Center squeeze

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 heatmap. The bias of FPTP, runoffs or primaries, and RCV (center-left column) towards extreme candidates is clearly visible.
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In social choice, a center squeeze is a kind of spoiler effect common to plurality-elimination rules like the two-round system, plurality-with-primaries, and ranked-choice voting (RCV).[1] In a center squeeze, a majority-preferred and socially-optimal candidate is eliminated in favor of a more extreme alternative.[2][3] Extreme or polarizing candidates who focus on appealing to a small base of core supporters can thus "squeeze" broadly-popular candidates trapped between them, starving them of the first preferences they need to survive early rounds.[1][4][5]

The term "center squeeze" refers to candidates who are close to the center of public opinion, and as a result is not limited to centrists along the traditional political spectrum.[6] Center squeezes can occur in any situation where voters prefer candidates who hold views similar to their own.[7] By Black's theorem, the candidate who appeals most to the median voter will be the majority-preferred candidate, which means they will be elected by any method compatible with majority-rule.[1][2] However, in methods that strongly prioritize first preferences, these candidates are often eliminated early on because they aim for broad appeal rather than strong base support.[1][8][9]

Voting systems that suffer from the center-squeeze effect incentivize candidates to avoid the political center,[4][10] creating political polarization in the long run.[8][10][11] As a result, rules like RCV can lead to extreme winners even if center-squeezes seem empirically rare, because the rules disincentivize moderates from running for office in the first place.[10][12][13] The effect was first predicted by social choice theorists in the 1940s[14] and has since been confirmed empirically by studies of politics in Australia,[12][15][16] California,[17][18] Maine,[19] and Fiji.[20][21]

Famous examples of center-squeezes include the 2022 Alaska special election, where Nick Begich III was eliminated in the first round by right-wing spoiler Sarah Palin,[22][23] despite a majority of voters preferring Begich to either one of his opponents.[22][24] 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 majority- or rated-voting rules, but being squeezed out by both the IRV and primary election rules.[25][26][27]

The voting systems most strongly affected by center squeeze are plurality-with-primaries, two-round runoff, and ranked-choice voting (RCV).[1][28] By contrast, Condorcet and rated voting methods are not affected by this pathology. Condorcet methods are insulated from center-squeezes by the median voter theorem,[28][21][29] while rated voting systems like score or approval voting are protected by closely-related results.[30][31][32]

  1. ^ a b c d e 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
  2. ^ a b 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.
  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. ^ a b 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.
  5. ^ "IRV and Core Support". The Center for Election Science. Retrieved December 4, 2019.
  6. ^ Davis, Otto A.; Hinich, Melvin J.; Ordeshook, Peter C. (1970-01-01). "An Expository Development of a Mathematical Model of the Electoral Process". The American Political Science Review. 64 (2): 426–448. doi:10.2307/1953842. JSTOR 1953842. S2CID 1161006. 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.
  7. ^ Lewyn, Michael (2012). "Two Cheers for Instant Runoff Voting". 6 Phoenix L. Rev. 117. Rochester, NY. SSRN 2276015. third place 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, C would prevail over both Candidates A ... and B ... in a one-on-one runoff election. Yet, C would not prevail under IRV because he or she finished third and thus would be the first candidate eliminated.
  8. ^ a b Ogren, Marcus (2024-08-01). "Candidate incentive distributions: How voting methods shape electoral incentives". Electoral Studies. 90: 102799. arXiv:2306.07147. doi:10.1016/j.electstud.2024.102799. ISSN 0261-3794.
  9. ^ Lewyn, Michael (2012). "Two Cheers for Instant Runoff Voting". 6 Phoenix L. Rev. 117. Rochester, NY. SSRN 2276015. 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
  10. ^ a b c Robinette, Robbie (2023-09-01). "Implications of strategic position choices by candidates". Constitutional Political Economy. 34 (3): 445–457. doi:10.1007/s10602-022-09378-6. ISSN 1572-9966.
  11. ^ 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.
  12. ^ a b Mussel, Johanan D.; Schlechta, Henry (2023-07-21). "Australia: No party convergence where we would most expect it". Party Politics. doi:10.1177/13540688231189363. ISSN 1354-0688.
  13. ^ Ogren, Marcus (2024-05-08). "The primordial election that is never held". Medium. Retrieved 2024-09-05.
  14. ^ Black, Duncan (1948). "On the Rationale of Group Decision-making". Journal of Political Economy. 56 (1): 23–34. doi:10.1086/256633. ISSN 0022-3808. JSTOR 1825026.
  15. ^ Lewyn, Michael (2012). "Two Cheers for Instant Runoff Voting". 6 Phoenix L. Rev. 117. Rochester, NY. SSRN 2276015.
  16. ^ Ogren, Marcus (2022-11-16). "RCV in the 2022 Australian Election". Medium. Retrieved 2024-09-05.
  17. ^ Kousser, Thad; Phillips, Justin; Shor, Boris (2016). "Reform and Representation: A New Method Applied to Recent Electoral Changes*". Political Science Research and Methods. 6 (4): 809–827. doi:10.1017/psrm.2016.43. ISSN 2049-8470. SSRN 2260083. neither the Citizens Redistricting Commission nor the top-two primary immediately halted the continuing partisan polarization of California's elected lawmakers or their drift away from the average voter
  18. ^ Kousser, Thad. "California's jungle primary sets up polarized governor's race for November". The Conversation. Retrieved 2018-06-23. The idea was that by opening up primaries to all voters, regardless of party, a flood of new centrist voters would arrive. That would give moderate candidates a route to victory .. Candidates did not represent voters any better after the reforms, taking positions just as polarized as they did before the top two. We detected no shift toward the ideological middle.
  19. ^ "The Effect of Ranked-Choice Voting in Maine | MIT Election Lab". electionlab.mit.edu. Retrieved 2024-07-25. One of the main claims made by reformers about RCV is that it will make campaigns more civil, as campaigns will have the incentive to seek the second-place vote of supporters of different candidates. To study this claim, I first conducted a difference-in-differences analysis on independent expenditures for and against candidates. In this analysis, I found that negative spending increased significantly in Maine following the implementation of ranked-choice voting, casting doubt on the claim that RCV makes campaigns more civil. To provide more evidence, I also created a dataset of all Facebook advertisements that mentioned any congressional candidates for 2018, the first year that RCV was used in Maine. I then conducted a sentiment analysis to find each advertisement's sentiment (whether it was negative or not). I then used genetic matching to approximate an experiment to find the impact of RCV on civility. In doing so, I found that the 2018 campaign was even more negative than in paired districts around the country.
  20. ^ Fraenkel, Jon; Grofman, Bernard (2006-06-01). "Does the Alternative Vote Foster Moderation in Ethnically Divided Societies?: The Case of Fiji". Comparative Political Studies. 39 (5): 623–651. doi:10.1177/0010414005285032. ISSN 0010-4140. Fiji's objective of ameliorating ethnic divisions by the adoption of AV was not successful. In elections in 1999 and 2001, moderate parties would have fared better under a proportional representation system
  21. ^ a b Fraenkel, Jon; Grofman, Bernard (2006-06-01). "The Failure of the Alternative Vote as a Tool for Ethnic Moderation in Fiji: A Rejoinder to Horowitz". Comparative Political Studies. 39 (5): 663–666. doi:10.1177/0010414005285035. ISSN 0010-4140.
  22. ^ a b 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
  23. ^ 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 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.
  24. ^ Maskin, Eric; Foley, Edward B. (2022-11-01). "Alaska's ranked-choice voting is flawed. But there's an easy fix". Washington Post. ISSN 0190-8286. Retrieved 2024-02-09.
  25. ^ Potthoff, Richard F.; Munger, Michael C. (November 2021). "Condorcet Loser in 2016: Apparently Trump; Condorcet Winner: Not Clinton?". American Politics Research. 49 (6): 618–636. doi:10.1177/1532673X211009499. ISSN 1532-673X.
  26. ^ Igersheim, Herrade; Durand, François; Hamlin, Aaron; Laslier, Jean-François (2022). "Comparing Voting Methods : 2016 US Presidential Election". European Journal of Political Economy. 71. doi:10.1016/j.ejpoleco.2021.102057.
  27. ^ Atkinson, Nathan; Foley, Edward B.; Ganz, Scott (2023). "Beyond the Spoiler Effect: Can Ranked Choice Voting Solve the Problem of Political Polarization?". SSRN Electronic Journal. doi:10.2139/ssrn.4411173. ISSN 1556-5068.
  28. ^ a b Foley, Edward B. (2024-08-17). "What is "Centripetalism" and Why Does It Matter?". Common Ground Democracy. Retrieved 2024-08-18. Instant Runoff Voting, however, achieves the most centripetal result (when it does) only by happenstance, not intrinsically, and fails to do so when the electorate is especially polarized
  29. ^ Black, Duncan (1948). "On the Rationale of Group Decision-making". Journal of Political Economy. 56 (1): 23–34. doi:10.1086/256633. ISSN 0022-3808. JSTOR 1825026.
  30. ^ Laslier, Jean-François (January 2009). "The Leader Rule: A Model of Strategic Approval Voting in a Large Electorate". Journal of Theoretical Politics. 21 (1): 113–136. doi:10.1177/0951629808097286. ISSN 0951-6298.
  31. ^ Cox, Gary W. (1985). "Electoral Equilibrium under Approval Voting". American Journal of Political Science. 29 (1): 112–118. doi:10.2307/2111214. ISSN 0092-5853. JSTOR 2111214.
  32. ^ Laslier, Jean-François; Sanver, M. Remzi, eds. (2010). Handbook on Approval Voting. Studies in Choice and Welfare. Berlin, Heidelberg: Springer Berlin Heidelberg. p. 2. doi:10.1007/978-3-642-02839-7. ISBN 978-3-642-02838-0. 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.