Center squeeze

A center squeeze is a kind of spoiler effect shared by rules like the two-round system, plurality-with-primaries, and ranked-choice voting (RCV).^[1] In a center squeeze, the majority-preferred and socially optimal candidate is eliminated in favor of a more extreme alternative before having a chance to face another candidate in a one-on-one race.^[2]^[3] Systems with center-squeeze are sometimes called centrifugal ("center-fleeing") because they encourage political polarization.^[4]

Candidates focused on appealing to a small base of core supporters can "squeeze" broadly-popular candidates trapped between them out of the race, by splitting the first-round vote needed to survive earlier rounds.^[1]^[5]^[6] This effect was first predicted by social choice theorists in the 1940s and 50s, and has since been documented in various countries using plurality-style electoral systems.

Famous examples of center squeezes include the Alaska's 2022 special election (where Nick Begich III was eliminated in the first round by Sarah Palin)^[7] as well as the 2007 French presidential election, where moderate liberal François Bayrou was eliminated by left-populist Ségolène Royal, allowing the right-wing Nicolas Sarkozy to win the second round.^[8]^[9]

^ ^a ^b Merrill, Samuel (1985). "A statistical model for Condorcet efficiency based on simulation under spatial model assumptions". Public Choice. 47 (2): 389–403. doi:10.1007/bf00127534. ISSN 0048-5829. the 'squeeze effect' that tends to reduce Condorcet efficiency if the relative dispersion (RD) of candidates is low. This effect is particularly strong for the plurality, runoff, and Hare systems, for which the garnering of first-place votes in a large field is essential to winning
^ Merrill, Samuel (1984). "A Comparison of Efficiency of Multicandidate Electoral Systems". American Journal of Political Science. 28 (1): 23–48. doi:10.2307/2110786. ISSN 0092-5853. JSTOR 2110786. However, squeezed by surrounding opponents, a centrist candidate may receive few first-place votes and be eliminated under Hare.
^ Atkinson, Nathan; Ganz, Scott C. (2022-10-30). "The flaw in ranked-choice voting: rewarding extremists". The Hill. Retrieved 2023-05-14. 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.
^ Foley, Edward B. (2024-08-17). "What is "Centripetalism" and Why Does It Matter?". Common Ground Democracy. Retrieved 2025-01-30.
^ McGann, Anthony J.; Koetzle, William; Grofman, Bernard (2002). "How an Ideologically Concentrated Minority Can Trump a Dispersed Majority: Nonmedian Voter Results for Plurality, Run-off, and Sequential Elimination Elections". American Journal of Political Science. 46 (1): 134–147. doi:10.2307/3088418. ISSN 0092-5853. JSTOR 3088418. As with simple plurality elections, it is apparent the outcome will be highly sensitive to the distribution of candidates.
^ "IRV and Core Support". The Center for Election Science. Retrieved December 4, 2019.
^ Graham-Squire, Adam; McCune, David (2022-09-11). "A Mathematical Analysis of the 2022 Alaska Special Election for US House". p. 2. arXiv:2209.04764v3 [econ.GN]. 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
^ Balinski, Michel; Laraki, Rida (2011), Dolez, Bernard; Grofman, Bernard; Laurent, Annie (eds.), "Election by Majority Judgment: Experimental Evidence", In Situ and Laboratory Experiments on Electoral Law Reform: French Presidential Elections, New York, NY: Springer, pp. 13–54, doi:10.1007/978-1-4419-7539-3_2, ISBN 978-1-4419-7539-3, retrieved 2024-10-31
^ Balinski, Michel; Laraki, Rida (2020-03-01). "Majority judgment vs. majority rule". Social Choice and Welfare. 54 (2): 429–461. doi:10.1007/s00355-019-01200-x. ISSN 1432-217X.

[Merril_198522422232-1] Merrill, Samuel (1985). "A statistical model for Condorcet efficiency based on simulation under spatial model assumptions". Public Choice. 47 (2): 389–403. doi:10.1007/bf00127534. ISSN 0048-5829. the 'squeeze effect' that tends to reduce Condorcet efficiency if the relative dispersion (RD) of candidates is low. This effect is particularly strong for the plurality, runoff, and Hare systems, for which the garnering of first-place votes in a large field is essential to winning

[Merrill_19842223-2] Merrill, Samuel (1984). "A Comparison of Efficiency of Multicandidate Electoral Systems". American Journal of Political Science. 28 (1): 23–48. doi:10.2307/2110786. ISSN 0092-5853. JSTOR 2110786. However, squeezed by surrounding opponents, a centrist candidate may receive few first-place votes and be eliminated under Hare.

[:0322232-3] Atkinson, Nathan; Ganz, Scott C. (2022-10-30). "The flaw in ranked-choice voting: rewarding extremists". The Hill. Retrieved 2023-05-14. 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.

[4] Foley, Edward B. (2024-08-17). "What is "Centripetalism" and Why Does It Matter?". Common Ground Democracy. Retrieved 2025-01-30.

[:8522222-5] McGann, Anthony J.; Koetzle, William; Grofman, Bernard (2002). "How an Ideologically Concentrated Minority Can Trump a Dispersed Majority: Nonmedian Voter Results for Plurality, Run-off, and Sequential Elimination Elections". American Journal of Political Science. 46 (1): 134–147. doi:10.2307/3088418. ISSN 0092-5853. JSTOR 3088418. As with simple plurality elections, it is apparent the outcome will be highly sensitive to the distribution of candidates.

[:2322-6] "IRV and Core Support". The Center for Election Science. Retrieved December 4, 2019.

[Analysis_Alaska323-7] Graham-Squire, Adam; McCune, David (2022-09-11). "A Mathematical Analysis of the 2022 Alaska Special Election for US House". p. 2. arXiv:2209.04764v3 [econ.GN]. 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

[8] Balinski, Michel; Laraki, Rida (2011), Dolez, Bernard; Grofman, Bernard; Laurent, Annie (eds.), "Election by Majority Judgment: Experimental Evidence", In Situ and Laboratory Experiments on Electoral Law Reform: French Presidential Elections, New York, NY: Springer, pp. 13–54, doi:10.1007/978-1-4419-7539-3_2, ISBN 978-1-4419-7539-3, retrieved 2024-10-31

[9] Balinski, Michel; Laraki, Rida (2020-03-01). "Majority judgment vs. majority rule". Social Choice and Welfare. 54 (2): 429–461. doi:10.1007/s00355-019-01200-x. ISSN 1432-217X.

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