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{{Electoral systems sidebar|expanded=Paradox}}
{{Electoral systems sidebar|expanded=Paradox}}


In [[social choice theory]] and [[politics]], a '''spoiler effect''' happens when a losing candidate affects the results of an election simply by participating.<ref name=":3">{{Cite book |last1=Heckelman |first1=Jac C. |url=https://books.google.com/books?id=KrckCwAAQBAJ |title=Handbook of Social Choice and Voting |last2=Miller |first2=Nicholas R. |date=2015-12-18 |publisher=Edward Elgar Publishing |isbn=9781783470730 |language=en |quote=A spoiler effect occurs when a single party or a candidate entering an election changes the outcome to favor a different candidate.}}</ref><ref name=":4">{{Cite web |title=The Spoiler Effect |url=https://electionscience.org/library/the-spoiler-effect/ |access-date=2024-03-03 |website=The Center for Election Science |language=en-US}}</ref> Voting rules that are not affected by spoilers are said to be '''spoilerproof'''.<ref name=":04">{{Cite journal |last=Miller |first=Nicholas R. |date=2019-04-01 |title=Reflections on Arrow's theorem and voting rules |url=https://doi.org/10.1007/s11127-018-0524-6 |journal=Public Choice |language=en |volume=179 |issue=1 |pages=113–124 |doi=10.1007/s11127-018-0524-6 |issn=1573-7101 |hdl-access=free |hdl=11603/20937}}</ref>'''<ref name=":7">{{cite arXiv |eprint=2403.03228 |last1=McCune |first1=David |last2=Wilson |first2=Jennifer |title=Multiwinner Elections and the Spoiler Effect |date=2024 |class=stat.ME }}</ref>'''
In [[social choice theory]] and [[politics]], a '''spoiler effect''' happens when a losing candidate affects the results of an election simply by participating.<ref name=":3">{{Cite book |last1=Heckelman |first1=Jac C. |url=https://books.google.com/books?id=KrckCwAAQBAJ |title=Handbook of Social Choice and Voting |last2=Miller |first2=Nicholas R. |date=2015-12-18 |publisher=Edward Elgar Publishing |isbn=9781783470730 |language=en |quote=A spoiler effect occurs when a single party or a candidate entering an election changes the outcome to favor a different candidate.}}</ref> Voting rules that are not affected by spoilers are said to be '''spoilerproof'''<ref name=":04">{{Cite journal |last=Miller |first=Nicholas R. |date=2019-04-01 |title=Reflections on Arrow's theorem and voting rules |url=https://doi.org/10.1007/s11127-018-0524-6 |journal=Public Choice |language=en |volume=179 |issue=1 |pages=113–124 |doi=10.1007/s11127-018-0524-6 |issn=1573-7101 |hdl-access=free |hdl=11603/20937|url-access=subscription }}</ref>'''<ref name=":7">{{Citation |last1=McCune |first1=David |title=Multiwinner Elections and the Spoiler Effect |date=2024-03-03 |arxiv=2403.03228 |last2=Wilson |first2=Jennifer}}</ref>''' and satisfy [[independence of irrelevant alternatives]].<ref name=":3" /><ref name=":7" /><ref name="McCune">{{Cite journal |last1=McCune |first1=David |last2=Wilson |first2=Jennifer |date=July 2023 |title=Ranked-choice voting and the spoiler effect |url=https://link.springer.com/10.1007/s11127-023-01050-3 |journal=Public Choice |language=en |volume=196 |issue=1–2 |pages=19–50 |doi=10.1007/s11127-023-01050-3 |issn=0048-5829|url-access=subscription }}</ref>


The frequency and severity of spoiler effects depends substantially on the voting method. [[Instant-runoff voting]] (IRV), the [[two-round system]] (TRS), and especially [[First-past-the-post voting|first-past-the-post]] (FPP) without [[Partisan primary|winnowing or primary elections]]<ref>{{Cite journal |last1=Borodin |first1=Allan |last2=Lev |first2=Omer |last3=Shah |first3=Nisarg |last4=Strangway |first4=Tyrone |date=2024-04-01 |title=Primarily about primaries |url=https://www.sciencedirect.com/science/article/abs/pii/S0004370224000316 |journal=Artificial Intelligence |volume=329 |pages=104095 |doi=10.1016/j.artint.2024.104095 |issn=0004-3702|url-access=subscription }}</ref> are highly sensitive to spoilers (though IRV and TRS less so in some circumstances), and all three rules are affected by [[Center squeeze|center-squeeze]] and vote splitting.<ref name="Poundstone, William.-201323">{{Cite book |last=Poundstone, William. |title=Gaming the vote : why elections aren't fair (and what we can do about it) |date=2013 |publisher=Farrar, Straus and Giroux |isbn=9781429957649 |pages=168, 197, 234 |oclc=872601019 |quote=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}}</ref><ref name="Merril 19852222">{{Cite journal |last=Merrill |first=Samuel |date=1985 |title=A statistical model for Condorcet efficiency based on simulation under spatial model assumptions |url=http://dx.doi.org/10.1007/bf00127534 |journal=Public Choice |volume=47 |issue=2 |pages=389–403 |doi=10.1007/bf00127534 |issn=0048-5829 |quote=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 |via=|url-access=subscription }}</ref><ref>{{Cite journal |last1=McGann |first1=Anthony J. |last2=Koetzle |first2=William |last3=Grofman |first3=Bernard |date=2002 |title=How an Ideologically Concentrated Minority Can Trump a Dispersed Majority: Nonmedian Voter Results for Plurality, Run-off, and Sequential Elimination Elections |url=https://www.jstor.org/stable/3088418 |journal=American Journal of Political Science |volume=46 |issue=1 |pages=134–147 |doi=10.2307/3088418 |jstor=3088418 |issn=0092-5853 |quote="As with simple plurality elections, it is apparent the outcome will be highly sensitive to the distribution of candidates."|url-access=subscription }}</ref><ref name="Borgers223">{{Cite book |last=Borgers |first=Christoph |url=https://books.google.com/books?id=u_XMHD4shnQC |title=Mathematics of Social Choice: Voting, Compensation, and Division |date=2010-01-01 |publisher=SIAM |isbn=9780898716955 |quote=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}}</ref> [[Condorcet method|Majority-rule (or Condorcet) methods]] are only rarely affected by spoilers, which are limited to rare<ref name=":53322">{{Cite journal |last=Gehrlein |first=William V. |date=2002-03-01 |title=Condorcet's paradox and the likelihood of its occurrence: different perspectives on balanced preferences* |url=https://doi.org/10.1023/A:1015551010381 |journal=Theory and Decision |language=en |volume=52 |issue=2 |pages=171–199 |doi=10.1023/A:1015551010381 |issn=1573-7187|url-access=subscription }}</ref><ref name=":63322">{{Cite journal |last=Van Deemen |first=Adrian |date=2014-03-01 |title=On the empirical relevance of Condorcet's paradox |url=https://doi.org/10.1007/s11127-013-0133-3 |journal=Public Choice |language=en |volume=158 |issue=3 |pages=311–330 |doi=10.1007/s11127-013-0133-3 |issn=1573-7101|url-access=subscription }}</ref> situations called [[Condorcet paradox|cyclic ties]].<ref name=":53322"/><ref name=":63322"/><ref name="Holliday3">{{Citation |last1=Holliday |first1=Wesley H. |title=Stable Voting |date=2023-02-11 |arxiv=2108.00542 |last2=Pacuit |first2=Eric}}. "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."</ref> [[Rated voting|Rated voting systems]] are not subject to [[Arrow's impossibility theorem|Arrow's theorem]]. Whether such methods are spoilerproof depends on the nature of the rating scales the voters use to express their opinions.<ref name="x031">{{cite web | last=Morreau | first=Michael | title=Arrow's Theorem | website=Stanford Encyclopedia of Philosophy | date=2014-10-13 | url=https://plato.stanford.edu/entries/arrows-theorem/#ConAga | access-date=2024-10-09 | quote=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. }}</ref><ref name=":04"/><ref name="Poundstone, William.-201323"/><ref name=":02">{{cite news |date=2015-05-20 |title=The Spoiler Effect |url=https://electology.org/spoiler-effect |access-date=2017-01-29 |newspaper=[[The Center for Election Science]] |language=en}}</ref>
The frequency and severity of spoiler effects depends substantially on the voting method. [[First-past-the-post voting]] without [[Partisan primary|winnowing or primary elections]]{{citation needed|date=July 2025}} is sensitive to spoilers. And so, to a degree, are [[Instant-runoff voting|Instant-runoff or ranked-choice voting (RCV)]] and the [[Two-round system|two-round system (TRS)]].<ref name="McCune" /><ref name="Merril 19852222">{{Cite journal |last=Merrill |first=Samuel |date=1985 |title=A statistical model for Condorcet efficiency based on simulation under spatial model assumptions |url=http://dx.doi.org/10.1007/bf00127534 |journal=Public Choice |volume=47 |issue=2 |pages=389–403 |doi=10.1007/bf00127534 |issn=0048-5829 |quote=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 |via=|url-access=subscription }}</ref><ref>{{Cite journal |last1=McGann |first1=Anthony J. |last2=Koetzle |first2=William |last3=Grofman |first3=Bernard |date=2002 |title=How an Ideologically Concentrated Minority Can Trump a Dispersed Majority: Nonmedian Voter Results for Plurality, Run-off, and Sequential Elimination Elections |url=https://www.jstor.org/stable/3088418 |journal=American Journal of Political Science |volume=46 |issue=1 |pages=134–147 |doi=10.2307/3088418 |jstor=3088418 |issn=0092-5853 |quote="As with simple plurality elections, it is apparent the outcome will be highly sensitive to the distribution of candidates."|url-access=subscription }}</ref><ref name="Borgers223">{{Cite book |last=Borgers |first=Christoph |url=https://books.google.com/books?id=u_XMHD4shnQC |title=Mathematics of Social Choice: Voting, Compensation, and Division |date=2010-01-01 |publisher=SIAM |isbn=9780898716955 |quote=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}}</ref> [[Condorcet method|Majority-rule (or Condorcet) methods]] are only rarely affected by spoilers, which are limited to rare<ref name=":53322">{{Cite journal |last=Gehrlein |first=William V. |date=2002-03-01 |title=Condorcet's paradox and the likelihood of its occurrence: different perspectives on balanced preferences* |url=https://doi.org/10.1023/A:1015551010381 |journal=Theory and Decision |language=en |volume=52 |issue=2 |pages=171–199 |doi=10.1023/A:1015551010381 |issn=1573-7187|url-access=subscription }}</ref><ref name=":63322">{{Cite journal |last=Van Deemen |first=Adrian |date=2014-03-01 |title=On the empirical relevance of Condorcet's paradox |url=https://doi.org/10.1007/s11127-013-0133-3 |journal=Public Choice |language=en |volume=158 |issue=3 |pages=311–330 |doi=10.1007/s11127-013-0133-3 |issn=1573-7101|url-access=subscription }}</ref> situations called [[Condorcet paradox|cyclic ties]].<ref name=":53322"/><ref name=":63322"/><ref name="Holliday3">{{Citation |last1=Holliday |first1=Wesley H. |title=Stable Voting |date=2023-02-11 |arxiv=2108.00542 |last2=Pacuit |first2=Eric}}. "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."</ref> [[Rated voting|Rated voting systems]] are not subject to [[Arrow's impossibility theorem|Arrow's theorem]], allowing them to be spoilerproof so long as voters' ratings are consistent across elections.<ref name=":04"/><ref name=":02">{{cite news |date=2015-05-20 |title=The Spoiler Effect |url=https://electology.org/spoiler-effect |access-date=2017-01-29 |newspaper=[[The Center for Election Science]] |language=en}}</ref><ref name="Poundstone, William.-201323">{{Cite book |last=Poundstone, William. |title=Gaming the vote : why elections aren't fair (and what we can do about it) |date=2013 |publisher=Farrar, Straus and Giroux |isbn=9781429957649 |pages=168, 197, 234 |oclc=872601019 |quote=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}}</ref><ref name="x031">{{cite web | last=Morreau | first=Michael | title=Arrow's Theorem | website=Stanford Encyclopedia of Philosophy | date=2014-10-13 | url=https://plato.stanford.edu/entries/arrows-theorem/#ConAga | access-date=2024-10-09 | quote=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. }}</ref>


Spoiler effects can also occur in some methods of [[proportional representation]], such as the [[Single transferable vote|single transferable vote (STV or RCV-PR)]] and the [[largest remainders method]] of party-list representation, where it is called a [[New states paradox|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.'''<ref name=":03">{{cite book |last1=Balinski |first1=Michel L. |url=https://archive.org/details/fairrepresentati00bali |title=Fair Representation: Meeting the Ideal of One Man, One Vote |last2=Young |first2=H. Peyton |publisher=Yale University Press |year=2001 |isbn=0-300-02724-9 |location=New Haven |url-access=registration |orig-date=1982}}</ref>''' This kind of spoiler effect is avoided by [[divisor method]]s and [[Proportional approval voting|proportional approval]].'''<ref name=":03" />{{Rp|Thm.8.3}}'''
Spoiler effects can also occur in some methods of [[proportional representation]], such as the [[Single transferable vote|single transferable vote (STV or RCV-PR)]] and the [[largest remainders method]] of party-list representation, where it is called the [[Apportionment paradox#New states paradox|new states 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.'''<ref name=":03">{{cite book |last1=Balinski |first1=Michel L. |url=https://archive.org/details/fairrepresentati00bali |title=Fair Representation: Meeting the Ideal of One Man, One Vote |last2=Young |first2=H. Peyton |publisher=Yale University Press |year=2001 |isbn=0-300-02724-9 |location=New Haven |url-access=registration |orig-date=1982}}</ref>''' This kind of spoiler effect is avoided by [[divisor method]]s and [[Proportional approval voting|proportional approval]].'''<ref name=":03" />{{Rp|Thm.8.3}}'''


== Motivation ==
== Motivation ==
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{{anchor|Strategic nomination|Manipulation}}
{{anchor|Strategic nomination|Manipulation}}
=== Manipulation by politicians ===
=== Manipulation by politicians ===
Voting systems that violate independence of irrelevant alternatives are susceptible to being manipulated by ''strategic nomination''. Such systems may produce an ''incentive to entry'', increasing a candidate's chances of winning if similar candidates join the race, or an ''incentive to exit'', reducing the candidate's chances of winning.
Voting systems that violate independence of irrelevant alternatives are susceptible to being manipulated by ''strategic nomination''. Such systems may produce an ''incentive to entry'', increasing a candidate's chances of winning if similar candidates join the race, or an ''incentive to exit'', reducing the candidate's chances of winning.
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|-
|-
|[[Score voting|Score]] or [[Highest median voting rules|Medians]]
|[[Score voting|Score]] or [[Highest median voting rules|Medians]]
|Depends
|None
|}
|}


Different [[electoral system]]s have different levels of vulnerability to spoilers. In general, spoilers are common with [[plurality voting]], somewhat common in [[Instant-runoff voting|plurality-runoff methods]], rare with [[Condorcet method|majoritarian methods]], and with a varying level of spoiler vulnerability with most [[rated voting|rated voting methods]].{{Notetag|Strategic voting can sometimes create additional spoiler-like behavior. However, this does not substantially affect the general order described here.}}
Different [[electoral system]]s have different levels of vulnerability to spoilers. In general, spoilers are common with [[plurality voting]], somewhat common in [[Instant-runoff voting|plurality-runoff methods]], rare with [[Condorcet method|majoritarian methods]], and impossible for most [[rated voting|rated voting methods]].{{Notetag|Strategic voting can sometimes create additional spoiler-like behavior. However, this does not substantially affect the general order described here.}}


=== First-preference plurality ===
=== First-preference plurality ===
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=== Tournament (Condorcet) voting ===
=== Tournament (Condorcet) voting ===
Spoiler effects rarely occur when using [[tournament solution]]s, where candidates are compared in one-on-one matchups to determine relative preference. For each pair of candidates, there is a count for how many voters prefer the first candidate in the pair to the second candidate. The resulting table of pairwise counts eliminates the step-by-step redistribution of votes, which is usually the cause for spoilers in other methods.<ref name="Holliday3"/> This pairwise comparison means that spoilers can only occur when there is a [[Condorcet cycle]], where there is no single candidate preferred to all others.<ref name="Holliday3"/><ref name=":53"/><ref name=":63"/>
Spoiler effects rarely occur when using [[tournament solution]]s, where candidates are compared in one-on-one matchups to determine relative preference. For each pair of candidates, there is a count for how many voters prefer the first candidate in the pair to the second candidate The resulting table of pairwise counts eliminates the step-by-step redistribution of votes, which is usually the cause for spoilers in other methods.<ref name="Holliday3"/> This pairwise comparison means that spoilers can only occur when there is a [[Condorcet cycle]], where there is no single candidate preferred to all others.<ref name="Holliday3"/><ref name=":53"/><ref name=":63"/>


Theoretical models suggest that somewhere between 90% and 99% of real-world elections have a Condorcet winner,<ref name=":53">{{Cite journal |last=Gehrlein |first=William V. |date=2002-03-01 |title=Condorcet's paradox and the likelihood of its occurrence: different perspectives on balanced preferences* |url=https://doi.org/10.1023/A:1015551010381 |journal=[[Theory and Decision]] |language=en |volume=52 |issue=2 |pages=171–199 |doi=10.1023/A:1015551010381 |issn=1573-7187|url-access=subscription }}</ref><ref name=":63">{{Cite journal |last=Van Deemen |first=Adrian |date=2014-03-01 |title=On the empirical relevance of Condorcet's paradox |url=https://doi.org/10.1007/s11127-013-0133-3 |journal=[[Public Choice (journal)|Public Choice]] |language=en |volume=158 |issue=3 |pages=311–330 |doi=10.1007/s11127-013-0133-3 |issn=1573-7101|url-access=subscription }}</ref> and the first Condorcet cycle in a ranked American election was found in 2021.<ref name="s192">{{cite journal | last1=McCune | first1=David | last2=McCune | first2=Lori | title=The Curious Case of the 2021 Minneapolis Ward 2 City Council Election | journal=The College Mathematics Journal | date=2023-05-24 | issn=0746-8342 | doi=10.1080/07468342.2023.2212548 | pages=1–5 |arxiv=2111.09846 |quote=The 2021 Minneapolis election for city council seat in Ward 2 contained three candidates, each of whom has a legitimate claim to be the winner, the first known example of an American political election without a Condorcet winner ...}}</ref> Some systems like the [[Schulze method]] and [[ranked pairs]] have stronger spoiler resistance guarantees that limit which candidates can spoil an election without a [[Condorcet winner]].<ref name="Schulze">{{cite arXiv | last=Schulze | first=Markus | title=The Schulze Method of Voting | eprint=1804.02973 | class=cs.GT| date=2018-03-15 |quote="The Smith criterion and Smith-IIA (where IIA means “independence of irrelevant alternatives”) say that weak alternatives should have no impact on the result of the elections ... the Schulze method, as defined in section 2.2, satisfies Smith-IIA."}}</ref>{{rp|228–229}}
Theoretical models suggest that somewhere between 90% and 99% of real-world elections have a Condorcet winner,<ref name=":53">{{Cite journal |last=Gehrlein |first=William V. |date=2002-03-01 |title=Condorcet's paradox and the likelihood of its occurrence: different perspectives on balanced preferences* |url=https://doi.org/10.1023/A:1015551010381 |journal=[[Theory and Decision]] |language=en |volume=52 |issue=2 |pages=171–199 |doi=10.1023/A:1015551010381 |issn=1573-7187|url-access=subscription }}</ref><ref name=":63">{{Cite journal |last=Van Deemen |first=Adrian |date=2014-03-01 |title=On the empirical relevance of Condorcet's paradox |url=https://doi.org/10.1007/s11127-013-0133-3 |journal=[[Public Choice (journal)|Public Choice]] |language=en |volume=158 |issue=3 |pages=311–330 |doi=10.1007/s11127-013-0133-3 |issn=1573-7101|url-access=subscription }}</ref> and the first Condorcet cycle in a ranked American election was found in 2021.<ref name="s192">{{cite journal | last1=McCune | first1=David | last2=McCune | first2=Lori | title=The Curious Case of the 2021 Minneapolis Ward 2 City Council Election | journal=The College Mathematics Journal | date=2023-05-24 | issn=0746-8342 | doi=10.1080/07468342.2023.2212548 | pages=1–5 |arxiv=2111.09846 |quote=The 2021 Minneapolis election for city council seat in Ward 2 contained three candidates, each of whom has a legitimate claim to be the winner, the first known example of an American political election without a Condorcet winner ...}}</ref> Some systems like the [[Schulze method]] and [[ranked pairs]] have stronger spoiler resistance guarantees that limit which candidates can spoil an election without a [[Condorcet winner]].<ref name="Schulze">{{cite arXiv | last=Schulze | first=Markus | title=The Schulze Method of Voting | eprint=1804.02973 | class=cs.GT| date=2018-03-15 |quote="The Smith criterion and Smith-IIA (where IIA means “independence of irrelevant alternatives”) say that weak alternatives should have no impact on the result of the elections ... the Schulze method, as defined in section 2.2, satisfies Smith-IIA."}}</ref>{{rp|228–229}}
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Rated voting methods ask voters to assign each candidate a score on a scale (e.g. rating them from 0 to 10), instead of listing them from first to last. [[Highest median voting rules|Highest median]] and [[score voting|score (highest mean) voting]] are the two most prominent examples of rated voting rules. Whenever voters rate candidates independently, the rating given to one candidate does not affect the ratings given to the other candidates. Any new candidate cannot change the winner of the race without becoming the winner themselves, which would disqualify them from the definition of a spoiler. For this to hold, in some elections, some voters must use less than their full voting power despite having meaningful preferences among viable candidates.
Rated voting methods ask voters to assign each candidate a score on a scale (e.g. rating them from 0 to 10), instead of listing them from first to last. [[Highest median voting rules|Highest median]] and [[score voting|score (highest mean) voting]] are the two most prominent examples of rated voting rules. Whenever voters rate candidates independently, the rating given to one candidate does not affect the ratings given to the other candidates. Any new candidate cannot change the winner of the race without becoming the winner themselves, which would disqualify them from the definition of a spoiler. For this to hold, in some elections, some voters must use less than their full voting power despite having meaningful preferences among viable candidates.


The outcome of rated voting depends on the scale used by the voter or assumed by the mechanism.<ref name="w444">{{cite journal | last=Roberts | first=Kevin W. S. | title=Interpersonal Comparability and Social Choice Theory | journal=The Review of Economic Studies | publisher=[Oxford University Press, Review of Economic Studies, Ltd.] | volume=47 | issue=2 | year=1980 | issn=0034-6527 | jstor=2297002 | pages=421–439 | doi=10.2307/2297002 | url=http://www.jstor.org/stable/2297002 | access-date=2024-09-25 |quote=If f satisfies U, I, P, and CNC then there exists a dictator.| url-access=subscription }}</ref> If the voters use relative scales, i.e. scales that depend on what candidates are running, then the outcome can change if candidates who don't win drop out.<ref name="ArrowC">{{cite book | last=Arrow | first=Kenneth J. | title=Social Choice and Individual Values | publisher=Yale University Press | year=2012 | isbn=978-0-300-17931-6 | jstor=j.ctt1nqb90 | url=http://www.jstor.org/stable/j.ctt1nqb90 | access-date=2024-09-25 | pages=10–11 |quote=At best, it is contended that, for an individual, his utility function is uniquely determined up to a linear transformation ... the value of the aggregate (say a sum) are dependent on how the choice is made for each individual.}}</ref> Empirical results from panel data suggest that judgments are at least in part relative.<ref name="Stadt Kapteyn Geer 1985 pp. 179–187">{{cite journal | last1=Stadt | first1=Huib van de | last2=Kapteyn | first2=Arie | last3=Geer | first3=Sara van de | title=The Relativity of Utility: Evidence from Panel Data | journal=The Review of Economics and Statistics | publisher=The MIT Press | volume=67 | issue=2 | year=1985 | issn=0034-6535 | jstor=1924716 | pages=179–187 | doi=10.2307/1924716 | url=http://www.jstor.org/stable/1924716 | access-date=2024-04-28}}</ref><ref>{{cite journal |last1=Richard H. |last2=Diener |first2=Ed |last3=Wedell |first3=Douglas H. |title=Intrapersonal and Social Comparison Determinants of Happiness: A Range-Frequency Analysis |journal=Journal of Personality and Social Psychology |date=1989 |volume=56 |issue=3 |pages=317–325 |doi=10.1037/0022-3514.56.3.317 |pmid=2926632 |url=https://psycnet.apa.org/record/1989-18931-001|url-access=subscription }}</ref> Thus, rated methods, as used in practice, may exhibit a spoiler effect caused by the interaction between the voters and the system, even if the system itself passes IIA given an absolute scale.
The outcome of rated voting depends on the scale used by the voter or assumed by the mechanism.<ref name="w444">{{cite journal | last=Roberts | first=Kevin W. S. | title=Interpersonal Comparability and Social Choice Theory | journal=The Review of Economic Studies | publisher=[Oxford University Press, Review of Economic Studies, Ltd.] | volume=47 | issue=2 | year=1980 | issn=0034-6527 | jstor=2297002 | pages=421–439 | doi=10.2307/2297002 | url=http://www.jstor.org/stable/2297002 | access-date=2024-09-25 |quote=If f satisfies U, I, P, and CNC then there exists a dictator.}}</ref> If the voters use relative scales, i.e. scales that depend on what candidates are running, then the outcome can change if candidates who don't win drop out.<ref name="ArrowC">{{cite book | last=Arrow | first=Kenneth J. | title=Social Choice and Individual Values | publisher=Yale University Press | year=2012 | isbn=978-0-300-17931-6 | jstor=j.ctt1nqb90 | url=http://www.jstor.org/stable/j.ctt1nqb90 | access-date=2024-09-25 | pages=10–11 |quote=At best, it is contended that, for an individual, his utility function is uniquely determined up to a linear transformation ... the value of the aggregate (say a sum) are dependent on how the choice is made for each individual.}}</ref> Empirical results from panel data suggest that judgments are at least in part relative.<ref name="Stadt Kapteyn Geer 1985 pp. 179–187">{{cite journal | last1=Stadt | first1=Huib van de | last2=Kapteyn | first2=Arie | last3=Geer | first3=Sara van de | title=The Relativity of Utility: Evidence from Panel Data | journal=The Review of Economics and Statistics | publisher=The MIT Press | volume=67 | issue=2 | year=1985 | issn=0034-6535 | jstor=1924716 | pages=179–187 | doi=10.2307/1924716 | url=http://www.jstor.org/stable/1924716 | access-date=2024-04-28| url-access=subscription }}</ref><ref>{{cite journal |last1=Richard H. |last2=Diener |first2=Ed |last3=Wedell |first3=Douglas H. |title=Intrapersonal and Social Comparison Determinants of Happiness: A Range-Frequency Analysis |journal=Journal of Personality and Social Psychology |date=1989 |volume=56 |issue=3 |pages=317–325 |doi=10.1037/0022-3514.56.3.317 |pmid=2926632 |url=https://psycnet.apa.org/record/1989-18931-001}}</ref> Thus, rated methods, as used in practice, may exhibit a spoiler effect caused by the interaction between the voters and the system, even if the system itself passes IIA given an absolute scale.


=== Proportional representation ===
=== Proportional representation ===
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=== United States ===
=== United States ===
{{See also|Electoral fusion in the United States}}A spoiler campaign in the United States is often one that cannot realistically win but can still determine the outcome by pulling support from a more competitive candidate.<ref name=":1">{{Cite web |date=April 18, 2024 |title=The Spoiled Election: Independents and the 2024 Election |url=https://harvardpolitics.com/the-spoiled-election-independents-and-the-2024-election/ |access-date=2024-08-24 |website=[[Harvard Political Review]] |quote=Perot was running what is commonly referred to as a “spoiler campaign,” a campaign that cannot win the election but still impacts its outcome.}}</ref> The two major parties in the United States, the [[Republican Party (United States)|Republican Party]] and [[Democratic Party (United States)|Democratic Party]], have regularly won 98% of all state and federal seats.<ref name="Masket">{{Cite journal |last=Masket |first=Seth |date=Fall 2023 |title=Giving Minor Parties a Chance |url=https://democracyjournal.org/magazine/70/giving-minor-parties-a-chance/ |journal=[[Democracy (journal)|Democracy]] |volume=70}}</ref> The US presidential elections most consistently cited as having been spoiled by third-party candidates are [[1844 United States presidential election|1844]]<ref name=":5">{{Cite book |last=Green |first=Donald J. |title=Third-party matters: politics, presidents, and third parties in American history |date=2010 |publisher=Praeger |isbn=978-0-313-36591-1 |location=Santa Barbara, Calif |pages=153–154}}</ref> and [[2000 United States presidential election|2000]].<ref name=":10">{{Cite journal |last=Burden |first=Barry C. |date=September 2005 |title=Ralph Nader's Campaign Strategy in the 2000 U.S. Presidential Election |url=http://dx.doi.org/10.1177/1532673x04272431 |journal=[[American Politics Research]] |volume=33 |issue=5 |pages=672–699 |doi=10.1177/1532673x04272431 |issn=1532-673X |s2cid=43919948|url-access=subscription }}</ref><ref name="spoiler-myth-ucla">{{Cite journal |last1=Herron |first1=Michael C. |last2=Lewis |first2=Jeffrey B. |date=April 24, 2006 |title=Did Ralph Nader spoil Al Gore's Presidential bid? A ballot-level study of Green and Reform Party voters in the 2000 Presidential election |journal=[[Quarterly Journal of Political Science]] |publisher=Now Publishing Inc. |volume=2 |issue=3 |pages=205–226 |doi=10.1561/100.00005039}} [https://wayback.archive-it.org/all/20080216081328/http://www.sscnet.ucla.edu/polisci/faculty/lewis/pdf/greenreform9.pdf Pdf.]</ref><ref name=":6">{{cite news |last=Roberts |first=Joel |date=July 27, 2004 |title=Nader to crash Dems' party? |url=http://www.cbsnews.com/news/nader-to-crash-dems-party/ |work=[[CBS News]]}}</ref><ref name=":5" /> The [[2016 United States presidential election|2016]] election is more disputed as to whether it contained spoiler candidates or not.<ref name=":9">{{Cite journal |last1=Devine |first1=Christopher J. |last2=Kopko |first2=Kyle C. |date=2021-09-01 |title=Did Gary Johnson and Jill Stein Cost Hillary Clinton the Presidency? A Counterfactual Analysis of Minor Party Voting in the 2016 US Presidential Election |url=https://www.degruyter.com/document/doi/10.1515/for-2021-0011/html?lang=en |journal=The Forum |language=en |volume=19 |issue=2 |pages=173–201 |doi=10.1515/for-2021-0011 |issn=1540-8884 |s2cid=237457376 |quote=The perception that Johnson and Stein 'stole' the 2016 presidential election from Clinton is widespread...Our analysis indicates that Johnson and Stein did not deprive Clinton of an Electoral College majority, nor Trump the legitimacy of winning the national popular vote.|url-access=subscription }}</ref><ref name="Haberman">{{Cite news |last1=Haberman |first1=Maggie |author-link=Maggie Haberman |last2=Hakim |first2=Danny |author-link2=Danny Hakim |last3=Corasaniti |first3=Nick |date=2020-09-22 |title=How Republicans Are Trying to Use the Green Party to Their Advantage |url=https://www.nytimes.com/2020/09/22/us/politics/green-party-republicans-hawkins.html?searchResultPosition=1 |access-date=2024-08-28 |work=The New York Times |language=en-US |issn=0362-4331 |quote=Four years ago, the Green Party candidate played a significant role in several crucial battleground states, drawing a vote total in three of them — Wisconsin, Michigan and Pennsylvania — that exceeded the margin between Donald J. Trump and Hillary Clinton.}}</ref><ref name=":22">{{Cite web |last=Schreckinger |first=Ben |date=2017-06-20 |title=Jill Stein Isn't Sorry |url=https://www.politico.com/magazine/story/2017/06/20/jill-stein-green-party-no-regrets-2016-215281 |access-date=2023-06-07 |website=POLITICO Magazine |language=en}}</ref> For the [[2024 United States presidential election|2024 presidential election]], Republican lawyers and operatives have fought to keep right-leaning third-parties like the [[Constitution Party (United States)|Constitution Party]] off swing state ballots<ref>{{Cite web |last=Levy |first=Marc |date=2024-08-21 |title=Democrats get a third-party hopeful knocked off Pennsylvania ballot, as Cornel West tries to get on |url=https://apnews.com/article/pennsylvania-ballot-2024-west-kennedy-cc5507101bcd198028b04945d2d03aa3 |access-date=2024-08-28 |website=AP News |language=en |quote=Republicans and Democrats view third-party candidates as a threat to siphon critical support from their nominees, especially considering that Pennsylvania was decided by margins of tens of thousands of votes both in 2020 for Democrat Joe Biden and in 2016 for Trump.}}</ref> while working to get [[Cornel West]] on battleground ballots.<ref name=":12">{{Cite web |last=Slodysko |first=Brian |date=2024-07-16 |title=Kennedy and West third-party ballot drives are pushed by secretive groups and Republican donors |url=https://apnews.com/article/kennedy-west-third-party-2024-election-10c4c166ad4d41cab73660c33a69a58a |access-date=2024-08-25 |website=AP News |language=en |quote=there are signs across the country that groups are trying to affect the outcome by using deceptive means — and in most cases in ways that would benefit Republican Donald Trump. Their aim is to whittle away President Joe Biden’s standing with the Democratic Party’s base by offering left-leaning, third-party alternatives who could siphon off a few thousand protest votes in close swing state contests.}}</ref> Democrats have helped some right-leaning third-parties gain ballot access while challenging ballot access of left-leaning third-parties like the [[Green Party of the United States|Green Party]].<ref name=":132">{{Cite news |last=Schleifer |first=Theodore |date=2024-08-29 |title=To Beat Trump, Democrats Seek to Help Anti-Abortion Candidate |url=https://www.nytimes.com/2024/08/29/us/politics/trump-terry-anti-abortion.html |access-date=2024-08-30 |work=The New York Times |language=en-US |issn=0362-4331}}</ref> [[Barry Burden]] argues that they have almost no chance of winning the 2024 election but are often motivated by particular issues.<ref>{{Cite web |last=Burden |first=Barry C. |date=2024-04-30 |title=Third parties will affect the 2024 campaigns, but election laws written by Democrats and Republicans will prevent them from winning |url=https://theconversation.com/third-parties-will-affect-the-2024-campaigns-but-election-laws-written-by-democrats-and-republicans-will-prevent-them-from-winning-226877 |access-date=2024-08-28 |website=The Conversation |language=en-US}}</ref>
{{See also|Electoral fusion in the United States}}A spoiler campaign in the United States is often one that cannot realistically win but can still determine the outcome by pulling support from a more competitive candidate.<ref name=":1">{{Cite web |date=April 18, 2024 |title=The Spoiled Election: Independents and the 2024 Election |url=https://harvardpolitics.com/the-spoiled-election-independents-and-the-2024-election/ |access-date=2024-08-24 |website=[[Harvard Political Review]] |quote=Perot was running what is commonly referred to as a “spoiler campaign,” a campaign that cannot win the election but still impacts its outcome.}}</ref> The two major parties in the United States, the [[Republican Party (United States)|Republican Party]] and [[Democratic Party (United States)|Democratic Party]], have regularly won 98% of all state and federal seats.<ref name="Masket">{{Cite journal |last=Masket |first=Seth |date=Fall 2023 |title=Giving Minor Parties a Chance |url=https://democracyjournal.org/magazine/70/giving-minor-parties-a-chance/ |journal=[[Democracy (journal)|Democracy]] |volume=70}}</ref> The US presidential elections most consistently cited as having been spoiled by third-party candidates are [[1844 United States presidential election|1844]]<ref name=":5">{{Cite book |last=Green |first=Donald J. |title=Third-party matters: politics, presidents, and third parties in American history |date=2010 |publisher=Praeger |isbn=978-0-313-36591-1 |location=Santa Barbara, Calif |pages=153–154}}</ref> and [[2000 United States presidential election|2000]].<ref name=":10">{{Cite journal |last=Burden |first=Barry C. |date=September 2005 |title=Ralph Nader's Campaign Strategy in the 2000 U.S. Presidential Election |url=http://dx.doi.org/10.1177/1532673x04272431 |journal=[[American Politics Research]] |volume=33 |issue=5 |pages=672–699 |doi=10.1177/1532673x04272431 |issn=1532-673X |s2cid=43919948|url-access=subscription }}</ref><ref name="spoiler-myth-ucla">{{Cite journal |last1=Herron |first1=Michael C. |last2=Lewis |first2=Jeffrey B. |date=April 24, 2006 |title=Did Ralph Nader spoil Al Gore's Presidential bid? A ballot-level study of Green and Reform Party voters in the 2000 Presidential election |journal=[[Quarterly Journal of Political Science]] |publisher=Now Publishing Inc. |volume=2 |issue=3 |pages=205–226 |doi=10.1561/100.00005039}} [https://wayback.archive-it.org/all/20080216081328/http://www.sscnet.ucla.edu/polisci/faculty/lewis/pdf/greenreform9.pdf Pdf.]</ref><ref name=":6">{{cite news |last=Roberts |first=Joel |date=July 27, 2004 |title=Nader to crash Dems' party? |url=http://www.cbsnews.com/news/nader-to-crash-dems-party/ |work=[[CBS News]]}}</ref><ref name=":5" /> The [[2016 United States presidential election|2016]] election is more disputed as to whether it contained spoiler candidates or not.<ref name=":9">{{Cite journal |last1=Devine |first1=Christopher J. |last2=Kopko |first2=Kyle C. |date=2021-09-01 |title=Did Gary Johnson and Jill Stein Cost Hillary Clinton the Presidency? A Counterfactual Analysis of Minor Party Voting in the 2016 US Presidential Election |url=https://www.degruyter.com/document/doi/10.1515/for-2021-0011/html?lang=en |journal=The Forum |language=en |volume=19 |issue=2 |pages=173–201 |doi=10.1515/for-2021-0011 |issn=1540-8884 |s2cid=237457376 |quote=The perception that Johnson and Stein 'stole' the 2016 presidential election from Clinton is widespread...Our analysis indicates that Johnson and Stein did not deprive Clinton of an Electoral College majority, nor Trump the legitimacy of winning the national popular vote.|url-access=subscription }}</ref><ref name="Haberman">{{Cite news |last1=Haberman |first1=Maggie |author-link=Maggie Haberman |last2=Hakim |first2=Danny |author-link2=Danny Hakim |last3=Corasaniti |first3=Nick |date=2020-09-22 |title=How Republicans Are Trying to Use the Green Party to Their Advantage |url=https://www.nytimes.com/2020/09/22/us/politics/green-party-republicans-hawkins.html?searchResultPosition=1 |access-date=2024-08-28 |work=The New York Times |language=en-US |issn=0362-4331 |quote=Four years ago, the Green Party candidate played a significant role in several crucial battleground states, drawing a vote total in three of them — Wisconsin, Michigan and Pennsylvania — that exceeded the margin between Donald J. Trump and Hillary Clinton.}}</ref><ref name=":22">{{Cite web |last=Schreckinger |first=Ben |date=2017-06-20 |title=Jill Stein Isn't Sorry |url=https://www.politico.com/magazine/story/2017/06/20/jill-stein-green-party-no-regrets-2016-215281 |access-date=2023-06-07 |website=POLITICO Magazine |language=en}}</ref> For the [[2024 United States presidential election|2024 presidential election]], Republican lawyers and operatives have fought to keep right-leaning third-parties like the [[Constitution Party (United States)|Constitution Party]] off swing state ballots<ref>{{Cite web |last=Levy |first=Marc |date=2024-08-21 |title=Democrats get a third-party hopeful knocked off Pennsylvania ballot, as Cornel West tries to get on |url=https://apnews.com/article/pennsylvania-ballot-2024-west-kennedy-cc5507101bcd198028b04945d2d03aa3 |access-date=2024-08-28 |website=AP News |language=en |quote=Republicans and Democrats view third-party candidates as a threat to siphon critical support from their nominees, especially considering that Pennsylvania was decided by margins of tens of thousands of votes both in 2020 for Democrat Joe Biden and in 2016 for Trump.}}</ref> while working to get [[Cornel West]] on battleground ballots.<ref name=":12">{{Cite web |last=Slodysko |first=Brian |date=2024-07-16 |title=Kennedy and West third-party ballot drives are pushed by secretive groups and Republican donors |url=https://apnews.com/article/kennedy-west-third-party-2024-election-10c4c166ad4d41cab73660c33a69a58a |access-date=2024-08-25 |website=AP News |language=en |quote=there are signs across the country that groups are trying to affect the outcome by using deceptive means — and in most cases in ways that would benefit Republican Donald Trump. Their aim is to whittle away President Joe Biden’s standing with the Democratic Party’s base by offering left-leaning, third-party alternatives who could siphon off a few thousand protest votes in close swing state contests.}}</ref> Democrats have helped some right-leaning third-parties gain ballot access while challenging ballot access of left-leaning third-parties like the [[Green Party of the United States|Green Party]].<ref name=":132">{{Cite news |last=Schleifer |first=Theodore |date=2024-08-29 |title=To Beat Trump, Democrats Seek to Help Anti-Abortion Candidate |url=https://www.nytimes.com/2024/08/29/us/politics/trump-terry-anti-abortion.html |access-date=2024-08-30 |work=The New York Times |language=en-US |issn=0362-4331}}</ref> According to the ''[[Associated Press]]'', the GOP effort to prop up possible spoiler candidates in 2024 appears more far-reaching than the Democratic effort.<ref>{{Cite web |last1=Slodysko |first1=Brian |last2=Merica |first2=Dan |date=2024-09-01 |title=GOP network props up liberal third-party candidates in key states, hoping to siphon off Harris votes |url=https://apnews.com/article/cornel-west-jill-stein-republican-network-harris-4089fb0c9ebb16002e56a1c254a21b0e |access-date=2024-09-06 |website=AP News |language=en}}</ref> [[Barry Burden]] argues that they have almost no chance of winning the 2024 election but are often motivated by particular issues.<ref>{{Cite web |last=Burden |first=Barry C. |date=2024-04-30 |title=Third parties will affect the 2024 campaigns, but election laws written by Democrats and Republicans will prevent them from winning |url=https://theconversation.com/third-parties-will-affect-the-2024-campaigns-but-election-laws-written-by-democrats-and-republicans-will-prevent-them-from-winning-226877 |access-date=2024-08-28 |website=The Conversation |language=en-US}}</ref>


[[Third party (U.S. politics)|Third party]] candidates are always controversial because almost anyone could play spoiler.<ref>{{Cite web |last=Gift |first=Thomas |date=2024-01-11 |title=US election: third party candidates can tip the balance in a tight race – here's why Robert F Kennedy Jr matters |url=https://theconversation.com/us-election-third-party-candidates-can-tip-the-balance-in-a-tight-race-heres-why-robert-f-kennedy-jr-matters-220578 |access-date=2024-08-27 |website=The Conversation |language=en-US}}</ref><ref name="Milligan">{{Cite news |last=Milligan |first=Susan |date=March 22, 2024 |title=The Promise and the Perils of the Third-Party Candidate |url=https://www.usnews.com/news/the-report/articles/2024-03-22/the-promise-and-the-perils-of-the-third-party-candidate |work=US News and World Report |quote=And despite the contenders' claims that the nation deserves an alternative to two unpopular major party choices, the reality, experts say, is that these back-of-the-pack candidates may well cement the election of the candidate they least want in the White House.}}</ref> This is especially true in close elections where the chances of a spoiler effect increase.<ref>{{Cite web |last=Skelley |first=Geoffrey |date=2023-07-13 |title=Why A Third-Party Candidate Might Help Trump — And Spoil The Election For Biden |url=https://fivethirtyeight.com/features/third-party-candidate-spoiler-trump-biden/ |access-date=2024-08-28 |website=FiveThirtyEight |language=en-US}}</ref> [[Strategic voting]], especially prevalent during high stakes elections with high [[Political polarization in the United States|political polarization]], often leads to a third-party that underperforms its poll numbers with voters wanting to make sure their least favorite candidate is not in power.<ref name="Masket" /><ref>{{Cite web |last=Burden |first=Barry C. |author-link=Barry Burden |date=2024-04-30 |title=Third parties will affect the 2024 campaigns, but election laws written by Democrats and Republicans will prevent them from winning |url=https://theconversation.com/third-parties-will-affect-the-2024-campaigns-but-election-laws-written-by-democrats-and-republicans-will-prevent-them-from-winning-226877 |access-date=2024-08-28 |website=The Conversation |language=en-US}}</ref><ref>{{Cite web |last=DeSilver |first=Drew |date=2024-06-27 |title=Third-party and independent candidates for president often fall short of early polling numbers |url=https://www.pewresearch.org/short-reads/2024/06/27/third-party-and-independent-candidates-for-president-often-fall-short-of-early-polling-numbers/ |access-date=2024-08-28 |website=Pew Research Center |language=en-US}}</ref> Third-party campaigns are more likely to result in the candidate a third party voter least wants in the White House.<ref name="Milligan" /> Third-party candidates prefer to focus on their platform than on their impact on the frontrunners.<ref name="Milligan" />
[[Third party (U.S. politics)|Third party]] candidates are always controversial because almost anyone could play spoiler.<ref>{{Cite web |last=Gift |first=Thomas |date=2024-01-11 |title=US election: third party candidates can tip the balance in a tight race – here's why Robert F Kennedy Jr matters |url=https://theconversation.com/us-election-third-party-candidates-can-tip-the-balance-in-a-tight-race-heres-why-robert-f-kennedy-jr-matters-220578 |access-date=2024-08-27 |website=The Conversation |language=en-US}}</ref><ref name="Milligan">{{Cite news |last=Milligan |first=Susan |date=March 22, 2024 |title=The Promise and the Perils of the Third-Party Candidate |url=https://www.usnews.com/news/the-report/articles/2024-03-22/the-promise-and-the-perils-of-the-third-party-candidate |work=US News and World Report |quote=And despite the contenders' claims that the nation deserves an alternative to two unpopular major party choices, the reality, experts say, is that these back-of-the-pack candidates may well cement the election of the candidate they least want in the White House.}}</ref> This is especially true in close elections where the chances of a spoiler effect increase.<ref>{{Cite web |last=Skelley |first=Geoffrey |date=2023-07-13 |title=Why A Third-Party Candidate Might Help Trump — And Spoil The Election For Biden |url=https://fivethirtyeight.com/features/third-party-candidate-spoiler-trump-biden/ |access-date=2024-08-28 |website=FiveThirtyEight |language=en-US}}</ref> [[Strategic voting]], especially prevalent during high stakes elections with high [[Political polarization in the United States|political polarization]], often leads to a third-party that underperforms its poll numbers with voters wanting to make sure their least favorite candidate is not in power.<ref name="Masket" /><ref>{{Cite web |last=Burden |first=Barry C. |author-link=Barry Burden |date=2024-04-30 |title=Third parties will affect the 2024 campaigns, but election laws written by Democrats and Republicans will prevent them from winning |url=https://theconversation.com/third-parties-will-affect-the-2024-campaigns-but-election-laws-written-by-democrats-and-republicans-will-prevent-them-from-winning-226877 |access-date=2024-08-28 |website=The Conversation |language=en-US}}</ref><ref>{{Cite web |last=DeSilver |first=Drew |date=2024-06-27 |title=Third-party and independent candidates for president often fall short of early polling numbers |url=https://www.pewresearch.org/short-reads/2024/06/27/third-party-and-independent-candidates-for-president-often-fall-short-of-early-polling-numbers/ |access-date=2024-08-28 |website=Pew Research Center |language=en-US}}</ref> Third-party campaigns are more likely to result in the candidate a third party voter least wants in the White House.<ref name="Milligan" /> Third-party candidates prefer to focus on their platform than on their impact on the frontrunners.<ref name="Milligan" />
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4061 (Wright)
4061 (Wright)
|[[Copeland score|'''3/4 Wins''']]
|[[Copeland score|'''3/4 Wins''']]
|'''''IRV winner'''''
|'''''RCV winner'''''
|-
|-
![[File:Republican_Disc.svg|60x60px]]
![[File:Republican_Disc.svg|60x60px]]
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| colspan="2" |'''''Spoiler for Montroll'''''
| colspan="2" |'''''Spoiler for Montroll'''''
|-
|-
![[File:Independent Candidate Disc.svg|60x60px]]
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!Dan Smith ([[Independent politician|I]])
!Dan Smith ([[Independent politician|I]])
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Latest revision as of 19:10, 5 November 2025

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

The frequency and severity of spoiler effects depends substantially on the voting method. First-past-the-post voting without winnowing or primary electionsScript error: No such module "Unsubst". is sensitive to spoilers. And so, to a degree, are Instant-runoff or ranked-choice voting (RCV) and the two-round system (TRS).[4][5][6][7] Majority-rule (or Condorcet) methods are only rarely affected by spoilers, which are limited to rare[8][9] situations called cyclic ties.[8][9][10] Rated voting systems are not subject to Arrow's theorem, allowing them to be spoilerproof so long as voters' ratings are consistent across elections.[2][11][12][13]

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 the new states 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.[14] This kind of spoiler effect is avoided by divisor methods and proportional approval.[14]Template:Rp

Motivation

In decision theory, independence of irrelevant alternatives is a fundamental principle of rational choice which says that a decision between two outcomes, A or B, should not depend on the quality of a third, unrelated outcome C. A famous joke by Sidney Morgenbesser illustrates this principle:[15]

A man is deciding whether to order apple, blueberry, or cherry pie before settling on apple. The waitress informs him that the cherry pie is very good and a favorite of most customers. The man replies "in that case, I'll have the blueberry."

Politicians and social choice theorists have long argued for the unfairness of spoiler effects. The mathematician and political economist Nicolas de Condorcet was the first to study the spoiler effect, in the 1780s.[16]

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Manipulation by politicians

Voting systems that violate independence of irrelevant alternatives are susceptible to being manipulated by strategic nomination. Such systems may produce an incentive to entry, increasing a candidate's chances of winning if similar candidates join the race, or an incentive to exit, reducing the candidate's chances of winning.

Some systems are particularly infamous for their ease of manipulation, such as the Borda count, which exhibits a particularly severe entry incentive, letting 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,"[17][18] and eventually led to its abandonment by the French Academy of Sciences.[18]

Other systems exhibit an exit incentive. The vote splitting effect in plurality voting demonstrates this method's strong exit incentive: if multiple candidates with similar views run in an election, their supporters' votes will be diluted, which may cause a unified opposition candidate to win despite having less support. This effect encourages groups of similar candidates to form an organization to make sure they don't step on each other's toes.[19]

By electoral system

Susceptibility to spoilers
Electoral system Spoiler effect
Plurality voting High
Runoffs or RCV Medium
Condorcet methods Low
Score or Medians None

Different electoral systems have different levels of vulnerability to spoilers. In general, spoilers are common with plurality voting, somewhat common in plurality-runoff methods, rare with majoritarian methods, and impossible for most rated voting methods.Template:Notetag

First-preference plurality

In cases where there are many similar candidates, spoiler effects occur most often in first-preference plurality (FPP).Script error: No such module "Unsubst". For example, in the United States, vote splitting is common in primaries, where many similar candidates run against each other. The purpose of a primary election is to eliminate vote splitting among candidates from the same party in the general election by running only one candidate. In a two-party system, party primaries effectively turn FPP into a two-round system.[20][21][22]

Vote splitting is the most common cause of spoiler effects in FPP. In these systems, the presence of many ideologically-similar candidates causes their vote total to be split between them, placing these candidates at a disadvantage.[23][24] This is most visible in elections where a minor candidate draws votes away from a major candidate with similar politics, thereby causing a strong opponent of both to win.[23][25]

Runoff systems

Plurality-runoff methods like the two-round system and RCV still experience vote-splitting in each round. This produces a kind of spoiler effect called a center squeeze. Compared to plurality without primaries, the elimination of weak candidates in earlier rounds reduces their effect on the final results; however, spoiled elections remain common compared to other systems.[24][26][27] As a result, instant-runoff voting still tends towards two-party rule through the process known as Duverger's law.[12][28] A notable example of this can be seen in Alaska's 2024 race, where party elites pressured candidate Nancy Dahlstrom into dropping out to avoid a repeat of the spoiled 2022 election.[29][30][31]

Tournament (Condorcet) voting

Spoiler effects rarely occur when using tournament solutions, where candidates are compared in one-on-one matchups to determine relative preference. For each pair of candidates, there is a count for how many voters prefer the first candidate in the pair to the second candidate The resulting table of pairwise counts eliminates the step-by-step redistribution of votes, which is usually the cause for spoilers in other methods.[10] This pairwise comparison means that spoilers can only occur when there is a Condorcet cycle, where there is no single candidate preferred to all others.[10][32][33]

Theoretical models suggest that somewhere between 90% and 99% of real-world elections have a Condorcet winner,[32][33] and the first Condorcet cycle in a ranked American election was found in 2021.[34] Some systems like the Schulze method and ranked pairs have stronger spoiler resistance guarantees that limit which candidates can spoil an election without a Condorcet winner.[35]Template:Rp

Rated voting

Rated voting methods ask voters to assign each candidate a score on a scale (e.g. rating them from 0 to 10), instead of listing them from first to last. Highest median and score (highest mean) voting are the two most prominent examples of rated voting rules. Whenever voters rate candidates independently, the rating given to one candidate does not affect the ratings given to the other candidates. Any new candidate cannot change the winner of the race without becoming the winner themselves, which would disqualify them from the definition of a spoiler. For this to hold, in some elections, some voters must use less than their full voting power despite having meaningful preferences among viable candidates.

The outcome of rated voting depends on the scale used by the voter or assumed by the mechanism.[36] If the voters use relative scales, i.e. scales that depend on what candidates are running, then the outcome can change if candidates who don't win drop out.[37] Empirical results from panel data suggest that judgments are at least in part relative.[38][39] Thus, rated methods, as used in practice, may exhibit a spoiler effect caused by the interaction between the voters and the system, even if the system itself passes IIA given an absolute scale.

Proportional representation

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.[14] This kind of spoiler effect is avoided by divisor methods and proportional approval.[14]Template:Rp

Spoiler campaign

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United States

Script error: No such module "Labelled list hatnote".A spoiler campaign in the United States is often one that cannot realistically win but can still determine the outcome by pulling support from a more competitive candidate.[40] The two major parties in the United States, the Republican Party and Democratic Party, have regularly won 98% of all state and federal seats.[41] The US presidential elections most consistently cited as having been spoiled by third-party candidates are 1844[42] and 2000.[43][44][45][42] The 2016 election is more disputed as to whether it contained spoiler candidates or not.[46][47][48] For the 2024 presidential election, Republican lawyers and operatives have fought to keep right-leaning third-parties like the Constitution Party off swing state ballots[49] while working to get Cornel West on battleground ballots.[50] Democrats have helped some right-leaning third-parties gain ballot access while challenging ballot access of left-leaning third-parties like the Green Party.[51] According to the Associated Press, the GOP effort to prop up possible spoiler candidates in 2024 appears more far-reaching than the Democratic effort.[52] Barry Burden argues that they have almost no chance of winning the 2024 election but are often motivated by particular issues.[53]

Third party candidates are always controversial because almost anyone could play spoiler.[54][55] This is especially true in close elections where the chances of a spoiler effect increase.[56] Strategic voting, especially prevalent during high stakes elections with high political polarization, often leads to a third-party that underperforms its poll numbers with voters wanting to make sure their least favorite candidate is not in power.[41][57][58] Third-party campaigns are more likely to result in the candidate a third party voter least wants in the White House.[55] Third-party candidates prefer to focus on their platform than on their impact on the frontrunners.[55]

Notable unintentional spoilers

An unintentional spoiler is one that has a realistic chance of winning but falls short and affects the outcome of the election. Some third-party candidates express ambivalence about which major party they prefer and their possible role as spoiler[59][60] or deny the possibility.[61]

2009 Burlington mayoral election

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 most voters preferred Montroll to Kiss.[62] The results of every possible one-on-one election can be completed as follows:

File:Democratic Disc.svg Andy Montroll (D) 6262 (Montroll) –

591 (Simpson)

4570 (Montroll) –

2997 (Smith)

4597 (Montroll) –

3664 (Wright)

4064 (Montroll) –

3476 (Kiss)

4/4 Wins
File:Progressive Disk.png Bob Kiss (P) 5514 (Kiss) –

844 (Simpson)

3944 (Kiss) –

3576 (Smith)

4313 (Kiss) –

4061 (Wright)

3/4 Wins RCV winner
File:Republican Disc.svg Kurt Wright (R) 5270 (Wright) –

1310 (Simpson)

3971 (Wright) –

3793 (Smith)

2/4 Wins Spoiler for Montroll
Dan Smith (I) 5570 (Smith) –

721 (Simpson)

1/4 Wins
File:Green Disc.svg James Simpson (G) 0/4 Wins

This leads to an overall preference ranking of:

  1. Montroll – defeats all candidates below, including Kiss (4,064 to 3,476)
  2. Kiss – defeats all candidates below, including Wright (4,313 to 4,061)
  3. Wright – defeats all candidates below, including Smith (3,971 to 3,793)
  4. Smith – defeats Simpson (5,570 to 721) and the write-in candidates

Montroll was therefore preferred over Kiss by 54% of voters, over Wright by 56%, and over Smith by 60%. Had Wright not run, Montroll would have won instead of Kiss.[62][63]

Because all ballots were fully released, it is possible to reconstruct the winners under other voting methods. While Wright would have won under plurality, Kiss won under IRV, and would have won under a two-round vote or a traditional nonpartisan blanket primary. Montroll, being the majority-preferred candidate, would have won if the ballots were counted using ranked pairs (or any other Condorcet method).[64]

2022 Alaska's at-large congressional district special election

In Alaska's first-ever IRV election, Nick Begich was eliminated in the first round to advance Mary Peltola and Sarah Palin. However, the pairwise comparison shows that Begich was the Condorcet winner while Palin was both the Condorcet loser and a spoiler:[65]

Pairwise comparison matrix by vote totals[66][65]
Begich Peltola Palin
Begich - 88,126 101,438
Peltola 79,486 - 91,375
Palin 63,666 86,197 -
Pairwise as a percentage
Winner Loser Winner Loser
Begich vs. Peltola 52.6% vs. 47.4%
Begich vs. Palin 61.4% vs. 38.6%
Peltola vs. Palin 51.5% vs. 48.5%

In the wake of the election, a poll found 54% of Alaskans, including a third of Peltola voters, supported a repeal of RCV.[67][68][69] Observers noted such pathologies would have occurred under Alaska's previous primary system as well, leading several to suggest Alaska adopt any one of several alternatives without this behavior.[70]

See also

Notes


References

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External links

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