Spoiler effect
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In social choice theory and politics, the spoiler effect refers to a situation where the entry of 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.
By
Rated voting systems are not subject to Arrow's theorem; as a result, many satisfy independence of irrelevant alternatives (sometimes called spoilerproofness).[3][8]
Motivation
Social choice theorists have long argued that voting methods should be spoiler-independent, at least as far as this is possible, since at least the 1950s (with work by economists and mathematicians such as Kenneth Arrow and John von Neumann). The Marquis de Condorcet studied similar properties at least as far back as the 1780s.
Rational behavior
In
Manipulation by politicians
Voting systems that violate independence of irrelevant alternatives are susceptible to being manipulated by strategic nomination. Some systems are particularly infamous for their ease of manipulation, such as the Borda count, which lets any party "clone their way to victory" by running a large number of candidates. This famously forced de Borda to concede that "my system is meant only for honest men,"[9][10] leading to its abandonment by the French Academy of Sciences.[10]
Vote-splitting systems like
In some situations, a spoiler can extract concessions from other candidates by threatening to remain in the race unless they are bought off, typically with a promise of a high-ranking political position.
Fairness
Because a candidate's quality and popularity clearly do not depend on whether an unpopular candidate runs for office, it seems intuitively unfair or undemocratic for a voting system to behave as if it does. A voting system that is objectively fair to candidates and their supporters should not behave like a lottery; it should select the highest-quality candidate regardless of factors outside of a candidate's control (like whether or not another politician decides to run).
Arrow's theorem
Arrow's impossibility theorem is a major result in social choice theory, which proves that every ranked-choice voting system is vulnerable to spoiler effects.
However,
By electoral system
Different
Plurality-runoff methods like the two-round system[11] and instant-runoff voting[8] still suffer from vote-splitting in each round. As a result, they do not eliminate the spoiler effect. The elimination of weak spoilers in earlier rounds somewhat reduces their effects on the results compared to single-round plurality voting,[12] but spoiled elections remain common, moreso than in other systems.[3]
Modern tournament voting eliminates vote splitting effects completely, because every one-on-one matchup is evaluated independently.[11][12] If there is a Condorcet winner, Condorcet methods are completely invulnerable to spoilers; in practice, somewhere between 90% and 99% of real-world elections have a Condorcet winner.[5][6] Some systems like ranked pairs have even stronger spoilerproofing guarantees that are applicable to most situations without a Condorcet winner.
Plurality voting
Vote splitting most easily occurs in
Runoff systems
Spoilers also occur in the
In Burlington, Vermont's second IRV election, spoiler Kurt Wright knocked out Democrat Andy Montroll in the second round, leading to the election of Bob Kiss (despite the election results showing Montroll would have won a one-on-one election with Kiss).[17] In Alaska's first-ever IRV election, Nick Begich was defeated in the first round by spoiler candidate Sarah Palin.[18]
Tournament (Condorcet) voting
Spoiler effects rarely occur when using
For each pair of candidates, there is a count for how many voters prefer the first candidate (in the pair) to the second candidate, and how many voters have the opposite preference. The resulting table of pairwise counts eliminates the step-by-step redistribution of votes, which causes vote splitting in other methods.
Rated voting
Rated voting methods ask voters to assign each candidate a score on a scale (usually from 0 to 10), instead of listing them from first to last. The best-known of these methods is score voting, which elects the candidate with the highest total number of points. Because voters rate candidates independently, changing one candidate's score does not affect those of other candidates, which is what allows rated methods to evade Arrow's theorem.
While true spoilers are not possible under score voting, voters who behave strategically in response to candidates can create pseudo-spoiler effects (which can be distinguished from true spoilers in that they are caused by voter behavior, rather than the voting system itself).
Weaker forms
Several weaker forms of independence of irrelevant alternatives (IIA) have been proposed as a way to compare ranked voting methods. Usually these procedures try to insulate the process from weak spoilers, ensuring that only a handful of candidates can change the outcome.
Local independence
A weaker criterion proposed by H. Peyton Young and A. Levenglick is called local independence from irrelevant alternatives (LIIA).[19] LIIA requires that both of the following conditions always hold:
- If the option that finished in last place is deleted from all the votes, then the order of finish of the remaining options must not change. (The winner must not change.)
- If the winning option is deleted from all the votes, the order of finish of the remaining options must not change. (The option that finished in second place must become the winner.)
In other words, for any group of candidates who are listed consecutively in the finish order, eliminating every candidate who is not part of that group shouldn't change how the method orders the members of that group.
LIIA is satisfied by only a few voting methods. These include
Independence of worst candidates
One may also consider a weakening of LIIA where only the first point is required to hold - that eliminating the n worst candidates does not alter the order of the remaining candidates.
This criterion is passed by methods that eliminate losers one at a time, because eliminating the worst candidates is part of its natural procedure.[citation needed]
If a method passes this criterion and reversal symmetry, it also passes LIIA. As a consequence, common elimination methods like instant-runoff voting almost invariably fail reversal symmetry.
Some social choice authors distinguish between methods that select a single winner and methods that determine a rank of finish. They then construct the latter from the former by repeatedly eliminating winners and using the elimination order as order of finish. If a method constructed in this manner passes independence of worst candidates, it also passes LIIA.
Condorcet independence criteria
Besides its interpretation in terms of majoritarianism, the
Smith-independence is another kind of spoiler-resistance for Condorcet methods. This criterion says that a candidate should not affect the results of an election, unless they have a "reasonable claim" to the title of Condorcet winner (fall in the Smith set). Smith candidates are ones who can defeat every other candidate either directly or indirectly (by beating some candidate A who defeats B).
Independence of clones
Independence of clones is the most commonly-fulfilled spoiler-resistance criterion, and says that "cloning" a candidate—adding a new candidate identical to an existing one—should not affect the results. Two candidates are considered identical if they are ranked equally on every ballot. The criterion is satisfied by instant-runoff voting, all systems that satisfy independence of irrelevant alternatives (including cardinal systems), and most tournament solutions.
However, it is worth noting this criterion is extremely fragile, as even a single voter expressing a preference for one candidate over the other (or placing another candidate between them) can nullify a system's protection.
Examples by system
Borda count
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].
Condorcet methods
A single example is enough to show that every Condorcet method must fail independence of irrelevant alternatives. Say that 3 candidates are in a
This example also shows why Condorcet elections are rarely (if ever) spoiled: spoilers can only happen if there is no Condorcet winner. Condorcet cycles are rare in large elections,[5][6] and the median voter theorem shows cycles are impossible whenever candidates are arrayed on a left-right spectrum.
Plurality
Plurality voting is a
- 3 voters rank (A>B>C)
- 2 voters rank (B>A>C)
- 2 voters rank (C>B>A)
In an election, initially only A and B run: B wins with 4 votes to A's 3, but the entry of C into the race makes A the new winner.
The relative positions of A and B are reversed by the introduction of C, an "irrelevant" alternative.
See also
- Electoral threshold
- Independence of clones
- Independence of Smith-dominated alternatives
- Independence of irrelevant alternatives
- Strategic nomination
- Comparison of electoral systems
Notes
- ^ In election science, ranked voting systems include plurality rule, which is equivalent to ranking all candidates and selecting the one with the most first-place votes.
- ^ Results can still be irrational if voters fail independence of irrelevant alternatives, i.e. if they change their ballots in response to another candidate joining or dropping out. However, in this situation, it is the voters, not the voting rule, that generates the incoherence; the system still passes IIA.
- ^ Strategic voting can sometimes create the appearance of a spoiler for any method (including rated methods). However, this does not greatly affect the general ordering described here, except by making cardinal and Condorcet methods closer to even.
References
- ISBN 9781783470730.
A spoiler effect occurs when a single party or a candidate entering an election changes the outcome to favor a different candidate.
- ^ a b "The Spoiler Effect". The Center for Election Science. Retrieved 2024-03-03.
- ^ a b c d e "The Spoiler Effect". The Center for Election Science. 2015-05-20. Retrieved 2017-01-29.
- ^ ISBN 9780898716955.
Candidates C and D spoiled the election for B ... With them in the running, A won, whereas without them in the running, B would have won. ... Instant runoff voting ... does not do away with the spoiler problem entirely, although it ... makes it less likely
- ^ ISSN 1573-7187.
- ^ ISSN 1573-7101.
- ^ arXiv:2108.00542, retrieved 2024-03-11. "This is a kind of stability property of Condorcet winners: you cannot dislodge a Condorcet winner A by adding a new candidate B to the election if A beats B in a head-to-head majority vote. For example, although the 2000 U.S. Presidential Election in Florida did not use ranked ballots, it is plausible (see Magee 2003) that Al Gore (A) would have won without Ralph Nader (B) in the election, and Gore would have beaten Nader head-to-head. Thus, Gore should still have won with Nader included in the election."
- ^ OCLC 872601019.
IRV is subject to something called the "center squeeze." A popular moderate can receive relatively few first-place votes through no fault of her own but because of vote splitting from candidates to the right and left. ... Approval voting thus appears to solve the problem of vote splitting simply and elegantly. ... Range voting solves the problems of spoilers and vote splitting
- ISBN 9780898381894.
- ^ ISBN 978-0472104505.
- ^ ISSN 0028-7504. Retrieved 2019-07-20.
plurality-rule voting is seriously vulnerable to vote-splitting ... runoff voting ... as French history shows, it too is highly subject to vote-splitting. ... [Condorcet] majority rule avoids such vote-splitting debacles because it allows voters to rank the candidates and candidates are compared pairwise
- ^ a b c Ending The Hidden Unfairness In U.S. Elections explains why plurality and runoff voting methods are vulnerable to vote splitting.
- ^ "Top 5 Ways Plurality Voting Fails". The Center for Election Science. 2015-03-30. Retrieved 2017-10-07.
You likely have opinions about all those candidates. And yet, you only get a say about one.
- ^ ISBN 9781440841163.
Those votes that are cast for minor party candidates are perceived as taking away pivotal votes from major party candidates. ... This phenomenon is known as the 'spoiler effect'.
- ISBN 9780199759965.
a spoiler effect occurs when entry by a third-party candidate causes party A to defeat party B even though Party B would have won in a two-candidate race.
- ISBN 9781429957649.
IRV is excellent for preventing classic spoilers-minor candidates who tip the election from one major candidate to another. It is not so good when the 'spoiler' has a real chance of winning
- ^ Stensholt, Eivind (2015-10-07). "What Happened in Burlington?". Discussion Papers: 13.
There is a Condorcet ranking according to distance from the center, but Condorcet winner M, the most central candidate, was squeezed between the two others, got the smallest primary support, and was eliminated.
- arXiv:2303.00108
- ISSN 0895-3309.