Spoiler effect

In social choice theory and politics, a spoiler effect happens when a losing candidate affects the results of an election simply by participating.^[1]^[2] Voting rules that are not affected by spoilers are said to be spoilerproof^[3]^[4]

The frequency and severity of spoiler effects depends substantially on the voting method. Instant-runoff or ranked-choice voting (RCV), the two-round system (TRS), and especially first-past-the-post (FPP) without winnowing or primary elections^[5] are highly sensitive to spoilers (though RCV and TRS less so in some circumstances), and all three rules are affected by center-squeeze and vote splitting.^[6]^[7]^[8]^[9] Majority-rule (or Condorcet) methods are only rarely affected by spoilers, which are limited to rare^[10]^[11] situations called cyclic ties.^[12]^[13]^[14] Rated voting systems are not subject to Arrow's theorem. Whether such methods are spoilerproof depends on the nature of the rating scales the voters use to express their opinions.^[15]^[16]^[17]^[18]

Spoiler effects can also occur in some methods of proportional representation, such as the single transferable vote (STV or RCV-PR) and the largest remainders method of party-list representation, where it is called a new party paradox. A new party entering an election causes some seats to shift from one unrelated party to another, even if the new party wins no seats.^[19] This kind of spoiler effect is avoided by divisor methods and proportional approval.^[19]^: Thm.8.3

^ 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.
^ "The Spoiler Effect". The Center for Election Science. Retrieved 2024-03-03.
^ Miller, Nicholas R. (2019-04-01). "Reflections on Arrow's theorem and voting rules". Public Choice. 179 (1): 113–124. doi:10.1007/s11127-018-0524-6. hdl:11603/20937. ISSN 1573-7101.
^ McCune, David; Wilson, Jennifer (2024-03-03), Multiwinner Elections and the Spoiler Effect, doi:10.48550/arXiv.2403.03228, retrieved 2024-12-27
^ Borodin, Allan; Lev, Omer; Shah, Nisarg; Strangway, Tyrone (2024-04-01). "Primarily about primaries". Artificial Intelligence. 329: 104095. doi:10.1016/j.artint.2024.104095. ISSN 0004-3702.
^ Poundstone, William. (2013). Gaming the vote : why elections aren't fair (and what we can do about it). Farrar, Straus and Giroux. pp. 168, 197, 234. ISBN 9781429957649. 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
^ Merrill, Samuel (1985). "A statistical model for Condorcet efficiency based on simulation under spatial model assumptions". Public Choice. 47 (2): 389–403. doi:10.1007/bf00127534. ISSN 0048-5829. the 'squeeze effect' that tends to reduce Condorcet efficiency if the relative dispersion (RD) of candidates is low. This effect is particularly strong for the plurality, runoff, and Hare systems, for which the garnering of first-place votes in a large field is essential to winning
^ 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. JSTOR 3088418. As with simple plurality elections, it is apparent the outcome will be highly sensitive to the distribution of candidates.
^ 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
^ 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.
^ 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. "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."
^ Morreau, Michael (2014-10-13). "Arrow's Theorem". Stanford Encyclopedia of Philosophy. Retrieved 2024-10-09. One important finding was that having cardinal utilities is not by itself enough to avoid an impossibility result. ... Intuitively speaking, to put information about preference strengths to good use it has to be possible to compare the strengths of different individuals' preferences.
^ Miller, Nicholas R. (2019-04-01). "Reflections on Arrow's theorem and voting rules". Public Choice. 179 (1): 113–124. doi:10.1007/s11127-018-0524-6. hdl:11603/20937. ISSN 1573-7101.
^ Poundstone, William. (2013). Gaming the vote : why elections aren't fair (and what we can do about it). Farrar, Straus and Giroux. pp. 168, 197, 234. ISBN 9781429957649. 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
^ "The Spoiler Effect". The Center for Election Science. 2015-05-20. Retrieved 2017-01-29.
^ ^a ^b Balinski, Michel L.; Young, H. Peyton (2001) [1982]. Fair Representation: Meeting the Ideal of One Man, One Vote. New Haven: Yale University Press. ISBN 0-300-02724-9.

[:3-1] 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.

[:4-2] "The Spoiler Effect". The Center for Election Science. Retrieved 2024-03-03.

[:04-3] Miller, Nicholas R. (2019-04-01). "Reflections on Arrow's theorem and voting rules". Public Choice. 179 (1): 113–124. doi:10.1007/s11127-018-0524-6. hdl:11603/20937. ISSN 1573-7101.

[:7-4] McCune, David; Wilson, Jennifer (2024-03-03), Multiwinner Elections and the Spoiler Effect, doi:10.48550/arXiv.2403.03228, retrieved 2024-12-27

[5] Borodin, Allan; Lev, Omer; Shah, Nisarg; Strangway, Tyrone (2024-04-01). "Primarily about primaries". Artificial Intelligence. 329: 104095. doi:10.1016/j.artint.2024.104095. ISSN 0004-3702.

[Poundstone,_William.-201323-6] Poundstone, William. (2013). Gaming the vote : why elections aren't fair (and what we can do about it). Farrar, Straus and Giroux. pp. 168, 197, 234. ISBN 9781429957649. 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

[Merril_19852222-7] Merrill, Samuel (1985). "A statistical model for Condorcet efficiency based on simulation under spatial model assumptions". Public Choice. 47 (2): 389–403. doi:10.1007/bf00127534. ISSN 0048-5829. the 'squeeze effect' that tends to reduce Condorcet efficiency if the relative dispersion (RD) of candidates is low. This effect is particularly strong for the plurality, runoff, and Hare systems, for which the garnering of first-place votes in a large field is essential to winning

[8] 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. JSTOR 3088418. As with simple plurality elections, it is apparent the outcome will be highly sensitive to the distribution of candidates.

[Borgers223-9] 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

[:53322-10] 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.

[:63322-11] 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.

[:533-12] 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.

[:633-13] 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.

[Holliday3-14] Holliday, Wesley H.; Pacuit, Eric (2023-02-11), Stable Voting, arXiv:2108.00542. "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."

[x031-15] Morreau, Michael (2014-10-13). "Arrow's Theorem". Stanford Encyclopedia of Philosophy. Retrieved 2024-10-09. One important finding was that having cardinal utilities is not by itself enough to avoid an impossibility result. ... Intuitively speaking, to put information about preference strengths to good use it has to be possible to compare the strengths of different individuals' preferences.

[:0-16] Miller, Nicholas R. (2019-04-01). "Reflections on Arrow's theorem and voting rules". Public Choice. 179 (1): 113–124. doi:10.1007/s11127-018-0524-6. hdl:11603/20937. ISSN 1573-7101.

[Poundstone,_William.-20132-17] Poundstone, William. (2013). Gaming the vote : why elections aren't fair (and what we can do about it). Farrar, Straus and Giroux. pp. 168, 197, 234. ISBN 9781429957649. 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

[:02-18] "The Spoiler Effect". The Center for Election Science. 2015-05-20. Retrieved 2017-01-29.

[:03-19] Balinski, Michel L.; Young, H. Peyton (2001) [1982]. Fair Representation: Meeting the Ideal of One Man, One Vote. New Haven: Yale University Press. ISBN 0-300-02724-9.

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