Spoiler effect
In social choice theory and politics, the spoiler effect refers to a situation where a losing (that is, irrelevant) candidate affects the results of an election.[1][2] A voting system that is not affected by spoilers satisfies independence of irrelevant alternatives or independence of spoilers.[3]
For the same effect in sports, see Elimination from postseason contention § Spoiler effect.
Arrow's impossibility theorem is a well-known theorem showing that all rank-based voting systems[note 1] are vulnerable to the spoiler effect. However, the frequency and severity of spoiler effects depends on the voting method.
Plurality and instant-runoff (colloquially called ranked-choice voting in the United States) are highly sensitive to spoilers,[4][5] and can manufacture spoiler effects even when doing so is not forced.[6][2][7][8] Majority-rule methods are usually not affected by spoilers, which are limited to rare[9][10] situations called cyclic ties.[11]
Rated voting systems are not subject to Arrow's theorem; as a result, many satisfy independence of irrelevant alternatives (sometimes called spoilerproofness).[3][12][8]
Examples by system[edit]
Borda count[edit]
In a Borda count, 5 voters rank 5 alternatives [A, B, C, D, E].
3 voters rank [A>B>C>D>E]. 1 voter ranks [C>D>E>B>A]. 1 voter ranks [E>C>D>B>A].
Borda count (a=0, b=1): C=13, A=12, B=11, D=8, E=6. C wins.
Now, the voter who ranks [C>D>E>B>A] instead ranks [C>B>E>D>A]; and the voter who ranks [E>C>D>B>A] instead ranks [E>C>B>D>A]. They change their preferences only over the pairs [B, D], [B, E] and [D, E].
The new Borda count: B=14, C=13, A=12, E=6, D=5. B wins.
The social choice has changed the ranking of [B, A] and [B, C]. The changes in the social choice ranking are dependent on irrelevant changes in the preference profile. In particular, B now wins instead of C, even though no voter changed their preference over [B, C].