Talk:Two-round system

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A 45% B 40% C 15%

ELECTION TWO Features candidates A and B in a "Run-off"

Advantages of a Run-Off Election

In a run-off election, the possibility of a "third party spoiler" is eliminated because no voter is forced to cast a vote for a candidate they do not favor. Here is an example:

If the US Presidential election were a run-off system, you might see this scenario. Voter 1 favors Ralph Nader. Voter 2 favors George W. Bush. Voter 3 favors John Kerry. In a regular election, assuming every voter votes their conscience, you see this result: Bush 1 Kerry 1 Nader 1 If voters vote strategically you might see this result: Voter 1 - Kerry Voter 2 - Bush Voter 3 - Kerry

Voter 3 has voted strategically, but in the process has voted against his preference. This is the heart of the spoiler issue in an electoral system. Voters who vote for a third candidate that is weaker than the top two, often prefer one of the top two candidates to the other. If they vote for the third candidate, their vote may be "wasted" because they could vote a candidate they prefer, and actually cause the candidate they least prefer to be elected by doing so. If they vote strategically, they will assure a candidate that they prefer is elected, but not the one they most prefer, which is the assumption in an electoral system.

A run-off system compensates by allowing voters to vote their first preference in the first election. In the second election, only the top two candidates are allowed to participate, so the possibility of a third party spoiler has been eliminated.

Requested move[edit]

Runoff votingTwo-round system – I know, I know, I know; all varieties of English are equally valid. However, the paragraph about terminology -- the last two sentences, complete with self-reference, are the smoking gun -- indicates that we need a move with either a redirect dab at its new location or a dab at the current location (probably unnecessary). Also see the discussion over longcase clock, a case of the inverse: the generic but uncommon name (longcase) instead of the common but non-inclusive one (grandfather). Moulder 06:56, 24 July 2006 (UTC)


The following discussion is an archived debate of the proposal. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.

The result of the debate was move and create a disambiguation page. -- tariqabjotu (joturner) 03:17, 1 August 2006 (UTC)

  • Support. Moulder 06:56, 24 July 2006 (UTC)
  • Weak support. This is a tricky one, but I think the matter of precision demands it be at the article about the specific type, with Runoff voting a disambiguation page (rather than a redirect). --Dhartung | Talk 07:35, 24 July 2006 (UTC)
  • Support renaming this page and creating a disambiguation page at "Runoff voting". Kafziel 15:38, 24 July 2006 (UTC)
  • Oppose. This is a common name for this. If necessary, add aticles for the way it is handled in other countries, but this works for the US. If anything, we could add a pointer to a dab page on Elections requiring voting again. Vegaswikian 19:38, 30 July 2006 (UTC)
The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.


My support is for the disambig option now despite previously thinking it unnecessary. (Or maybe a generic article about the concept of "runoff voting" and how it developed, if applicable.) This is mainly to distinguish between the exhaustive system and instant-runoff voting. The trickiness of this question is why I decided to be conservative instead of bold. Moulder 22:25, 24 July 2006 (UTC)

(Re: Vegaswikian) An article about generic runoff voting, i.e. comparing and contrasting the different systems and how the term runoff applies to them, should suffice; the initial paragraph can mention the fact that the US calls two-round voting runoff voting, and then each of the systems that employs runoffs can get a mention. Moulder 22:18, 30 July 2006 (UTC)

What happens if one candidate does receive an absolute majority? & other clarifications[edit]

What happens if one candidate does receive an absolute majority? Does he/she/it win without another round of voting? If so, that needs to be stated.

What happens if candidates draw, or if you had an election which went something like this: A - 25%, B - 24%, C - 23%, D, C, E, F... - 1% each? Would C still be eliminated in the second round?

Njál 16:17, 29 April 2007 (UTC)

Most runoff systems currently in use have a rule that a candidate receiving an absolute majority wins without needing a runoff. This is not, however, required by the method.

What happens in the case of an exact tie for second place has to be settled by something external to this method. In the near-tie situation you mentioned, C would indeed be eliminated in the second round, leaving an A v B runoff. (This actually happened in the 2002 Presidential election in France, where Jean-Marie Le Pen finished in second place, less than a percentage point ahead of Lionel Jospin.)Jack Rudd (talk) 00:58, 29 May 2008 (UTC)

Majority or absolute majority?[edit]

Does most elections really need an absolute majority (50% of all voters) or "just" a majority (50% of all votes cast)? I have noticed that other sources too write "absolute majority" ([1]). I am not familiar with the detailed laws (or language) but it seems strange that a election should fail, despite having a winner, because of low turnout. (?) Markuswestermoen (talk) 15:06, 1 December 2015 (UTC)

8/9/07 changes[edit]

Various spelling errors in the article were corrected —Preceding unsigned comment added by (talk) 20:37, 9 September 2007 (UTC)


I assume that runoff-voting satisfies the monotonicity criterion? Intuitively, it seems obvious that it would, but is there proof? (If the proof is trivial then in my opinion, that's all the more reason to add it to the article.) If, however, it does not in fact satisfy monotonicity, then can somebody please come up with a counter-example? (talk) 02:36, 17 May 2008 (UTC)
It doesn't satisfy it. Here's a counter-example:

39 prefer Edwards to Roemer to Duke
22 prefer Roemer to Edwards to Duke
8 prefer Roemer to Duke to Edwards
31 prefer Duke to Roemer to Edwards

So 39 vote Edwards, 31 Duke and 30 Roemer. The top two vote-getters are Edwards and Duke, who advance to a runoff, which Edwards wins.

Now make two of the Duke voters switch to Edwards. Then Edwards gets 41 votes, Roemer 30 and Duke 29. Edwards and Roemer advance to a runoff, which Roemer wins.

This same example, incidentally, shows that runoff voting fails the favourite-betrayal criterion, although the more usual favourite-betrayal would be for voters to switch from Duke to Roemer in the first round.
Jack Rudd (talk) 00:17, 29 May 2008 (UTC)

In France[edit]

Have changed the reference to every French election. Versions of the "two-round system" as decribed here are used, with differing rules, in presidential, legislative (National Assembly), and cantonal (Département general council) elections. For regional elections, however, the system used is

  • scrutin de liste selon un système mixte combinant les règles des scrutins majoritaire et proportionnel, en un ou deux tours, et sans panachage,

while for municipal elections there are two systems depending upon the size of the commune:

  • scrutin de liste à deux tours avec représentation proportionnelle
  • scrutin majoritaire plurinominal à deux tours avec panachage.

The last two systems provide for two rounds, but they do not fit the definition of "two-round system" as given in the lead-in to this article, since neither of them is "used to elect a single winner".

The present article, as it stands, covers only one particular variety of two-round voting: what the French, more precisely, call the

  • scrutin uninominal majoritaire à deux tours. -- Picapica (talk) 11:05, 11 October 2008 (UTC)

Page name is unclear[edit]

Looking at the name of this page, it can only possibly make sense once you are at it. Standalone it lacks clarity or specificity that it relates to VOTING. I would suggest that for clarity that the page should be named Two-round voting system Let me say that I know that this poses some difficulties due to the underlying nature of redirects, however, IMNSHO it needs to be done. -- billinghurst (talk) 03:10, 15 October 2008 (UTC)

The article first sentence makes it clear enough. Two-round system is the standard name for it. Any links to this article can give a longer description if desired, like Two round voting system. Tom Ruen (talk) 03:52, 15 October 2008 (UTC)

Removed section[edit]

I removed this section. There's no citations, and I have no evidence these systems are used, or even if they exist, whether they belong under a "two-round system" article. Tom Ruen (talk) 00:54, 11 November 2009 (UTC)

Viability Threshold Voting[edit]

In some types of runoffs, the initial round of voting is used to determine viable candidates, which can possibly total more than just two[citation needed].

For example, some precincts in American runoff elections[citation needed] count any candidate receiving at least 15% of the total vote a "viable" candidate, and their name will appear on the subsequent general election ballot (the general election only requires a plurality to win).

In other versions[citation needed], candidates must receive at least the average percentage for major candidates. For example, in a primary with 5 candidates, the average threshold would be 20%. Each candidate receiving at least 20% of the vote progresses to the second round. Another option in a reiterative count is to implement a bulk exclusion rule where candidates whose sum of all votes are less votes then then candidate(s) under consideration are excluded at the same time.

Condorcet winner and runoffs[edit]

Just to clear on why I'm reverting the recent change, if you have forced elimination in any round based on votes cast, you can eliminate the Condorcet winner. I don't see how you can say otherwise.... I glanced at the paper, but can you provide a simple example? Suppose you have three candidates, A, B and C. C is the Condorcet winner, but trails both A and B in core support and finishes third. How can you say the Condorcet winner will win if C is eliminated based on the first round results? RRichie (talk) 20:13, 25 June 2011 (UTC)

The complex model involves a game-theory equilibrium. In such an equilibrium, every voter votes in such a way that no voter has anything to gain by voting differently. Their actual votes may thus appear inconsistent with their internal preferences. The paper is saying that under that kind of equilibrium, and a limited number of candidates, the CW always wins. If there is a Condorcet winner (according to the voters' internal preferences), then the game-theoretical (robust political, which is basically trembling hand plus coordination) equilibrium is where voters vote in such a manner that the Condorcet winner is elected. (This can be proved through backward induction.)
In that way, it's like Approval. Approval voting doesn't let people specify relative rank of the candidate beyond simple approve/disapprove. Therefore, you would think Approval can't find a Condorcet winner since it has no way of knowing when a candidate is a Condorcet winner. But the game-theory equilibrium model mentioned in Approval voting is alike what I just said: it's a situation where no voter has anything to gain by voting differently. When voters vote according to that equilibrium, Approval picks the Condorcet winner (according to the voters' internal preferences) when there is one, and so does the two-round system with three candidates.
As for your example, if you have:
46 voters prefer A to C to B
44 voters prefer B to C to A
10 voters prefer C to A to B
then the equilibrium has the 44-voter group vote for C in the first round. If they vote for B, then no matter what the C-first group does (besides voting for their most disliked candidate), A wins; but if the 44-voter group votes for C, the C-first group has no reason to vote for any other candidate than C and so C wins outright. (talk) 23:43, 25 June 2011 (UTC)
This may be intellectually interesting, but it has no bearing on what would happen in real-life two-round runoff elections, which is what your point seemingly is trying to address in the article itself. Candidate C would lose and not advance to the runoff. Period. .. Now of there were no forced elimination and a candidate had to win 50% to win, I suspect A and B voters would settle on C. That's the point of my edit. RRichie (talk) 05:01, 26 June 2011 (UTC)
The model is of what would happen if voters knew the others' preferences. The more they know about the preferences of each other, the closer it gets. Besides, this reasoning, and this explanation of models, is accepted for Approval voting (as one can see in the article on AV), and thus I don't see why one should accept it there but exclude it here. (talk) 06:25, 26 June 2011 (UTC)
I would say it doesn't belong in the approval voting article either, at least not mixed into the main text as if this were a real way to think about the system as it is. Furthermore, even if you know about the preferences of other voters, you need to rely on them all acting sincerely, when there's no guarantee of this being the case..Fankly, this seems like so much gibberish when applied to thinking about how these systems might work if tried. If anything, it should be a separate paragraph, if used at all -- both here and in the approval voting article, where editors have allowed it to be treated on an equal basis with thinking about the system as it really would be if implemented. Not good. RRichie (talk) 12:34, 26 June 2011 (UTC)
It's not just any modification of the ballots that would elect a given candidate (and thus require honesty). The equilibrium is stable in that there's no incentive for any player, or (for the robust political equilibrium) for any coalition of players to vote otherwise, except if that would lead them to another equilibrium. Therefore, it can arise from selfish cooperation, so insincerity in the act of voting doesn't really enter into it. To deviate from the equilibrium, once reached, would only harm the voter/s.
What I wrote in my edit is factually right (the paper shows that the equilibrium exists) and there's precedent from the approval voting article. Your edit, though, does not follow from the citation. You say that the game-theory equilibrium is unrealistic and the conditions required to reach it wouldn't happen in an ordinary election. Would you accept a compromise that keeps my original edit, but adds text to the effect that the game-theory result requires idealized conditions and therefore provides an upper bound on what can be achieved with coordination or knowledge of other voters' preferences, but that it may not hold for real elections, particularly not large ones? (talk) 17:54, 27 June 2011 (UTC)

That seems sensible, although I must confess that this whole kind of theoretical discussion doesn't seem to be included in the midst of discussion of criteria that affect elections as they are. In that way the whole approval voting presentation is very misleading too and really should be changed. Saying approval voting meets all these criteria under conditions that will never happen is quite questionable to me, and saying that runoffs will always elect the Condorcet winner under certain conditions also is quite confusing, as those conditions would never exist. RRichie (talk) 18:40, 27 June 2011 (UTC)

Weimar Republic --> German Empire[edit]

I corrected that. A two-round-system was used in the Kaiserreich, while the Weimar Republic used a method of proportional representation.

Greetings from Germany, Max — Preceding unsigned comment added by (talk) 13:39, 2 July 2011 (UTC)

Dr. Bouton's comment on this article[edit]

Dr. Bouton has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

In both rounds of an election conducted using runoff voting, the voter simply marks an "X" beside his/her favorite candidate. If no candidate has an absolute majority of votes (i.e. more than half) in the first round, then the two candidates with the most votes proceed to a second round, from which all others are excluded. In the second round, because there are only two candidates, one candidate will achieve an absolute majority. In the second round each voter is entirely free to change the candidate he votes for, even if his preferred candidate has not yet been eliminated but he has merely changed his mind.

Comment: this definition focuses on the case in which the required number of votes for outright victory is 50%. Since there are other types of two-round systems, it would be good to clarify the focus at the beginning of the paragraph.

This system can be coupled with a vote par circonscriptions when an area can provide multiple seats. For example, all French departements and territories, but the five less populated ones, have several deputies, like the 18 of Paris. French Polynesia, where most population is located on two islands, have 3 deputies at French parlement. The French Polynesia is so split in three sub-divided constituencies for this specific election. But this sub-divisions, aside from this election, have no reality and are not an administrative subdivision.

Comment: I don't think this paragraph is useful. I would delete it.

This example demonstrates how the first two candidates from the first round might not necessarily be those expected to be the most popular by virtue of their party affiliations.

Comment: This paragraph is misplaced. I would delete it.

I fail to see the usefulness of the section "Compliance with voting criteria" from a general audience standpoint.

Runoff voting is intended to reduce the potential for eliminating "wasted" votes by tactical voting. Under the "first past the post" (plurality) system voters are encouraged to vote tactically by voting for only one of the two leading candidates, because a vote for any other candidate will not affect the result. Under runoff voting this tactic, known as "compromising", is sometimes unnecessary because, even if a voter's favourite candidate is eliminated in the first round, they will still have an opportunity to influence the result of the election by voting for a more popular candidate in the second round. However the tactic of compromising can still be used in runoff voting because it is sometimes necessary to compromise as a way of influencing which two candidates will survive to the second round. In order to do this it is necessary to vote for one of the three leading candidates in the first round, just as in an election held under the plurality system it is necessary to vote for one of the two leading candidates.

Comment: A citation to Bouton (2013) A Theory of Strategic Voting in Runoff Elections, American Economic Review, 103(4), pp. 1248-1288 could be added. In that paper, I study strategic voting in runoff elections. I show that the incentives to coordinate behind two candidates that exist under plurality also exist in runoff elections.

Runoff voting is also vulnerable to another tactic called "push over".[citation needed] This is a tactic by which voters vote tactically for an unpopular "push over" candidate in the first round as a way of helping their true favourite candidate win in the second round. The purpose of voting for the "push over", in theory, is to ensure that it is this weak candidate, rather than a stronger rival, who survives to challenge a one's preferred candidate in the second round. But in practice, such a tactic may prove counter-productive. If so many voters give their first preferences to the "weak" candidate that it ends up winning the first round, it is highly likely they will gain enough campaign momentum to have a strong chance of winning the runoff, too, and with it, the election. At the very least, their opponent would have to start taking the so-called "weak" candidate seriously, particularly if the runoff follows quickly after the first round.

Comment: A citation to Bouton and Gratton (2015), Majority Runoff Elections: Strategic Voting and Duverger's Hypothesis, Theoretical Economics, 10(2), 2015, pp. 283-314 could be added. We show, among other things, that strategic voters do not use push over tactics in (strictly perfect equilibria).

Runoff voting encourages candidates to appeal to a broad cross-section of voters. This is because, in order to win an absolute majority in the second round, it is necessary for a candidate to win the support of voters whose favourite candidate has been eliminated. Under runoff voting, between rounds of voting, eliminated candidates, and the factions who previously supported them, often issue recommendations to their supporters as to whom to vote for in the second round of the contest. This means that eliminated candidates are still able to influence the result of the election. This influence leads to political bargaining between the two remaining candidates and the parties and candidates who have been eliminated, sometimes resulting in the two successful candidates making policy concessions to the less successful ones. Because it encourages conciliation and negotiation in these ways, runoff voting is advocated, in various forms, by some supporters of deliberative democracy.

Comment: A citation to Lizzeri and Persico (2005), The Drawbacks of Electoral Competition, Journal of the European Economic Association could be added. They show how runoff encourages candidates to appeal to a broad cross-section of voters by providing public goods instead of transfers.

Runoff voting is designed for single-seat constituencies. Therefore, like other single-seat methods, if used to elect a council or legislature it will not produce proportional representation (PR). This means that it is likely to lead to the representation of a small number of larger parties in an assembly, rather than a proliferation of small parties. In practice, runoff voting produces results very similar to those produced by the plurality system, and encourages a two-party system similar to those found in many countries that use plurality. Under a parliamentary system, it is more likely to produce single-party governments than are PR systems, which tend to produce coalition governments. While runoff voting is designed to ensure that each individual candidate elected is supported by a majority of those in their constituency, if used to elect an assembly it does not ensure this result on a national level. As in other non-PR systems, the party or coalition which wins a majority of seats will often not have the support of an absolute majority of voters across the nation.

Comment: I was surprised by the content of this paragraph. The claimed should either be backed up by references or deleted.

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

We believe Dr. Bouton has expertise on the topic of this article, since he has published relevant scholarly research:

  • Reference : Laurent Bouton, 2012. "A Theory of Strategic Voting in Runoff Elections," Boston University - Department of Economics - Working Papers Series WP2012-001, Boston University - Department of Economics.

ExpertIdeasBot (talk) 16:06, 11 July 2016 (UTC)

=> I really really dislike the idea of a bot commenting on our electoral system. Don't do this again, please.