The Spoiler Effect

In election parlance, a spoiler is a non-winning candidate whose presence on the ballot affects which candidate wins. In mathematical terms, the spoiler effect is when a voting method exhibits failure of a property known as Independence of Irrelevant Alternatives.

Spoilers are possible in all ordinal (“ranked”) voting methods, but not in Score Voting (aka Range Voting). That includes the simplest form of Score Voting, called Approval Voting.

Instant Runoff Voting/Ranked Choice Voting

We begin by demonstrating the spoiler for Instant Runoff Voting, including its simplified “top 3 limit” form, called Ranked Choice Voting. Proponents of IRV/RCV commonly claim that it “eliminates spoilers”. This is simply false. Here we use a hypothetical example featuring three candidates: a Democrat, a Republican, and a Progressive.

 % of voters
 Their ranking
34% P > D > R
29% D > P > R
37% R > D > P

The Democrat is eliminated with 29% of the first place votes. Then the Progressive trounces the Republican, 63% to 37%. And note, in case you think this example is contrived, it is actually a simplified approximation of what happened in the 2009 IRV mayoral election in Burlington, Vermont.

Now we remove the Republican from the ballots, and leave everything else exactly the same.

 % of voters
 Their ranking
34% P > D > R
29% D > P > R
37% R > D > P

Now the Democrat defeats the Progressive by a 66% to 34% margin. The Republican is a spoiler.

The counterargument

Proponents of IRV, particularly members of FairVote, will typically reject the claim that the Republican was a spoiler in this example, invoking a narrower definition of “spoiler”, which requires that a spoiler be a “weak” candidate.

We first note that this example can be arbitrarily extended to make the spoiler as weak as you like. In a race with millions of voters, it’s possible for a candidate to receive only two first-place votes, and to still be a spoiler.

However, we don’t have to rely on that example here, because in liberal Burlington, the Republican actually was the weakest of these three candidates, based on the following head-to-head comparisons.

Voters prefer the Democrat to the Progressive by 66% to 34%.
Voters prefer the Democrat to the Republican by 63% to 37%.
Voters prefer the Progressive to the Republican by 66% to 34%.

IRV proponents have suggested that the Democrat is actually the weakest of the three candidates, because the Democrat is the first one eliminated. But note, that order of elimination is due to the behavior of IRV, which we are arguing is flawed in the first place.

Score Voting (aka Range Voting), including Approval Voting

We note that that it is impossible to construct any such example like this for Score Voting or Approval Voting. Don’t believe us? Try it.

When the spoiler is from the same faction as the otherwise-winner

In the previous example, the Democrat would have won if the Republican hadn’t been a spoiler. But it’s possible for the spoiler to be from the same faction. I.e. a Progressive candidate enters the race, causing the winner to switch from Democrat to the Republican.

 % of voters
 Their ranking
26% P > D > R
23% D > P > R
2% D > R > P
49% R > D > P