IRV Degrades to Plurality

A commonly held misconception is that Instant Runoff Voting allows voters to support their sincere favorite candidates, without the fear of “throwing away their vote” on “spoilers”. We show why that is mistaken.
 

When IRV prevents a spoiler problem

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.

When IRV fails to prevent a spoiler problem

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

ALWAYS exaggerate

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)
  • 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. Which is precisely what a savvy tactical voter will do. And empirical evidence shows that people using ranked ballots (regardless of the tabulation mechanism) will naively exaggerate even if it doesn’t help them (we call this the Naive Exaggeration Strategy). So IRV actually behaves approximately the same as Plurality Voting, and maintains two-party domination, just like Plurality Voting does.

Empirical historical facts

And in fact that’s 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.

Realistic scenario?

If you thought the above scenario was “contrived” and unrealistic, we point out that it is a rough approximation/simplification of the actual 2008 mayoral election in Burlington, Vermont, USA. The actual first-round totals were as follows. The row highlighted in yellow represents the voters who could have gotten a better result by insincerely top-ranking their second choice (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
A keen observer might note that the two bloc of voter immediately beneath the highlighted one would not be helped by exaggerating by putting Kiss in first place. We note that it also would not hurt them. Kiss wins either way. This underscores the point in the “ALWAYS exaggerate” section. Even if the strategy had hurt them, that is still less likely than the case where it helps, so all voters should always top-rank one of the frontrunners, regardless of who their sincere favorite is.
 
Here is a much more mathematically rigorous analysis.
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