncation making elections easier to manipulate. In general, it makes them more difficult.--Fahrenheit451 17:50, 17 September 2005 (UTC)

Give some evidence that voter truncation can do something to prevent manipulation. I can't see how that would be possible, as it gives each voter more strategic options. Also, give an actual reason to remove this section from this article. Leave tactical voting, which is a different article, out of it. RSpeer 04:32, 18 September 2005 (UTC)

The voter is not forced to rank or rate choices that are unacceptable. This does not eliminate, but reduces opportunities and incentives for insincere ranking. Manipulation opportunities by strategic nomination are also reduced as there is now truncation information that needs to be collected to predict an outcome and this adds additional uncertainty into a forecast. I think this is obvious. Conitzer and Sandholm showed this with a prescribed truncation, but the general principle holds for an arbitrary truncation. I have to ask you why it would not if you still disagree.--Fahrenheit451 21:39, 19 September 2005 (UTC)
Say my preferences are A>B>C. If I think that B is a closer competitor to A, I have an incentive to vote A (if truncation is allowed) or A>C>B (if it isn't). The former strategy is less risky, in that it does not help C's score get any closer to A's. For example, I wrote earlier that a coordinated majority can impose their will on the result in Borda count. If truncation is allowed, this is extremely easy: all they have to do is rank their preferred candidate in first place and truncate against all candidates whom they like less. If truncation is not allowed, the majority has to have some knowledge of what the other voters will do. --Hermitage 22:57, 19 September 2005 (UTC)
What you state is correct in a limited context: It also depends on if the voter approves or disapproves of B and/or C if they would rank them.
It could be that A is the only acceptable choice to the voter and bullet voting A is sincere. A majority would need to be borg-like and perfectly coordinate a mass bullet vote to do what you propose. By the extension of your proposition, a majority could impose a ranking profile that is strategically contrived based on information about minority profiles. Yes, it is possible, but more likely, some majority subset coalitions of voters will choose second or third preferences. To manipulate such an election, one also needs to know which voters will truncate and to what extent, and which will not. I think you can see that more information would have to be collected and more uncertainty is added to the forecast. --Fahrenheit451 23:39, 19 September 2005 (UTC)
I don't see the logic to this argument. More information needs to be collected? If you want to perform strategy based on how others are voting, the information you want is what ballots they will cast. Why would it be harder to gather such information if ballots were truncated?
Anyway, my point holds: truncation strategies in truncation-allowed Borda tend on balance to be less risky and easier to coordinate and less risky than order reversal strategies if truncation is not allowed. Not that I am advocating Borda w/o truncation -- the main point is that allowing truncation doesn't magically get rid of Borda's high manipulability. --Hermitage
Hmm. This is becoming an interesting discussion. If borda can be voter truncated from the low rankings, that is, the highest ranking candidate would get the normal borda count point value and so on down the rankings, as opposed to modified borda count that is truncated from the high rankings, then would not such a borda variant satisfy the majority criterion? And if equal rankings were allowed, would it not also satisfy the mutual majority criterion?

I would be interested in your take on this.--Fahrenheit451 23:57, 19 September 2005 (UTC)

Truncation allowed or not, Borda fails MC and MMC. All you need to do to show that a method fails a criterion is to provide one failure example. If I provide an example without truncation in which Borda fails MC, and full rankings are at least allowed (if not mandatory), Borda fails MC in general. Am I understanding your question correctly? --Hermitage 01:25, 20 September 2005 (UTC)

What I am proposing is that when voter truncation from the bottom is allowed, this variant is not the same as standard BC. If equal ranking is allowed, that would be a different variant again. Do you see where I am going with this?-- 01:52, 20 September 2005 (UTC)

I understand borda does not comply with mc or mmc, but my point is that when you change the rules, different criteria can and cannot be satisfied.--Fahrenheit451 14:18, 20 September 2005 (UTC)

Yes, but a feature of the way MC is defined is if a method without truncation fails it, that method with truncation has to fail it too, because the same situation that makes it fail without truncation could appear in a situation where none of the voters happen to choose to truncate. Correct me if I'm misunderstanding the issue.

RSpeer 20:59, 20 September 2005 (UTC)

You are misunderstanding the issue. I was using mc and mmc just as a hypothetical example. What you state is correct, but my point was that changing balloting and tabulation rules can give rise to new criteria satisfaction and destroy others. Nothing more to it than that.--Fahrenheit451 01:05, 21 September 2005 (UTC)

Good faith[edit]

A thought about a comment you made way above: "It is long passed the point where I assume good faith from you."

I'm not sure you understand the significance of assuming good faith. It's part of being a Wikipedia editor, not something you can choose whether or not to do. For instance, since I know that you are not actually a vandal, and that your goal is to improve Wikipedia, I assume that your edits are constructive until I can pass further judgment. (And in most cases, they are.) I am not a vandal either, and my goal is to improve Wikipedia as well, so you likewise need to assume by default that my edits are constructive.

The issue here is that, on this article, we disagree on what would improve Wikipedia; if I can hazard a guess, I'd say that you think it would improve Wikipedia to have a more flattering picture of the Borda count. Clearly we disagree here; I think that Wikipedia's picture of the Borda count should include both its praise and its criticism by voting theorists, whenever it is significant, in a way that is accessible to the reader so the reader can make his own judgment.

So, as I said before, it's hard to assume good faith in a conflict like this. But it's necessary. And it's an interesting mental exercise to be civil to someone who you've never met and who you disagree with.

RSpeer 20:59, 20 September 2005 (UTC)

We agree in principle.--Fahrenheit451 01:07, 21 September 2005 (UTC)

Additional method of handling truncation?[edit]

I'm not a student of voting systems, but I was reading the article and it seemed that there's another viable method for handling truncation. Specifically, the method would be:

Any ranked candidates are given the normal number of points, and all unranked candidates are given the average number of points of the positions that were left unfilled. For example, if there are 10 candidates and a voter votes for candidate A first, candidate B second, and leaves all others unranked, then A would get 9 points, B would get 8 points, and all other candidates would get 3.5 points.

Is there any history of this method being talked about or used? It appears that it would satisfy the Plurality criterion but not the Non-compulsory support criterion. - Flooey 07:28, 21 November 2005 (UTC)

That's the first method of Borda truncation I heard of. I'm surprised it's not in the article. rspeer 20:58, 21 November 2005 (UTC)

I have never seen that method in an article anywhere, but recall it was mentioned in a email discussion. I suppose it could be added to the relevant section of the article. Yes, it would fail ncsc, but passes pc.--Fahrenheit451 22:46, 25 November 2005 (UTC)

I described this rule earlier on this talk page. It doesn't satisfy Plurality. I gave an example. KVenzke 06:14, 2 December 2005 (UTC)
51 A
50 B>C
The method I had in mind was to give A 102 points, but then B and C would split the 51 points that could have gone to one of them. Then B receives 100+25.5 points, and C receives 50+25.5. KVenzke 20:48, August 10, 2005 (UTC)

Big Brother[edit]

This system is used to nominate the Big Brother evictees. Housemates are called to the Diary Room and asked who they nominate for two points and reason for nomination, and who they nominate for one point and reason for nomination. The three with the most points win, and viewers use plurality vote to determine who gets evicted. Scott Gall 05:20, 30 June 2006 (UTC)

Low point, higher ranking approach?[edit]

I reverted these unreferenced additions to the intro:

You must note that the borda count method may also be used in a different configuration, where first place votes give 1 point to the candidate, and a last place vote gets the candidate points equal to the number of candidates. The results will end up exactly the same, but are examined like a golfscore: lowest sum of points wins 1st place, highest sum of points is last. Either the high score method or the low score method are considered the borda count method, as they both will yeild the same results no matter what the conditions of the votes are. The examples and formulas that follow will use the high score method. This is because most people identify a higher score being superior, therefore people glancing at the results can see the winner instinctively without having knowledge of the counting system.

Sorry, I don't think this adds anything to the article, and I don't believe readers must note this, even if it is interesting. MORE it is likely more confusing what to do about unranked candidates, although looks like all unranked candidates would get the maximum number of points. Tom Ruen 16:54, 29 September 2007 (UTC)

You were right to remove that. CRGreathouse (t | c) 02:46, 30 September 2007 (UTC)

Borda and the majority criterion[edit]

The article states that Borda count fails the majority criterion. I don't think that's strictly the case, though I'd like to run this by here before editing.

Whether the Borda count fails the majority criterion is dependent on the point values used, and is not inherent to the Borda process.

Specifically, if point values are power-based, 2^n or 2^n + 1 or the like, a candidate with a majority vote in a position cannot receive fewer points than a lower candidate.

I'm looking for some online sourcing for this, but can't find any. If I recall correctly, it's not a particularly difficult proof. No luck yet, though. Gnassar (talk) 23:10, 6 December 2007 (UTC)

Also, would anyone be opposed to putting the 2005 and prior conversation on an archive page? This is getting pretty huge. Gnassar (talk) 23:10, 6 December 2007 (UTC)

Borda can't satisify the Majority criterion because it doesn't ask the voters this question. For example, say one candidate is first-rank on a 51 ballots and is third-rank on 49 ballots, and another candidate is first-rank on 49 ballots and second-rank on 51 ballots. The first candidate could be a majority winner in a single-vote/plurality election, but would lose in a Borda landslide: 49*3+51*1=198 points, to 49*3+51*2=249 points. Thus the 51% majority LOST their best choice for honestly ranking their second best choice. Borda himself would say there's nothing special about 51% and that the second candidate in this example is a better winner for having wider acceptance. (On archiving, of course no objection) Tom Ruen (talk) 23:25, 6 December 2007 (UTC)
Granted it doesn't ask the voters the question; nevertheless, my argument is that proper score selection leads to the majority criterion being met. You chose the standard natural-numbers sequence for Borda, which admittedly will fail that criterion. I honestly can't recall what the least bound is for picking Borda scores that maintain majority, but for triviality's sake, let's use your example with scores of 100 for first, 2 for second, and 1 for third. The candidate with 51 first ballots and 49 thirds would get 5149 points, while the candidate with 49 first ballots and 51 seconds would get 5002 points. This in a general sense does not trivialize the Borda method, as non-majority multi-candidate splits are still dependent on score totals which can bring a candidate with a number of lower rankings higher than one with fewer higher rankings (though given, the difference in number of votes required is much more, now by design.)
I apologize for my lack of rigor, as I can't seem to find a lower bound calculation, but depending on the details of the election, a sufficiently large difference between Borda scores of two rankings can assure the majority criterion for those two rankings. This can be done for all pairings of rankings to achieve the majority criterion for any given election.
This is all IIRC, as I can't find sources. Frustrating! I'll keep trying.
And I'll give that the disparity in scores has to normally be pretty dramatic, and that no "real" election has ever occurred to my knowledge with such score disparities. Really, I state this less because of the "practical" use, and more because it seems the page is at least somewhat interested in a bit of mathematical rigor. A statement along the lines of "Though the Borda method itself doesn't inherently violate the majority criterion, practical applications tend to dictate scoring systems which do so" would be fine with me. If I'm correct about this, that is. (talk) 06:50, 7 December 2007 (UTC)
Apologies -- I neglected to log in for that prior comment. Gnassar (talk) 06:52, 7 December 2007 (UTC)
First of all, the Borda count gives n, n-1, n-2, ..., 1 points to the candidates; other different amounts of points are not the Borda count but general point methods (unless of course the two give the same results in all cases, like 2n-2, 2n-4, 2n-6, ..., 0).
Second, any point method giving a points to the first place, b points for the second place, and c points for third place, a,b>c, can give the win to a majority loser if there are enough votes.
In your example, if 100 people vote A > B > C and 99 vote B > C > A then B wins even though A has a majority.
CRGreathouse (t | c) 16:23, 7 December 2007 (UTC)

Borda vs. range voting?[edit]

I got reverted: (rm confusing change to opening -- this isn't range voting!)

But how is Borda count not a special case of range voting, in the same sense that approval voting is a special case of range voting? --Damian Yerrick (talk | stalk) 02:21, 30 January 2009 (UTC)

It's an ordinal/positional voting system, which means it's actually not very similar to range voting (which is cardinal) at all. CRGreathouse (t | c) 17:21, 30 January 2009 (UTC)
It's a positional voting system that's counted just like range voting. Compare this passage from the lead of Wikipedia's article about one voting system:
[One voting system] determines the winner of an election by giving each candidate a certain number of points corresponding to the position in which he or she is ranked by each voter. Once all votes have been counted the candidate with the most points is the winner.
to this passage from another article's lead:
[There is another] voting system for one-seat elections under which voters score each candidate, the scores are added up, and the candidate with the highest score wins.
The parallelism between the passages implies that Borda is just range voting where the scores are restricted to integers from 1 through n_candidates, and no ballot can give two candidates the same score. --Damian Yerrick (talk | stalk) 00:02, 31 January 2009 (UTC)
If you ask me, the answer depends on how one looks at Borda. I find Borda quite flawed for the exact reasons that it needlessly restricts values to integers and imposes a ranking by a voter. To me, in practice, Borda does seem like a special case of range voting, but then I can't add that to the article without a reference. --AB (talk) 01:31, 31 January 2009 (UTC)
Then go stick a {{fact}} on Condorcet criterion#Range voting, which makes exactly the same comparison between Borda and range voting that got reverted from this article. --Damian Yerrick (talk | stalk) 01:57, 1 February 2009 (UTC)
I went to that article, hopeful that I could remove something (or at least slap on a {{cn}} tag), but no. That article is just saying that the two fail Condorcet for the same reason, it doesn't draw any further conclusions.
CRGreathouse (t | c) 04:06, 1 February 2009 (UTC)
The main difference between Range/Approval and Borda is that in Range and Approval, the ranks available to give to one candidate do not depend on the ranks given to the other candidates. This is a fundamental difference, and is the basis of several of the mathematical proofs about Range in [1]. Thus it is not appropriate to view Borda as a special case of Range. Homunq (talk) 16:44, 10 June 2009 (UTC)

2008 Heisman?[edit]

It seems the 2008 Heisman Trophy results is notable enough to add to this page as a real-world example. Tim Tebow got the majority of first place votes (309 vs. 300 for winner Sam Bradford and 266 for runner-up Colot McCoy), but ended up third. I considered adding it but wasn't sure where it should go as there wasn't an obvious section for it. Ballot totals are on Wikipedia at Sam Bradford and probably elsewhere too. RoyLeban (talk) 16:37, 10 February 2009 (UTC)


The borda count can be used for many seat counstituencies not just single, from memory, I liked it the most when I read about it. (talk) 17:26, 23 May 2014 (UTC)

Propposal for use in Astronomy[edit]

Seems relevant as a possible use of the Borda count:

johantheghost (talk) 14:57, 7 May 2015 (UTC)