Editing Spoiler effect (section)

{{Short description|Losing candidate affecting election result}}
{{for|the same effect in sports|Elimination from postseason contention#Spoiler effect}}
{{Redirect|Independence of spoilers|the logical property in decision theory|Independence of irrelevant alternatives}}
{{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>'''

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>

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}}'''