IRV Degrades to Plurality

Here is the common “optimistic” conception of how IRV works, where M1 and M2 are the major parties, lowercase “m” is a minor party, and an asterisk (*) means “all other candidates”.

% of voters          Their ranking

44%                     M1>*
40%                     M2>M1>m
16%                      m>M2>M1

In this scenario, a 56% majority of voters prefer M2 over M1. If they voted sincerely with Plurality Voting, M1 would win with only 44% of the vote. But with IRV, m would be eliminated and transfer 16% of the votes to M2, causing M2 to win by a 56% majority to M1. IRV seems to have worked.

But what if the minor party ceases to be written off as an unelectable spoiler, and grows in popularity in a subsequent election, leading to a scenario like this one?

% of voters          Their ranking

34%                      M1>*
29%                      M2>M1>m
37%                      m>M2>M1

Now M2 is eliminated, and 29% of the votes are transferred to M1, causing M1 to defeat m in next round with a 63% majority. The bottom row of voters, comprising 37% of the electorate, has gotten their least favorite of these candidates.

But imagine if some them had insincerely ranked M2 in first place. Then M2 would have advanced to the next round, and defeated M1 by a huge 66% majority. Here we show this happening with a as few as 5% of the voters using this strategy:

% of voters           Their ranking
34%                         M1>*
34% (29% + 5%)    M2>M1>m
32% (37% – 5%)     m>M2>M1

You might think that such scenarios are rare. And even when they occur, it might seem difficult to exploit them without prior knowledge of election outcomes. But for a tactical voter, that’s irrelevant. The question is, “what is more likely to result from this strategy?”

Top-ranking my favorite frontrunner will cause him to win instead of the frontrunner I like less (i.e. the strategy works), OR
Top-ranking my favorite frontrunner will cause him to win instead of the minor party candidate I actually prefer (i.e. the strategy backfires)

Since a candidate who is not a frontrunner is by definition not very likely to win, the first scenario is much more likely than the second. That is, using this strategy helps more often than it backfires. So it makes sense to almost always use it.

And in fact the above exaggeration strategy is exactly what has happened in the Australian House of Representatives, which has used IRV since 1918, and is dominated by the NatLibs and Labor, and typically has zero third-party candidates. And this is in spite of the fact their Senate uses the proportional STV system, and thus has several seats occupied by e.g. Greens. And this is in spite of the fact that ordinary (not “instant”) runoff elections have escaped duopoly even in single-member districts, in most of the 27 countries that use them.

This example shows what happened when voters naively supported their favorite in an IRV election. This is a simplification of an actual 2009 mayoral election in Burlington, Vermont, USA. The actual first-round totals were as follows. You can find a more complete analysis with all the data here.

In this election, Wright was the IRV spoiler. In this election, IRV eliminated Montroll who had the least first-choice votes. This elimination sent Kiss and Wright to the final round where Kiss won with more first-choice votes. Wright can’t win against Montroll or Kiss in a one-on-one election. Wright’s sole role is as a spoiler, changing the election outcome. Interestingly, Montroll is able to beat both Kiss and Wright one-on-one (a Condorcet winner). But IRV did not pick Montroll.

The row highlighted in green represents the voters who could have gotten a better result by insincerely top-ranking their second choice, Montroll, as first.

(Montroll=Democrat, Kiss=Progressive, Wright=Republican).

# of voters      Their ranking

1332                  M>K>W
767                   M>W>K
455                   M
2043                K>M>W
371                    K>W>M
568                   K
1513                   W>M>K
495                   W>K>M
1289                  W

This election was a bit interesting in that a Republican, a major party in the US, played the role of spoiler. It just happens that Burlington is a very liberal town where the Progressive Party is more popular than the Republican Party. For a growing traditional third party, Burlington’s IRV lesson plays out in exactly the same way.