Instant runoff voting

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Instant runoff voting or voting with integrated runoff voting ( English instant runoff voting , also alternative vote in Great Britain ) is a ranking system , i.e. one of the voting systems in which the voter can specify a ranking of his preferred candidates: He indicates on the Ballot, which of the candidates he would most like to have in office, which would be the second most - if the first is not elected - and so on. In this way, he can express his preferences much more precisely than with the classic majority vote .

In public elections for only one post, there is sometimes a runoff election. The effort for this can be saved with just one “ substitute vote” in a single ballot - a simple special case.

The ascertained ranking can also be used to fill several mandates, whether for members of a body with equal rights or for an office holder, his first and his second representative. This related problem is attempted to be solved by the system of transferable individual voting. The instant run-off voting and transferable individual votes presented here are identical if only one seat is available.

The procedure

A single ranking is determined as the election result from the ranking in all votes. The basic idea is an election with subsequent runoff elections, where the applicant with the fewest votes is eliminated in each ballot. The number of (here virtual) ballots is therefore equal to the number of candidates who are not elected.

It works like this:

  1. Any voter can put one candidate in first place, one in second place, and so on. So he assigns no, some or all candidates positions in a ranking.
  2. When counting, it is now determined which candidate received the fewest number 1 votes. This is removed from all ballot papers, and the subordinate candidates move up.
  3. The process is repeated from step 2 until there are only two candidates left. Of these, the one with the higher number of votes wins.

If only one mandate is available, the procedure can be terminated as soon as a candidate has more than half of the first place votes, because no one could overtake him by counting the votes of other ranks. The further steps can only influence the ranking of the remaining candidates (second, third place, etc.).

There are also simpler evaluation methods; they lead to a different allocation of seats for a small part of the election results.


Instant runoff voting allows you to cast the first vote even for practically hopeless candidates and still participate in the choice between the most promising ones. Sometimes large, sometimes small parties can benefit from an immediate runoff election,

  • large, because hopeless candidates can hardly take votes away from them (perhaps when several hopeless candidates stand before one promising one);
  • small ones because their voters can vote for their favorite candidates and still have a say in the big ones if this vote remains ineffective.

Instant runoff voting tries to explore and use the popularity of the candidates or parties more precisely than the majority vote.

Application in the world

Instant run-off voting is used in Australia , Ireland , presidential elections in Sri Lanka and the Californian city ​​of San Francisco . In the United Kingdom , it has been in force in elections of hereditary peers to the House of Lords since 1999 . The idea of ​​introducing the system for the House of Commons elections , however, failed in a referendum held on May 5, 2011 (see referendum on voting rights in the United Kingdom ). In the US state of Maine, instant runoff voting was used for the first time at the midterm elections in November 2018 after two referendums in 2016 and 2018 .

Instant runoff voting is particularly popular in countries and areas where politics is dominated by a few powerful parties (see two-party system ). It is being discussed in the USA as an alternative to the majority election there : In the 2000 presidential elections in Florida (USA), the Green Party may have prevented the Democrats from winning. To prevent such a thing from happening as much as possible, many voters in the US will vote for the candidate from the major party that appears to them to be the lesser evil, rather than the candidate with whom they identify most strongly. Instant runoff voting makes this stopgap solution unnecessary.


Let's say the class representative is to be elected in a small class of 12 students. Four candidates are nominated: Alex, Berta, Christoph and Doris. There is a group around Alex that supports him, but he is rather unpopular with the rest of the class. Each student now writes the first letters (A, B, C and D) on a piece of paper in the order that they indicate how well they find a candidate. The choice will be made as follows and will be evaluated in three rounds:

1 round
Note 1st place 2nd place 3rd place 4th Place
1 C. D. B. A.
2 A. D. B. C.
3 A. B. C. D.
4th D. B. A. C.
5 A. D. B. C.
6th C. D. B. A.
7th B. A. C. D.
8th B. D. C. A.
9 C. D. A. B.
10 D. A. B. C.
11 A. B. D. C.
12 D. C. A. B.

"1st place" votes:

Alex: 4th
Berta: 2
Christoph: 3
Doris: 3

In a relative majority vote , Alex would have won the election. Because Berta received the fewest votes, she is deleted and the second votes distributed to the respective candidates: The voter with ballot 7 would vote for Alex if Berta is not elected; and ballot 8 prefers Doris if Berta is not elected. Alex and Doris each get one more vote.

2nd round
Note 1st place 2nd place 3rd place 4th Place
1 C. D. A.
2 A. D. C.
3 A. C. D.
4th D. A. C.
5 A. D. C.
6th C. D. A.
7th A. C. D.
8th D. C. A.
9 C. D. A.
10 D. A. C.
11 A. D. C.
12 D. C. A.

"1st place" votes:

Alex: 5
Christoph: 3
Doris: 4th

So Christoph is deleted and the process continued: Everyone who would have liked to see Christoph as the winner now prefers Doris as the second best class representative. Doris receives three additional votes.

3rd round
Note 1st place 2nd place 3rd place 4th Place
1 D. A.
2 A. D.
3 A. D.
4th D. A.
5 A. D.
6th D. A.
7th A. D.
8th D. A.
9 D. A.
10 D. A.
11 A. D.
12 D. A.

"1st place" votes:

Alex: 5
Doris: 7th

Doris wins the election because she has now received the largest number of votes - even though Alex was the most popular candidate with the first votes.


In social election theory, there are a few criteria for determining the quality of an electoral system, among which instant runoff voting fares as follows:

Instant runoff voting meets the majority criterion, the Condorcet loser criterion, independence from clone alternatives and the later no harm criterion.

Instant runoff voting violates the Condorcet criterion, the independence from irrelevant alternatives, the consistency criterion, the participation criterion, the monotony criterion, the reversal symmetry criterion and the favorite betrayal criterion.

Compliance with the later-no-harm criterion

Since the lower rank information of a ballot paper is only requested if a candidate of higher rank has been eliminated, filling in lower ranks does not change the chances of the higher ranks. Neither for the positive (this immunity is called Later-No-Help) nor for the negative (this immunity is called Later-No-Harm). From this it follows that there is no tactical advantage in placing competition excessively deep ("burying" it), a tactic from which rank choice and Borda choice in particular suffer, and to a certain extent also Condorcet methods . However, there can be a tactical advantage in placing competition excessively high. This is a consequence of the violation of the monotony criterion.

Violation of the monotony criterion

If a voter places a candidate better on the ballot paper, it can result in them not winning the election, while winning the election if they are worse off. Elective systems in which this paradox does not occur meet the so-called monotony criterion. The decisive factor for the occurrence of this paradox in instant runoff voting is the fact that the order of the eliminations is decisive for the outcome of the election. If you succeed in eliminating a candidate who is close to your own favorite early on, your own favorite can usually take over his votes.

Another American example of this strategic choice:

Suppose I am a Democrat. We also assume that the Greens are the strongest “smaller” party and that their voters have the Democrats as a second preference, while the Republicans have the Greens as a second preference. The other preferences are irrelevant for the result and are shown in italics in the table . At some point in the counting process, all parties except the Democrats, Republicans and the Greens are eliminated.
If the Republicans have the fewest number of first-place votes, the Republican candidates are expelled and their votes are transferred to the Greens. And so the Greens could beat the Democrats. So, as a supporter of the Democrats, I should make sure that the Republicans don't drop out so early. I would have to give my vote to the Republicans I don't want for my favored Democrats to win.
Let us illustrate this with the following numerical example. With the "honest" values ​​the result is as follows:
49% of citizens 26% of citizens 25% of citizens
1. democratic 1. green 1. Republican
2. Republican 2. democratic 2. green
3. green 3. Republican 3. democratic
The Republicans are the first to be deleted. Now the Greens have more votes and win with 51% versus 49%.
But if instead 2% of Democratic voters give Republicans their first preference, the following table results:
47% of citizens 2% of citizens 26% of citizens 25% of citizens
1. democratic 1. Republican 1. green 1. Republican
2. Republican 2. democratic 2. democratic 2. green
3. green 3. green 3. Republican 3. democratic
The greens are the first to be painted here. I didn't really want that, but that's how the second votes of the Greens are used and the Democrats win the election with 73% to 27%. The result corresponds to my assumed will of the voters - contrary to the first scenario. But I didn't have to give my vote to precisely those who I prefer.

Violation of the Condorcet criterion

Instant runoff voting also violates the Condorcet criterion , according to which a Condorcet winner must win the election, if one exists. This is not the case in the following example:

42% of citizens 26% of citizens 15% of citizens 17% of citizens
1. A 1. B 1. C 1. D
2 B 2. C 2. D 2. C
3. C 3. D 3. B. 3. B.
4. D 4. A. 4. A. 4. A.

B is Condorcet winner: With 68% he wins his duels against C and D, with 58% against A.

However, with IRV, B does not win the election:

In the first ballot, C is excluded with only 15% of the vote. In the second ballot, B is eliminated because D now has 32% of the votes. In the third ballot, D wins with 58% of the votes against A.

See also

Web links

Individual evidence

  1. - Monotoni City and Instant Runoff Voting. In: Retrieved September 13, 2015 .