Spoiler effect

In social choice theory and politics, the spoiler effect or Arrow's paradox refers to a situation where a losing (that is, irrelevant) spoiler candidate affects the results of an election.^[1] A voting system that is not affected by spoilers satisfies independence of irrelevant alternatives or independence of spoilers.^[2]

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 substantially on the voting method. Majority-rule methods are only rarely affected by spoilers, which are limited to rare^[3]^[4] situations called cyclic ties.^[5] Plurality is the most sensitive to spoilers, while ranked-choice voting (RCV-IRV) is less sensitive in most scenarios.^[6]^[7]^[8]

Spoiler effects exist but may be less common in some methods of proportional representation, such as the single transferable vote (STV-PR or RCV-PR) and the largest remainders method of party-list representation. Here, a new party entering an election can cause seats to shift from one unrelated party to another, even if the new party wins no seats; this is known as the new states paradox.

^ Heckelman, Jac C.; Miller, Nicholas R. (2015-12-18). Handbook of Social Choice and Voting. Edward Elgar Publishing. ISBN 9781783470730. A spoiler effect occurs when a single party or a candidate entering an election changes the outcome to favor a different candidate.
^ Miller, Nicholas R. (2019-04-01). "Reflections on Arrow's theorem and voting rules". Public Choice (journal). 179 (1): 113–124. doi:10.1007/s11127-018-0524-6. hdl:11603/20937. ISSN 1573-7101.
^ Gehrlein, William V. (2002-03-01). "Condorcet's paradox and the likelihood of its occurrence: different perspectives on balanced preferences*". Theory and Decision. 52 (2): 171–199. doi:10.1023/A:1015551010381. ISSN 1573-7187.
^ Van Deemen, Adrian (2014-03-01). "On the empirical relevance of Condorcet's paradox". Public Choice. 158 (3): 311–330. doi:10.1007/s11127-013-0133-3. ISSN 1573-7101.
^ Holliday, Wesley H.; Pacuit, Eric (2023-02-11), Stable Voting, 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."
^ McGann, Anthony J.; Koetzle, William; Grofman, Bernard (2002). "How an Ideologically Concentrated Minority Can Trump a Dispersed Majority: Nonmedian Voter Results for Plurality, Run-off, and Sequential Elimination Elections". American Journal of Political Science. 46 (1): 134–147. doi:10.2307/3088418. ISSN 0092-5853. In terms of the performance of the different election systems, we confirm the results of Merrill (1984, 1985, 1988) that in multicandidate elections run-off and sequential elimination systems perform far better than plurality elections, in that they are more likely to pick the Condorcet winner, and have a lower variance in their outcomes. This is true even if the distribution is skewed or bimodal. However, with skewed distributions, run-off and sequential elimination elections still have a bias away from the median in the direction of the mode, although this is typically smaller than that with plurality election.
^ Borgers, Christoph (2010-01-01). Mathematics of Social Choice: Voting, Compensation, and Division. SIAM. 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
^ Cite error: The named reference :2 was invoked but never defined (see the help page).

Cite error: There are <ref group=note> tags on this page, but the references will not show without a {{reflist|group=note}} template (see the help page).

[1] Heckelman, Jac C.; Miller, Nicholas R. (2015-12-18). Handbook of Social Choice and Voting. Edward Elgar Publishing. ISBN 9781783470730. A spoiler effect occurs when a single party or a candidate entering an election changes the outcome to favor a different candidate.

[:0-2] Miller, Nicholas R. (2019-04-01). "Reflections on Arrow's theorem and voting rules". Public Choice (journal). 179 (1): 113–124. doi:10.1007/s11127-018-0524-6. hdl:11603/20937. ISSN 1573-7101.

[:533-4] Gehrlein, William V. (2002-03-01). "Condorcet's paradox and the likelihood of its occurrence: different perspectives on balanced preferences*". Theory and Decision. 52 (2): 171–199. doi:10.1023/A:1015551010381. ISSN 1573-7187.

[:633-5] Van Deemen, Adrian (2014-03-01). "On the empirical relevance of Condorcet's paradox". Public Choice. 158 (3): 311–330. doi:10.1007/s11127-013-0133-3. ISSN 1573-7101.

[Holliday3-6] Holliday, Wesley H.; Pacuit, Eric (2023-02-11), Stable Voting, 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."

[7] McGann, Anthony J.; Koetzle, William; Grofman, Bernard (2002). "How an Ideologically Concentrated Minority Can Trump a Dispersed Majority: Nonmedian Voter Results for Plurality, Run-off, and Sequential Elimination Elections". American Journal of Political Science. 46 (1): 134–147. doi:10.2307/3088418. ISSN 0092-5853. In terms of the performance of the different election systems, we confirm the results of Merrill (1984, 1985, 1988) that in multicandidate elections run-off and sequential elimination systems perform far better than plurality elections, in that they are more likely to pick the Condorcet winner, and have a lower variance in their outcomes. This is true even if the distribution is skewed or bimodal. However, with skewed distributions, run-off and sequential elimination elections still have a bias away from the median in the direction of the mode, although this is typically smaller than that with plurality election.

[Borgers2232-8] Borgers, Christoph (2010-01-01). Mathematics of Social Choice: Voting, Compensation, and Division. SIAM. 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

[:2-9] Cite error: The named reference :2 was invoked but never defined (see the help page).

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