View source for Center squeeze

{{Short description|Spoiler effect that excludes moderate candidates}}
[[File:Center_squeeze_grid.png|right|thumb|370x370px|Distribution of winners on a simulated [[political compass]], showing how center-squeeze extends to more complex or multi-dimensional models. The number of winners is displayed as a [[Heat map|heatmap]]. The bias of [[First-past-the-post voting|FPTP]], [[Two-round system|runoffs]] or [[Primary election|primaries]], and [[Instant-runoff voting|RCV]] (center-left column) is clearly visible.]]
{{electoral systems|expanded=Paradox}}

'''Center squeeze''' is a kind of [[spoiler effect]] seen in a number of election rules, among them [[Two-round system|two-round]] and [[Instant-runoff voting|instant runoff]].<ref name="Merril 198522422232">{{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.}}</ref> In a center squeeze, the [[Majority-preferred candidate|majority-preferred]] Condorcet winner candidate loses in favor of a more [[Extremism|extreme]] alternative, even though the voters would have preferred the Condorcet winner to the actual winner.

In a center squeeze, the [[Condorcet winner criterion|Condorcet winner]] is eliminated or otherwise rendered irrelevant before they have the chance to face any of the other candidates in a one-on-one race (which by definition, they would win).<ref name="Merrill 19842223">{{Cite journal |last=Merrill |first=Samuel |date=1984 |title=A Comparison of Efficiency of Multicandidate Electoral Systems |url=http://dx.doi.org/10.2307/2110786 |journal=American Journal of Political Science |volume=28 |issue=1 |pages=23–48 |doi=10.2307/2110786 |issn=0092-5853 |jstor=2110786 |quote=However, squeezed by surrounding opponents, a centrist candidate may receive few first-place votes and be eliminated under Hare. |via=}}</ref><ref name=":0322232">{{Cite web |last1=Atkinson |first1=Nathan |last2=Ganz |first2=Scott C. |date=2022-10-30 |title=The flaw in ranked-choice voting: rewarding extremists |url=https://thehill.com/opinion/campaign/3711206-the-flaw-in-ranked-choice-voting-rewarding-extremists/ |access-date=2023-05-14 |website=The Hill |language=en-US |quote=However, ranked-choice voting makes it more difficult to elect moderate candidates when the electorate is polarized. For example, in a three-person race, the moderate candidate may be preferred by a majority of voters to each of the more extreme candidates. However, voters with far-left and far-right views will rank the candidate in second place rather than in first place. Since ranked-choice voting counts only the number of first-choice votes (among the remaining candidates), the moderate candidate would be eliminated in the first round, leaving one of the extreme candidates to be declared the winner.}}</ref> Systems with center-squeeze are sometimes called '''centrifugal''' ("center-fleeing") because they encourage [[political polarization]].<ref>{{Cite web |last=Foley |first=Edward B. |date=2024-08-17 |title=What is “Centripetalism” and Why Does It Matter? |url=https://edwardbfoley.substack.com/p/what-is-centripetalism-and-why-does |access-date=2025-01-30 |website=Common Ground Democracy |author-link=Edward B. Foley}}</ref>

In a center squeeze, candidates focused on appealing to a [[Political base|base]] of [[core support]]ers can squeeze broadly-popular [[Condorcet winner]] candidates trapped between them out of the race, by splitting the [[First-preference votes|first-round vote]] with them, allowing a more-extreme alternative to win.<ref name="Merril 198522422232" /><ref name=":8522222">{{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 |issn=0092-5853 |jstor=3088418 |quote="As with simple plurality elections, it is apparent the outcome will be highly sensitive to the distribution of candidates."}}</ref> This effect was first predicted by [[Social choice theory|social choice theorists]] in the 1940s and 50s,{{citation needed|date=February 2025}} and has since been documented in various countries using [[Plurality-rule family|plurality-style electoral systems]].

Famous examples of center squeezes include the [[2022 Alaska's at-large congressional district special election|2022 Alaska special election]] (where [[Nick Begich III]] was eliminated in the first round by [[Sarah Palin]])<ref name="Analysis Alaska323">{{Cite arXiv |eprint=2209.04764v3 |class=econ.GN |first1=Adam |last1=Graham-Squire |first2=David |last2=McCune |title=A Mathematical Analysis of the 2022 Alaska Special Election for US House |date=2022-09-11 |language=en |page=2 |quote=Since Begich wins both ... he is the Condorcet winner of the election ... AK election also contains a Condorcet loser: Sarah Palin. ... she is also a spoiler candidate}}</ref> as well as the [[2007 French presidential election]], where moderate liberal [[François Bayrou]] was eliminated by left-wing candidate [[Ségolène Royal]], allowing [[Nicolas Sarkozy]] to win the second round.<ref>{{Citation |last1=Balinski |first1=Michel |title=Election by Majority Judgment: Experimental Evidence |date=2011 |work=In Situ and Laboratory Experiments on Electoral Law Reform: French Presidential Elections |pages=13–54 |editor-last=Dolez |editor-first=Bernard |url=https://link.springer.com/chapter/10.1007/978-1-4419-7539-3_2 |access-date=2024-10-31 |place=New York, NY |publisher=Springer |language=en |doi=10.1007/978-1-4419-7539-3_2 |isbn=978-1-4419-7539-3 |last2=Laraki |first2=Rida |editor2-last=Grofman |editor2-first=Bernard |editor3-last=Laurent |editor3-first=Annie}}</ref><ref>{{Cite journal |last1=Balinski |first1=Michel |last2=Laraki |first2=Rida |date=2020-03-01 |title=Majority judgment vs. majority rule |journal=Social Choice and Welfare |language=en |volume=54 |issue=2 |pages=429–461 |doi=10.1007/s00355-019-01200-x |issn=1432-217X }}</ref>

== Overview ==
Center squeezes are a kind of [[independence of irrelevant alternatives]] violation in which the Condorcet winner is eliminated before the final round of an election.<ref name="Merrill 19842223"/><ref name=":0322232"/> Candidates focused on appealing to a small [[Political base|base]] of [[core support]]ers can squeeze Condorcet winners out of the race, by splitting the [[First-preference votes|first-round vote]] needed to survive earlier rounds.<ref name="Merril 19852242223">{{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=}}</ref><ref name=":8522222"/>

The "center" in "center squeeze" refers to candidates who are close to the center of public opinion'','' and is not limited to [[Centrism|centrists]] along a traditional, one-dimensional [[political spectrum]].<ref name="Davis 197022232">{{Cite journal |last1=Davis |first1=Otto A. |last2=Hinich |first2=Melvin J. |last3=Ordeshook |first3=Peter C. |date=1970-01-01 |title=An Expository Development of a Mathematical Model of the Electoral Process |journal=The American Political Science Review |volume=64 |issue=2 |pages=426–448 |doi=10.2307/1953842 |jstor=1953842 |s2cid=1161006 |quote=Since our model is multi-dimensional, we can incorporate all criteria which we normally associate with a citizen's voting decision process — issues, style, partisan identification, and the like.}}</ref> A center squeeze can occur in any situation where voters prefer candidates [[Single peaked preferences|who hold views similar to their own]].<ref name="Lewyn 20122232223">{{harvnb|Lewyn|2012|}}: "third place Candidate C is a centrist who is the second choice of Candidate A's left-wing supporters and Candidate B's right-wing supporters. ... In such a situation, Candidate C would prevail over both Candidates A ... and B ... in a one-on-one runoff election. Yet, Candidate C would not prevail under IRV because he or she finished third and thus would be the first candidate eliminated"</ref>

Center-squeeze has been observed in [[Australia]],<ref name=":2223222">{{Cite journal |last1=Mussel |first1=Johanan D. |last2=Schlechta |first2=Henry |date=2023-07-21 |title=Australia: No party convergence where we would most expect it |url=http://journals.sagepub.com/doi/10.1177/13540688231189363 |journal=Party Politics |volume=30 |issue=6 |pages=1040–1050 |language=en |doi=10.1177/13540688231189363 |issn=1354-0688}}</ref><ref>{{Cite journal |last=Lewyn |first=Michael |date=2012 |title=Two Cheers for Instant Runoff Voting |url=https://papers.ssrn.com/abstract=2276015 |journal=6 Phoenix L. Rev. |language=en |location=Rochester, NY |volume=117 |pages= |ssrn=2276015 |quote= |via=}}</ref> and various [[United States|US]] cities.<ref>{{Cite journal |last=Vishwanath |first=Arjun |date=2021 |title=Electoral Institutions and Substantive Representation in Local Politics: The Effects of Ranked Choice Voting |url=https://www.ssrn.com/abstract=3802566 |journal=SSRN Electronic Journal |language=en |doi=10.2139/ssrn.3802566 |issn=1556-5068}}</ref>

=== Susceptibility by system ===
Center squeeze is a major feature of two-party systems using [[Primary election|primaries]] or other multiple-round systems.<ref name="Merril 19852242223"/> In these methods, candidates must focus on appealing to their [[core support]]ers to ensure they can make it past the first round, where only first-preferences count.<ref name="Merril 19852242223" />

If voters assign scores to candidates based on ideological distance, [[score voting]] will always select the candidate closest to some [[central tendency]] of the voter distribution. As a result, while score voting does not always elect the candidate closest to the median voter, it often behaves like methods that do.<ref name=":12">{{Cite journal |last1=Potthoff |first1=Richard F. |last2=Munger |first2=Michael C. |date=November 2021 |title=Condorcet Loser in 2016: Apparently Trump; Condorcet Winner: Not Clinton? |journal=American Politics Research |language=en |volume=49 |issue=6 |pages=618–636 |doi=10.1177/1532673X211009499 |issn=1532-673X |doi-access=free}}</ref><ref name=":0">{{cite book |last=DeGroot |first=Morris H. |url=https://books.google.com/books?id=7rDY2_r4bmEC&pg=PA232 |title=Optimal Statistical Decisions |publisher=McGraw-Hill Book Co., New York-London-Sydney |year=1970 |isbn=9780471680291 |page=232 |mr=0356303}}</ref> Under most models of strategic voting, [[spoilerproof]] cardinal methods tend to behave like [[approval voting]] and thus converge on the Condorcet winner.<ref name=":0223">{{Cite journal |last=Laslier |first=Jean-François |date=January 2009 |title=The Leader Rule: A Model of Strategic Approval Voting in a Large Electorate |url=https://journals.sagepub.com/doi/10.1177/0951629808097286 |journal=Journal of Theoretical Politics |language=en |volume=21 |issue=1 |pages=113–136 |doi=10.1177/0951629808097286 |issn=0951-6298}}</ref><ref name="Handbook on Approval Voting23">{{Cite book |url=https://link.springer.com/10.1007/978-3-642-02839-7 |title=Handbook on Approval Voting |date=2010 |publisher=Springer Berlin Heidelberg |isbn=978-3-642-02838-0 |editor-last=Laslier |editor-first=Jean-François |series=Studies in Choice and Welfare |location=Berlin, Heidelberg |pages=2 |language=en |doi=10.1007/978-3-642-02839-7 |quote=By eliminating the squeezing effect, Approval Voting would encourage the election of consensual candidates. The squeezing effect is typically observed in multiparty elections with a runoff. The runoff tends to prevent extremist candidates from winning, but a centrist candidate who would win any pairwise runoff (the "Condorcet winner") is also often "squeezed" between the left-wing and the right-wing candidates and so eliminated in the first round. |editor-last2=Sanver |editor-first2=M. Remzi}}</ref><ref name=":1223">{{Cite journal |last=Cox |first=Gary W. |date=1985 |title=Electoral Equilibrium under Approval Voting |url=https://www.jstor.org/stable/2111214 |journal=American Journal of Political Science |volume=29 |issue=1 |pages=112–118 |doi=10.2307/2111214 |issn=0092-5853 |jstor=2111214}}</ref><ref name=":22">{{Cite journal |last1=Myerson |first1=Roger B. |last2=Weber |first2=Robert J. |date=1993 |title=A Theory of Voting Equilibria |url=https://www.jstor.org/stable/2938959 |journal=The American Political Science Review |volume=87 |issue=1 |pages=102–114 |doi=10.2307/2938959 |jstor=2938959 |issn=0003-0554}}</ref>

The opposite situation—a bias in favor of bland, inoffensive, or unknown candidates—is not common in any widely-used voting rules. However, it can occur for "negative" voting methods that choose candidates with the least opposition, like [[Anti-plurality voting|anti-plurality]], [[D21 – Janeček method|D21 – Janeček]], or [[Coombs' method]].<ref>{{Cite journal |last=Shankar |first=Karthik H. |date=2022-12-01 |title=Normed Negative Voting to Depolarize Politics |url=https://link.springer.com/article/10.1007/s10726-022-09799-6 |journal=Group Decision and Negotiation |language=en |volume=31 |issue=6 |pages=1097–1120 |doi=10.1007/s10726-022-09799-6 |issn=1572-9907|arxiv=2012.13657 }}</ref>

== Example ==
[[File:Center-Squeeze.svg|left|thumb|336x336px|
{| class="wikitable"
|+
!Start:
!Mid-Start:
!Mid-End:
!End:
|-
|33.4%
|17.2%
|13.4%
|35.9%
|}
]]In Alphabet Land, voters are divided based on how names should be arranged on lists. <math>A</math> thinks names should always be in alphabetical order; ''<math>Z</math>'' thinks they should be in reverse-alphabetical order; and <math>M</math> thinks the order should be randomized. In this example, voters' happiness with the outcome falls [[Linearity|linearly]] with the distance (number of letters) between the voter and the candidate.<!--[[WP:ROUTINE]] means the example doesn't need a citation-->

Because <math>M</math> is preferred to both <math>A</math> and <math>Z</math> in head-to-head match-ups, <math>M</math> is the [[Condorcet winner|majority-preferred (Condorcet) winner]].<!--WP:ROUTINE--> <math>M</math> is the [[Socially optimal winner|socially-optimal winner]] as well.<ref name=":0" /> Thus, <math>M</math> is the "best" or "most popular" candidate under both common metrics of candidate quality in [[social choice]].<ref name="Merrill 19842223"/>
[[File:Center Squeeze Example Bar Graph FPP.svg|thumb|336x336px|Vote totals of an example first-past-the-post election, which is the same as the first round of an RCV election.]]

=== First-preference plurality (FPP) ===
<math>Z</math> wins under a single-round of FPP, with 35.9% of voters choosing them as their favorite. However, over substantially more voters considered <math>Z</math> to be their least favorite, with 63.1% of voters preferring <math>M</math>. <math>Z</math> is elected, despite an overwhelming two-thirds majority preferring <math>M</math>.<!--WP:ROUTINE-->
=== Ranked-choice runoff (Alternative, Two-round) ===
[[Instant-runoff voting|Ranked-choice voting (RCV)]] tries to address vote-splitting in FPP by replacing it with a series of FPP elections, with the loser being eliminated in each round.<ref>{{cite web |author=<!--Not stated--> |date= |title=Ranked Choice Voting |url=https://fairvote.org/our-reforms/ranked-choice-voting/ |access-date=2024-07-22 |website=FairVote}}</ref><ref>{{cite web |author=<!--Not stated--> |date=2020-11-09 |title=Avoid Vote-Splitting and Weak Plurality Results |url=https://www.rcvresources.org/blog-post/avoid-vote-splitting-and-weak-plurality-results |access-date=2024-07-22 |website=RCV Resources |publisher=Ranked Choice Voting Resource Center}}</ref>

The first round of the election is the same as the FPP election. <math>M</math> has the least [[First-preference votes|first preferences]] and is therefore eliminated. Their votes are reassigned to <math>A</math> and <math>Z</math>, according to their ballot. In the second round, enough voters who preferred <math>M</math> as their first choice took <math>A</math> as their second choice and <math>A</math> wins the election.<!--WP:ROUTINE--> RCV thus fails to have a substantial moderating impact, instead causing only a swing from one extreme to the other.<ref>{{Cite journal |last1=Atkinson |first1=Nathan |last2=Foley |first2=Edward B. |last3=Ganz |first3=Scott |date=2023 |title=Beyond the Spoiler Effect: Can Ranked Choice Voting Solve the Problem of Political Polarization? |url=https://www.ssrn.com/abstract=4411173 |journal=SSRN Electronic Journal |language=en |doi=10.2139/ssrn.4411173 |issn=1556-5068}}</ref>

== Real-world occurrences ==
{{Globalize|1=section|2=US|date=October 2024}}

=== 2022 Alaska special election ===
{{Main|2022 Alaska's at-large congressional district special election}}

{{Infobox election
| election_name = Center squeeze
| country =
| type = by-election
| ongoing = no
| seats_for_election = {{ushr|AK|AL}}
| 1blank = First round
| 2blank = [[Instant-runoff voting|Final round]]
| turnout = 32.2%<ref name="akdoe1">{{Cite web |date=September 2, 2022 |title=State of Alaska {{!}} 2022 Special General Election {{!}} Election Summary Report {{!}} August 16, 2022 {{!}} Official Results |url=https://www.elections.alaska.gov/results/22SSPG/ElectionSummaryReportRPTS.pdf |access-date=September 2, 2022 |website=Alaska Division of Elections |archive-url=https://web.archive.org/web/20220817053708/https://www.elections.alaska.gov/results/22SSPG/ElectionSummaryReportRPTS.pdf |archive-date=August 17, 2022 |url-status=live}}</ref>
| image_size = x150px
| image1 = File:Rep. Mary Peltola headshot (cropped) (cropped).jpg
| candidate1 = '''[[Mary Peltola]]'''
| party1 = Democratic Party (United States)
| 1data1 = '''74,817<br />39.7%'''
| 2data1 = '''91,266<br />51.5%'''
| image2 = Sarah Palin by Gage Skidmore 5 (cropped).jpg
| candidate2 = [[Sarah Palin]]
| party2 = Republican Party (United States)
| 1data2 = '''58,339<br />30.9%'''
| 2data2 = 86,026<br />48.5%
| candidate3 = [[Nick Begich III]]
| image3 = Nick Begich Official Campaign Profile Photo (Cropped).jpg
| party3 = Republican Party (United States)
| 1data3 = '''52,536<br />27.8%'''
| 2data3 = ''Eliminated''
}}

The [[2022 Alaska's at-large congressional district special election|2022 Alaska special election]] seat was an example of a center squeeze, where [[Nick Begich III]] was eliminated in the first round by [[right-wing]] spoiler [[Sarah Palin]],<ref name="Analysis Alaska323"/><ref name=":0222223">{{Cite web |last1=Atkinson |first1=Nathan |last2=Ganz |first2=Scott C. |date=2022-10-30 |title=The flaw in ranked-choice voting: rewarding extremists |url=https://thehill.com/opinion/campaign/3711206-the-flaw-in-ranked-choice-voting-rewarding-extremists/ |access-date=2023-05-14 |website=The Hill |language=en-US |quote=However, ranked-choice voting makes it more difficult to elect moderate candidates when the electorate is polarized. For example, in a three-person race, the moderate candidate may be preferred to each of the more extreme candidates by a majority of voters. However, voters with far-left and far-right views will rank the candidate in second place rather than in first place. Since ranked-choice voting counts only the number of first-choice votes (among the remaining candidates), the moderate candidate would be eliminated in the first round, leaving one of the extreme candidates to be declared the winner.}}</ref> despite a majority of voters preferring Begich to either one of his opponents.<ref name="Analysis Alaska323" /><ref name="easy fix2223">{{Cite news |last1=Maskin |first1=Eric |author-link=Eric Maskin |last2=Foley |first2=Edward B. |date=2022-11-01 |title=Alaska's ranked-choice voting is flawed. But there's an easy fix. |url=https://www.washingtonpost.com/opinions/2022/11/01/alaska-final-four-primary-begich-palin-peltola/ |access-date=2024-02-09 |newspaper=Washington Post |language=en-US |issn=0190-8286}}</ref> The ranked-choice runoff election involved one [[Democratic Party (United States)|Democrat]] ([[Mary Peltola]]) and two [[Republican Party (United States)|Republicans]] ([[Sarah Palin]] and [[Nick Begich III]]). Because the full ballot data for the race was released, [[Social choice theory|social choice theorists]] were able to confirm that Palin spoiled the race for Begich, with Peltola winning the race as a result of several [[Pathological (mathematics)|counter-intuitive]] behaviors that tend to characterize center-squeeze elections.<ref name="easy fix2223" /><ref name="Analysis Alaska323"/>

The election produced a winner opposed by a majority of voters, with a majority of voters ranking Begich above Peltola and Palin,<ref name=":133">{{Cite arXiv |eprint=2303.00108v1 |class=cs.CY |first=Jeanne N. |last=Clelland |title=Ranked Choice Voting And the Center Squeeze in the Alaska 2022 Special Election: How Might Other Voting Methods Compare? |date=2023-02-28 |language=en |page=6}}</ref><ref name="Analysis Alaska323"/><ref name=":0222223"/> and more than half giving Peltola no support at all.<ref name=":133" /><ref name="Analysis Alaska323" /> The election was also notable as a [[Participation criterion|no-show paradox]], where a candidate is eliminated as a result of votes cast in ''support'' of their candidacy. In this case, ballots ranking Palin first and Begich second instead allowed Peltola to win.<ref name="Analysis Alaska323"/><ref name=":3223">{{Cite journal |last1=Graham-Squire |first1=Adam |last2=McCune |first2=David |date=2024-01-02 |title=Ranked Choice Wackiness in Alaska |url=https://www.tandfonline.com/doi/full/10.1080/10724117.2023.2224675 |journal=Math Horizons |language=en |volume=31 |issue=1 |pages=24–27 |doi=10.1080/10724117.2023.2224675 |issn=1072-4117}}</ref><ref name=":0222223"/>

Many [[Social choice theory|social choice theorists]] criticized the ranked-choice runoff procedure for its [[Pathological (mathematics)|counter-intuitive behavior]].<ref name="easy fix222223">{{Cite news |last1=Maskin |first1=Eric |author-link=Eric Maskin |last2=Foley |first2=Edward B. |date=2022-11-01 |title=Opinion: Alaska's ranked-choice voting is flawed. But there's an easy fix. |url=https://www.washingtonpost.com/opinions/2022/11/01/alaska-final-four-primary-begich-palin-peltola/ |access-date=2024-02-09 |newspaper=Washington Post |language=en-US |issn=0190-8286}}</ref><ref name="Analysis Alaska323"/> Along with being a center squeeze, the election was a [[Monotonicity criterion|negative voting weight event]],<ref name=":3223" /> where a voter's ballot has the opposite of its intended effect (e.g. where a candidate would need ''more'' votes to lose).<ref name=":3223" /><ref>{{Cite journal |last1=Doron |first1=Gideon |last2=Kronick |first2=Richard |date=1977 |title=Single Transferrable Vote: An Example of a Perverse Social Choice Function |url=https://www.jstor.org/stable/2110496 |journal=American Journal of Political Science |volume=21 |issue=2 |pages=303–311 |doi=10.2307/2110496 |issn=0092-5853 |jstor=2110496}}</ref> In this race, Peltola would have lost if she had received more support from Palin voters,<ref>{{Cite web |last=Hamlin |first=Aaron |date=2022-09-16 |title=RCV Fools Palin Voters into Electing a Progressive Democrat |url=https://electionscience.org/archive/rcv-fools-palin-voters-into-electing-a-progressive-democrat/ |access-date=2024-07-11 |website=The Center for Election Science |language=en-US |quote=It's a good thing for Peltola that she didn't attract more Palin voters—she'd have lost [...] The strangeness continues. Peltola could have actually gotten more 1st choice votes in this election and caused herself to lose. How's that? Let's look. [...] Imagine if Peltola reached across the aisle and spoke directly to Palin voters. Imagine that she empathized with their position and identified issues they cared about that Palin and even Begich ignored. And let's say that as a consequence, Peltola got the first-choice votes of between 5,200 and 8,500 voters who would have otherwise ranked only Palin. What happens as a result? Palin would have gotten eliminated in the first round and Peltola would still not be able to beat Begich.}}</ref><ref name="Analysis Alaska323"/><ref name=":133"/> and won as a result of 5,200 ballots that ranked her last (after Palin then Begich).<ref name=":3223" /><ref name="Analysis Alaska323" /> However, [[Social choice theory|social choice theorists]] were careful to note the results likely would have been the same under Alaska's previous primary system as well. This led several to recommend replacing the system with any one of several [[Comparison of electoral systems|alternatives without these behaviors]], such as [[STAR voting|STAR]], [[Approval voting|approval]], or [[Condorcet method|Condorcet voting]].<ref name="easy fix2223" /><ref name=":133" />

=== 2009 Burlington mayoral election ===
{{main|2009 Burlington mayoral election}}

The [[2009 Burlington mayoral election]] was held in March 2009 for the city of [[Burlington, Vermont]], and serves as an example of a four-candidate center squeeze. This was the second mayoral election since the city's 2005 change to [[Instant-runoff voting|ranked-choice runoff voting]], after the [[2006 Burlington mayoral election|2006 mayoral election]].<ref name="burlington_votes23">{{cite web|url=http://www.burlingtonvotes.org/faq|title=Frequently Asked Questions about Burlington's use of Instant Runoff Voting|quote=4. How did this change to IRV come about?<br />Over 64% of Burlington voters voted in favor of the IRV Charter amendment in March 2005, and it went into effect on May 12, 2005, when the governor signed the ratification bill, H.505, which had been passed by both the House and Senate.|access-date=July 21, 2024|archive-date=January 30, 2008|archive-url=https://web.archive.org/web/20080130053047/http://www.burlingtonvotes.org/faq/|url-status=dead}}</ref> In the 2009 election, incumbent [[List of mayors of Burlington, Vermont|Burlington mayor]] [[Bob Kiss]] won reelection as a member of the [[Vermont Progressive Party]],<ref>{{cite web |title=Mayor Bob Kiss |url=http://www.ci.burlington.vt.us/mayor/ |url-status=dead |archive-url=https://web.archive.org/web/20071129081028/www.ci.burlington.vt.us/mayor/ |archive-date=November 29, 2007 |access-date=November 16, 2007 |website=City of Burlington}}</ref> defeating Kurt Wright in the final round with 48% of the vote.<ref>{{Cite web |date=July 25, 2011 |title=ChoicePlus Pro 2009 Burlington Mayor Round Detail Report |url=http://www.burlingtonvotes.org/20090303/2009%20Burlington%20Mayor%20Round.htm |archive-url=https://web.archive.org/web/20110725111725/http://www.burlingtonvotes.org/20090303/2009%20Burlington%20Mayor%20Round.htm |archive-date=July 25, 2011 |access-date=January 3, 2018}}</ref>

The election results were criticized by [[mathematicians]] and [[Voting theory|voting theorists]] for several [[Pathological (mathematics)|paradoxes]] associated with RCV. These included a [[no-show paradox]], where Kiss won only as a result of 750 votes ranking Kiss in last place.<ref>{{Cite journal |last1=Felsenthal |first1=Dan S. |last2=Tideman |first2=Nicolaus |date=2014 |title=Interacting double monotonicity failure with direction of impact under five voting methods |journal=Mathematical Social Sciences |volume=67 |pages=57–66 |doi=10.1016/j.mathsocsci.2013.08.001 |issn=0165-4896 |quote=A display of non-monotonicity under the Alternative Vote method was reported recently, for the March 2009 mayoral election in Burlington, Vermont.}}</ref><ref name=":823">{{Cite journal |last1=Ornstein |first1=Joseph T. |last2=Norman |first2=Robert Z. |date=October 1, 2014 |title=Frequency of monotonicity failure under Instant Runoff Voting: estimates based on a spatial model of elections |journal=Public Choice |language=en |volume=161 |issue=1–2 |pages=1–9 |doi=10.1007/s11127-013-0118-2 |issn=0048-5829 |s2cid=30833409 |quote=Although the Democrat was the Condorcet winner (a majority of voters preferred him in all two way contests), he received the fewest first-place votes and so was eliminated ... 2009 mayoral election in Burlington, VT, which illustrates the key features of an upward monotonicity failure}}</ref><ref name="Voting Paradoxes23">{{cite web |last=Baruth |first=Philip |date=March 12, 2009 |title=Voting Paradoxes and Perverse Outcomes: Political Scientist Tony Gierzynski Lays Out A Case Against Instant Runoff Voting |url=http://vermontdailybriefing.com/?p=1213 |url-status=dead |archive-url=https://web.archive.org/web/20110726125814/http://vermontdailybriefing.com/?p=1213 |archive-date=July 26, 2011 |publisher=Vermont Daily Briefing}}</ref> Several [[electoral reform]] advocates branded the election a failure after Kiss was elected despite 54% of voters voting for Montroll over Kiss,<ref name="ScoreVotingNet23">{{Cite web |last1=Gierzynski |first1=Anthony |last2=Hamilton |first2=Wes |last3=Smith |first3=Warren D. |date=March 2009 |title=Burlington Vermont 2009 IRV mayoral election |url=http://scorevoting.net/Burlington.html |access-date=October 1, 2017 |website=RangeVoting.org |quote=Montroll was favored over Republican Kurt Wright 56% to 44% ... and over Progressive Bob Kiss 54% to 46% ... In other words, in voting terminology, Montroll was a 'beats-all winner,' also called a 'Condorcet winner' ... However, in the IRV election, Montroll came in third! ...  voters preferred Montroll over every other candidate ... Montroll is the most-approved}}</ref><ref name=":033">{{Cite journal |last1=Bristow-Johnson |first1=Robert |date=2023 |title=The failure of Instant Runoff to accomplish the purpose for which it was adopted: a case study from Burlington Vermont |journal=Constitutional Political Economy |volume=34 |issue=3 |pages=378–389 |doi=10.1007/s10602-023-09393-1}}</ref> violating the [[majority-rule principle]].<ref>{{Cite book |last=Ellenberg |first=Jordan |url=https://archive.org/details/hownottobewrongp0000elle |title=How Not to Be Wrong: The Power of Mathematical Thinking |date=May 29, 2014 |publisher=Penguin |isbn=9780698163843 |page=[https://archive.org/details/hownottobewrongp0000elle/page/385 385] |language=en |quote=a majority of voters liked the centrist candidate Montroll better than Kiss, and a majority of voters liked Montroll better than Wright ... yet Montroll was tossed in the first round. |url-access=registration}}</ref><ref name="Lewyn p. 122 note 19">{{harvnb|Lewyn|2012|p=122|loc=note 19}}: "election where Democratic candidate for mayor was Condorcet winner but finished third behind Republican and 'Progressive,'"</ref><ref>{{Cite journal |last=Stensholt |first=Eivind |date=October 7, 2015 |title=What Happened in Burlington? |journal=NHH Dept. Of Business and Management Science |language=en |volume=Discussion Paper No. 2015/26 |doi=10.2139/ssrn.2670462 |ssrn=2670462 |quote=K was elected even though M was a clear Condorcet winner and W was a clear Plurality winner. |hdl-access=free |hdl=11250/2356264}}</ref> Later analyses showed the race was spoiled, with Wright pulling moderate votes away from Montroll, who would have beat Kiss in a one-on-one race.<ref name="Lewyn p. 122 note 19" /><ref name="Laatu 200923">{{Cite web |last1=Laatu |first1=Juho |last2=Smith |first2=Warren D. |date=March 2009 |title=The Rank-Order Votes in the 2009 Burlington Mayoral Election |url=https://rangevoting.org/JLburl09.txt}}</ref>

The controversy culminated in a successful 2010 [[Popular initiative|initiative]] that repealed RCV by a vote of 52% to 48%,<ref name="rutland_herald23">{{cite web |date=April 27, 2010 |title=Instant run-off voting experiment ends in Burlington : Rutland Herald Online |url=http://www.rutlandherald.com/article/20100427/NEWS03/4270339/1004/NEWS03 |url-status=dead |archive-url=https://web.archive.org/web/20160304055602/http://www.rutlandherald.com/article/20100427/NEWS03/4270339/1004/NEWS03 |archive-date=March 4, 2016 |access-date=April 1, 2016 |website=Rutlandherald.com}}</ref><ref name="BVT2010030223">{{cite web |date=March 2, 2010 |title=Official Results Of 2010 Annual City Election |url=https://www.burlingtonvt.gov/sites/default/files/CT/ElectionResults/20100302/election_summary_report_20100302.pdf |work=City of Burlington}}</ref> a 16-point shift from the 64% who had supported the 2005 ratification.<ref name="burlington_votes23" /> The results of every possible one-on-one election are as follows:
{| class="wikitable"
!Party
!Candidate
!vs. Simpson
!vs. Smith
!vs. Wright
!vs. Kiss
![[Copeland's method|Win : Loss]]
|-
![[File:Democratic Disc.svg|60x60px]]
!Andy Montroll ([[Democratic Party (United States)|D]])
|'''6262 (Montroll) –'''
591 (Simpson)
|'''4570 (Montroll) –'''
2997 (Smith)
|'''4597 (Montroll) –'''
3664 (Wright)
|'''4064 (Montroll) –'''
3476 (Kiss)
|[[Copeland score|'''4 W : 0 L''']]
|-
![[File:Vermont Progressive Disc.svg|60x60px]]
!Bob Kiss ([[Vermont Progressive Party|P]])
|'''5514 (Kiss) –'''
844 (Simpson)
|'''3944 (Kiss) –'''
3576 (Smith)
|'''4313 (Kiss) –'''
4061 (Wright)
|[[Copeland score|'''3 W : 1 L''']]
|
|-
![[File:Republican Disc.svg|60x60px]]
!Kurt Wright ([[Republican Party (United States)|R]])
|'''5270 (Wright) –'''
1310 (Simpson)
|'''3971 (Wright) –'''
3793 (Smith)
|[[Copeland score|'''2 W : 2 L''']]
| colspan="2" |
|-
![[File:Independent Candidate Disc.svg|60x60px]]
!Dan Smith ([[Independent politician|I]])
|'''5570 (Smith) –'''
721 (Simpson)
|[[Copeland score|'''1 W : 3 L''']]
| colspan="3" |
|-
![[File:Green Disc.svg|60x60px]]
!James Simpson ([[Green Party of the United States|G]])
|[[Copeland score|'''0 W : 4 L''']]
| colspan="4" |
|}
This leads to an overall preference ranking of:

# '''Montroll''' – defeats all candidates below, including Kiss (4,064 to 3,476)
# '''Kiss''' – defeats all candidates below, including Wright (4,313 to 4,061)
# '''Wright''' – defeats all candidates below, including Smith (3,971 to 3,793)
# '''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% of voters, over Smith by 60%, and over Simpson by 91% of voters.<ref name="Stensholt23">{{cite journal |last=Stensholt |first=Eivind |year=2015 |title=What Happened in Burlington? |journal=SSRN Electronic Journal |publisher=Elsevier BV |pages=10–12 |doi=10.2139/ssrn.2670462 |issn=1556-5068 |hdl-access=free |hdl=11250/2356264}}</ref>

== Possible real-world occurrences revealed by polling ==

=== 2016 United States presidential election ===
{{Main|2016 United States presidential election}}
Another possible example is the [[2016 United States presidential election]], where polls found several alternatives including [[Bernie Sanders]] and [[Gary Johnson]] defeating both [[Donald Trump]] and [[Hillary Clinton]] under a [[Condorcet method|majority-]] or [[Rated voting|rated-voting rules]] but being squeezed out by both RCV and the [[primary election]] rules.<ref name=":12" /><ref>{{cite journal |last1=Igersheim |first1=Herrade |last2=Durand |first2=François |last3=Hamlin |first3=Aaron |last4=Laslier |first4=Jean-François |date=2022 |title=Comparing Voting Methods : 2016 US Presidential Election |url=https://hal.science/halshs-01972097/ |journal=European Journal of Political Economy |volume=71 |doi=10.1016/j.ejpoleco.2021.102057}}</ref>

=== 2024 United States presidential election ===
{{Main|2024 United States presidential election}}
Election law scholar [[Ned Foley]] criticized the [[two-round system]] variant used in the United States, which has been described as a first round of [[primaries]] before a ''de-facto'' runoff,<ref>{{cite web |last1=Santucci |first1=Jack |last2=Shugart |first2=Matthew |last3=Latner |first3=Michael S. |date=October 16, 2023 |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=July 16, 2024 |access-date=November 15, 2024 |website=Protect Democracy |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) 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>{{cite book |last1=Bowler |first1=Shaun |chapter=The United States: A Case of Duvergerian Equilibrium |date=2009 |title=Duverger's Law of Plurality Voting: The Logic of Party Competition in Canada, India, the United Kingdom and the United States |pages=135–146 |chapter-url=https://link.springer.com/chapter/10.1007/978-0-387-09720-6_9 |access-date=November 15, 2024 |location=New York, New York |publisher=Springer |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}}</ref> for creating a center squeeze in the 2024 presidential election and thus contributing to [[political polarization]]. Foley argued that both the primary system and a hypothetical [[instant-runoff voting]] system led to the election of [[Donald Trump]] by eliminating [[Nikki Haley]], the majority-preferred (or Condorcet) candidate according to polling.<ref>{{cite web |last=Foley |first=Edward B. |date=January 20, 2024 |title=Haley's Campaign Demonstrates the Need for Electoral Reform |url=https://edwardbfoley.substack.com/p/haleys-campaign-demonstrates-the |access-date=November 11, 2024 |website=Common Ground Democracy}}</ref><ref>{{cite web |last=Foley |first=Edward B. |date=November 6, 2024 |title=The Case for Condorcet Voting Is Clear |url=https://edwardbfoley.substack.com/p/the-case-for-condorcet-voting-is |access-date=November 15, 2024 |website=Common Ground Democracy}}</ref><ref name="e736">{{cite news | title=Haley fares best against Biden as Republican contenders hold national leads | publisher=CBS News | date=2024-01-14 | url=https://www.cbsnews.com/news/nikki-haley-fares-best-against-biden-2024-presidential-election-poll/ | access-date=2025-02-28}}</ref><ref name="a987">{{cite web | title=2024 General Election: Haley vs. Biden Polls | website=RealClearPolling | date=2025-02-25 | url=https://www.realclearpolling.com/polls/president/general/2024/haley-vs-biden | access-date=2025-02-28}}</ref>

== See also ==
* [[Centripetalism]]
* [[Independence of irrelevant alternatives]]
* [[Vote splitting]]
* [[Wasted vote]]

== References ==
{{Reflist}}
* {{Dual4|sourcepath=https://electowiki.org/wiki/Center_squeeze|sourcearticle=Center squeeze|revision=1222986402|author(s)=https://electowiki.org/wiki/Center_squeeze?action=history}}

== External links ==
* [https://electionscience.org/learn/library/education/vote-splitting Center for Election Science: Vote Splitting]
* [https://rangevoting.org/IrvCenterSqueeze.html The Center for Range Voting: IRV "center squeeze" pathology]
{{voting systems}}

[[Category:Electoral system criteria]]