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Instant Runoff (a.k.a. Preferential voting)

Instant Runoff is an ordinal voting method, which may be a good choice for people familiar with runoff voting, i.e. voting in multiple turns, where weaker candidates are removed and their votes are transferred to the remaining candidates. It is simpler and less robust than Condorcet and more complicated but more robust than the Borda method. It is used in the real world in Australian elections under the name of Preferential voting (or Alternative voting).

Voters rank the candidates as first, second, third, etc. Table 1 illustrates the IRV tallying procedure for an example with four candidates (A, B, C, D) and 16 voters.

Table 1: An example ballot with four candidates A, B, C, D

3: B A C
2: B C A
1: B D
2: A B D
1: A B C
1: A
1: D C B
1: D C A
1: D
1: C A B
1: C D A

The first step is to count the first choices. Candidate B got 6 of the 16 first choices, while A got 5, D got 3, and C got 2. If one candidate had received a majority of first choices, that candidate would have won, but nobody did in this case. The counting procedure therefore goes to a second round.

The candidate with the fewest first choices, candidate C, is now eliminated. Each vote for C is transferred to the next candidate. Thus, all C entries are eliminated and the remaining choices are pushed left, if necessary, to fill in the empty cells. Table 2 shows the result (the third column is no longer needed).

Table 2: Ballot after the first round

5: B A
1: B D
4: A B
1: A D
1: A
1: D B
2: D A
1: D

The top choices are now counted again. Candidate A gained one new top choice (the second from last vote) for a total of 6. Still no candidate has a majority, so the counting procedure goes to a third round. Candidate D now has the fewest top choices and is therefore eliminated. Table 3 shows the result.

Table 3: Ballot after the first round

7: B
8: A

In the final round, the third from last vote has been exhausted; so only 15 active votes remain. Candidate A picked up two votes and now has 8 votes, which is a majority of the remaining votes, so candidate A wins. In this example, candidate A had fewer first choices than candidate B in the first round, but ultimately won the election.

The maximum number of rounds is always one less than the number of candidates. In the case of ties for the fewest top choices, the tied candidate with the fewest second choices is eliminated (if those are also tied, look at third choices, etc.). In the case of a tie in the final round, a coin toss can break the tie.

IRV has serious problems. It allows a sufficiently small minority of voters to safely register “protest” votes for minor-party candidates – but only as long as their candidate is sure to lose. As soon as their candidate threatens to actually win, they risk hurting their own cause by ranking their favourite first, just as they do under our current plurality system. IRV is therefore unlikely to be any more successful than plurality at solving the classic “lesser of two evils” problem.

A variation of IRV allows voters to rank groups of candidates equally. For example, a voter could rank candidates B and C equally for first choice, and D for second choice. For technical reasons that will not be discussed here, this equal-ranking option significantly mitigates the serious problems of IRV, but not enough to make it a good election method.

IRV does have one potential advantage over plurality. It requires the same voting equipment and the same voting mechanics (ranking candidates) as Condorcet voting. IRV could therefore possibly be transitional to Condorcet voting, a far superior alternative to IRV. However, IRV could also get entrenched and preclude Condorcet voting.

Shortcomings of Instant Runoff

Instant Runoff has serious technical problems, since it fails the monotonic criteria:

With the relative order or rating of the other candidates unchanged, voting a candidate
higher should never cause the candidate to lose, nor should voting a candidate lower ever cause the candidate to win.

This means that there are peculiar cases where the Instant Runoff method lets the “wrong” candidate win, even if the votes are all sincere. One example of such a case is the following votes count with four candidates “A, B, C, D”:

7: A,B,C
6: B,A,C
5: C,B,A
3: D,C,B

Applying the rules of IRV, candidate A wins. But suppose the three voters who voted (D, C, B) now promote A from last choice all the way up to first choice, without changing the relative order of the other candidates. Now B wins instead of A. So by promoting A from last to first choice, those voters caused A to lose instead of win!

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