Editing Spoiler effect (section)

== By electoral system ==
{| class="wikitable" style="float:right; margin-left:1em;
|+Susceptibility to spoilers
!Electoral system
!Spoiler effect
|-
|[[First-past-the-post|Plurality voting]]
|High
|-
|[[Two-round system|Runoffs]] or [[Instant-runoff voting|RCV]]
|Medium
|-
|[[Condorcet method]]s
|Low
|-
|[[Score voting|Score]] or [[Highest median voting rules|Medians]]
|Depends
|}

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.}}

=== First-preference plurality ===
In cases where there are many similar candidates, spoiler effects occur most often in [[First-preference plurality|first-preference plurality (FPP)]].{{Citation needed|date=September 2024}} For example, in the United States, vote splitting is common in [[primary elections|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 [[First-preference plurality|FPP]] into a [[two-round system]].<ref name="Santucci">{{Cite web |last1=Santucci |first1=Jack |last2=Shugart |first2=Matthew |last3=Latner |first3=Michael S. |date=2023-10-16 |title=Toward a Different Kind of Party Government |url=https://protectdemocracy.org/work/toward-a-different-kind-of-party-government/ |url-status=live |archive-url=https://web.archive.org/web/20240716205506/https://protectdemocracy.org/work/toward-a-different-kind-of-party-government/ |archive-date=2024-07-16 |access-date=2024-07-16 |website=Protect Democracy |language=en-US |quote="Finally, we should not discount the role of primaries. When we look at the range of countries with [[first-past-the-post]] (FPTP) elections (given no primaries), none with an assembly larger than Jamaica’s (63) has a strict two-party system. These countries include the [[United Kingdom]] and [[Canada]] (where multiparty competition is in fact nationwide). Whether the U.S. should be called ‘FPTP’ itself is dubious, and not only because some states (e.g. [[Georgia (US State)|Georgia]]) hold runoffs or use the [[alternative vote]] (e.g. [[Maine]]). '''Rather, the U.S. has an unusual two-round system in which the first round winnows the field. This usually is at the intraparty level, although sometimes it is without regard to party (e.g. in Alaska and California).'''"}}</ref><ref name="Gallagher">{{Cite book |last1=Gallagher |first1=Michael |title=The Politics of Electoral Systems |last2=Mitchell |first2=Paul |date=2005-09-15 |publisher=OUP Oxford |isbn=978-0-19-153151-4 |page=192 |language=en |chapter=The American Electoral System |quote="American elections become a two-round run-off system with a delay of several months between the rounds." |chapter-url=https://books.google.com/books?id=Igdj1P4vBwMC&q=%22American+elections+become+a+two-round+run-off+system+with+a+delay+of+several+months+between+the+rounds.%22&pg=PA3}}</ref><ref name="Bowler">{{Citation |last1=Bowler |first1=Shaun |title=The United States: A Case of Duvergerian Equilibrium |date=2009 |work=Duverger's Law of Plurality Voting: The Logic of Party Competition in Canada, India, the United Kingdom and the United States |pages=135–146 |url=https://link.springer.com/chapter/10.1007/978-0-387-09720-6_9 |access-date=2024-08-31 |place=New York, NY |publisher=Springer |language=en |doi=10.1007/978-0-387-09720-6_9 |isbn=978-0-387-09720-6 |quote=In effect, the primary system means that the USA has a two-round runoff system of elections. |last2=Grofman |first2=Bernard |last3=Blais |first3=André|url-access=subscription }}</ref>

Vote splitting is the most common cause of spoiler effects in [[First-past-the-post voting|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.<ref name="King">{{Cite book |last1=King |first1=Bridgett A. |url=https://books.google.com/books?id=-bCJDAAAQBAJ |title=Why Don't Americans Vote? Causes and Consequences: Causes and Consequences |last2=Hale |first2=Kathleen |date=2016-07-11 |publisher=ABC-CLIO |isbn=9781440841163 |language=en |quote=Those votes that are cast for minor party candidates are perceived as taking away pivotal votes from major party candidates. ... This phenomenon is known as the 'spoiler effect'.}}</ref><ref name="Sen-2017">{{cite news |last1=Sen |first1=Amartya |last2=Maskin |first2=Eric |date=2017-06-08 |title=A Better Way to Choose Presidents |url=https://scholar.harvard.edu/files/maskin/files/the_new_york_review_of_books_-_a_better_way_to_choose_presidents_e._maskin_a._sen_.pdf |access-date=2019-07-20 |journal=New York Review of Books |language=en |issn=0028-7504 |quote=plurality-rule voting is seriously vulnerable to vote-splitting ... runoff voting ... as French history shows, it too is highly subject to vote-splitting. ... [Condorcet] majority rule avoids such vote-splitting debacles because it allows voters to rank the candidates and candidates are compared pairwise}}</ref> 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.<ref name="King" /><ref name="Buchler">{{Cite book |last=Buchler |first=Justin |url=https://books.google.com/books?id=9bzmTImCLfgC |title=Hiring and Firing Public Officials: Rethinking the Purpose of Elections |date=2011-04-20 |publisher=Oxford University Press, USA |isbn=9780199759965 |language=en |quote=a spoiler effect occurs when entry by a third-party candidate causes party A to defeat party B even though Party B would have won in a two-candidate race.}}</ref>

=== Runoff systems ===
Plurality-runoff methods like the [[two-round system]] and [[instant-runoff voting|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.<ref name="Sen-2017" /><ref name="Borgers2">{{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 |language=en |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><ref>{{Cite book |last=Poundstone |first=William |url=https://books.google.com/books?id=_24bJHyBV6sC |title=Gaming the Vote: Why Elections Aren't Fair (and What We Can Do About It) |date=2009-02-17 |publisher=Farrar, Straus and Giroux |isbn=9781429957649 |language=en |quote=IRV is excellent for preventing classic spoilers-minor candidates who tip the election from one major candidate to another. It is not so good when the 'spoiler' has a real chance of winning}}</ref> As a result, instant-runoff voting still tends towards [[Two-party system|two-party rule]] through the process known as [[Duverger's law]].<ref name="Poundstone, William.-201323"/><ref name=":35">{{Cite web |last=Drutman |first=Lee |date=2024-09-12 |title=We need more (and better) parties |url=https://leedrutman.substack.com/p/we-need-more-and-better-parties |access-date=2024-09-19 |website=Undercurrent Events}}</ref> A notable example of this can be seen in [[2024 United States House of Representatives election in Alaska|Alaska's 2024 race]], where party elites pressured candidate [[Nancy Dahlstrom]] into dropping out to avoid a repeat of the [[2022 Alaska's at-large congressional district special election|spoiled 2022 election]].<ref name=":14">{{Cite book |last=Volić |first=Ismar |url=http://dx.doi.org/10.2307/jj.7492228 |title=Making Democracy Count |date=2024-04-02 |publisher=Princeton University Press |isbn=978-0-691-24882-0 |publication-date=2024-04-02 |at=Ch. 2 |chapter=Duverger's law |doi=10.2307/jj.7492228}}</ref><ref>{{Cite news |last=Strassel |first=Kimberly A. |date=2024-08-27 |title=Ranked Choice May Die in Alaska |url=https://www.wsj.com/opinion/ranked-choice-may-die-in-alaska-4452235c |work=[[The Wall Street Journal]]}}</ref><ref>{{Cite web |last=Early |first=Wesley |date=2024-09-05 |title=Why candidates are withdrawing from Alaska's general election |url=https://alaskapublic.org/2024/09/04/why-candidates-are-withdrawing-from-alaskas-general-election/ |access-date=2024-09-20 |website=Alaska Public Media |publisher=[[NPR]] |place=[[Anchorage]], [[Alaska]] |language=en-US}}</ref>

=== 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"/>

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}}

=== 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 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.

=== Proportional representation ===
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" />''' This kind of spoiler effect is avoided by [[divisor method]]s and [[Proportional approval voting|proportional approval]].'''<ref name=":03" />{{Rp|Thm.8.3}}'''