The Spoiler Effect

Introduction

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.

Plurality

The most typical scenarios of the spoiler effect involve plurality voting, our choose-one method. Plurality is extremely vulnerable to the spoiler effect so that even candidates with little support can act as spoilers. Here, we'll give voter preferences in a simplified scenario.

% of voters          Their ranking
49%                    M1
48%                    M2
3%                      m>M2

"M1" is the Plurality winner here with the most votes (49%). Note, however, that 51% of the voters prefer "M2" to "M1".

Here, candidate "m" changes the election outcome with just a small percentage of the vote. "m" does not win, but voters for "m" preferred "M2" as a second choice. So had "m" not been in the election, those voters would have voted for "M2" instead, giving "M2" the victory.

Instant Runoff Voting / Ranked Choice Voting

Instant runoff voting (IRV) does a decent job at mitigating the spoiler effect by getting past plurality's faliure listed above. But it fails to do the job once other candidates become more competitive.

We begin by demonstrating the spoiler for instant runoff voting, including its simplified “top 3 limit” form, called ranked choice voting (RCV). Proponents of IRV/RCV commonly claim that it “eliminates spoilers”. This is simply false, as shown visually in the video below:

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.

To highlight the spoiler here, 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 IRV  Counterargument

Proponents of IRV will typically reject 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.

But we don’t have to rely on that example here. That's 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 can be quite erratic.

IRV Spoiler Within the Same Faction

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. For example, a progressive candidate can enter 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

Next round:

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

Score and Approval Voting

Both score and approval voting handle vote splitting among similar candidates extremely well. This is due to their ability to have equal or similar weight count towards multiple candidates. Approval and score voting are therefore highly robust to the spoiler effect, to the point of being arguably immune to it.

Critics attempt to argue, however, that approval and score voting fall prey to this effect due to bullet voting. But this is incorrect. Bullet voting is not an issue for these methods.

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