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) is clearly visible.

Center squeeze is a kind of independence of irrelevant alternatives violation seen in a number of election rules, such as two-round and instant runoff, for example. In a center squeeze, the Condorcet winner is eliminated before they have the chance to face any of the other candidates in a one-on-one race (which by definition, they would win). The term can also refer^{[ according to whom? ]} to tendency of such rules to encourage polarization among elected officials.

In a center squeeze, candidates focused on appealing to a base of core supporters can squeeze the Condorcet winner out of the race by splitting the first-round vote with them, allowing a more-extreme alternative to win. 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 2022 Alaska special election (where Nick Begich III was eliminated in the first round by Sarah Palin) ^[1] as well as the 2007 French presidential election, where moderate liberal François Bayrou was eliminated by left-wing populist candidate Ségolène Royal, allowing Nicolas Sarkozy to win the second round. ^{[2] [3]}

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. ^{[4] [5]} Candidates focused on appealing to a small base of core supporters can squeeze Condorcet winners out of the race, by splitting the first-round vote needed to survive earlier rounds. ^{[6] [7]}

The "center" in "center squeeze" refers to candidates who are close to the center of public opinion, and is not limited to centrists along a traditional, one-dimensional political spectrum. ^[8] A center squeeze can occur in any situation where voters prefer candidates who hold views similar to their own. ^[9]

Center-squeeze has been observed in Australia, ^{[10] [11]} and various US cities. ^[12]

Susceptibility by system

Center squeeze is a major feature of two-party systems using primaries or other multiple-round systems. ^[6] In these methods, candidates must focus on appealing to their core supporters to ensure they can make it past the first round, where only first-preferences count. ^{[6] [ citation needed ]}

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. ^{[13] [14]} Under most models of strategic voting, spoilerproof cardinal methods tend to behave like approval voting and thus converge on the Condorcet winner. ^{[15] [16] [17] [18]}

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, D21 – Janeček, or Coombs' method. ^[19]

Examples

Start:	Mid-Start:	Mid-End:	End:
33.4%	17.2%	13.4%	35.9%

Alphabet explanation

In Alphabet Land, voters are divided based on how names should be arranged on lists. ${\displaystyle A}$ thinks names should always be in alphabetical order; ${\displaystyle Z}$ thinks they should be in reverse-alphabetical order; and ${\displaystyle M}$ thinks the order should be randomized. In this example, voters' happiness with the outcome falls linearly with the distance (number of letters) between the voter and the candidate.

Because ${\displaystyle M}$ is preferred to both ${\displaystyle A}$ and ${\displaystyle Z}$ in head-to-head match-ups, ${\displaystyle M}$ is the majority-preferred (Condorcet) winner.${\displaystyle M}$ is the socially-optimal winner as well. ^[14] Thus, ${\displaystyle M}$ is the "best" or "most popular" candidate under both common metrics of candidate quality in social choice. ^[4]

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)

${\displaystyle Z}$ wins under a single-round of FPP, with 35.9% of voters choosing them as their favorite. However, over substantially more voters considered ${\displaystyle Z}$ to be their least favorite, with 63.1% of voters preferring ${\displaystyle M}$. ${\displaystyle Z}$ is elected, despite an overwhelming two-thirds majority preferring ${\displaystyle M}$.

Ranked-choice runoff (Alternative, Two-round)

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. ^{[20] [21]}

The first round of the election is the same as the FPP election. ${\displaystyle M}$ has the least first preferences and is therefore eliminated. Their votes are reassigned to ${\displaystyle A}$ and ${\displaystyle Z}$, according to their ballot. In the second round, enough voters who preferred ${\displaystyle M}$ as their first choice took ${\displaystyle A}$ as their second choice and ${\displaystyle A}$ wins the election. RCV thus fails to have a substantial moderating impact, instead causing only a swing from one extreme to the other. ^[22]

2022 Alaska special election

Main article: 2022 Alaska's at-large congressional district special election

Center squeeze

Alaska's at-large congressional district
Turnout	32.2% [23]
Candidate Mary Peltola Sarah Palin Nick Begich III Party Democratic Republican Republican First round 74,817 39.7% 58,339 30.9% 52,536 27.8% Final round 91,266 51.5% 86,026 48.5% Eliminated

The 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, ^{[1] [24]} despite a majority of voters preferring Begich to either one of his opponents. ^{[1] [25]} The ranked-choice runoff election involved one Democrat (Mary Peltola) and two Republicans (Sarah Palin and Nick Begich III). Because the full ballot data for the race was released, 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 behaviors that tend to characterize center-squeeze elections. ^{[25] [1]}

The election produced a winner opposed by a majority of voters, with a majority of voters ranking Begich above Peltola and Palin, ^{[26] [1] [24]} and more than half giving Peltola no support at all. ^{[26] [1]} The election was also notable as a 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. ^{[1] [27] [24]}

Many social choice theorists criticized the ranked-choice runoff procedure for its pathological behavior. ^{[28] [1]} Along with being a center squeeze, the election was a negative voting weight event, ^[27] where a voter's ballot has the opposite of its intended effect (e.g. where a candidate would need more votes to lose). ^{[27] [29]} In this race, Peltola would have lost if she had received more support from Palin voters, ^{[30] [1] [26]} and won as a result of 5,200 ballots that ranked her last (after Palin then Begich). ^{[27] [1]} However, 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 alternatives without these behaviors, such as STAR, approval, or Condorcet voting. ^{[25] [26]}

2009 Burlington mayoral election

Main article: 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 ranked-choice runoff voting, after the 2006 mayoral election. ^[31] In the 2009 election, incumbent Burlington mayor Bob Kiss won reelection as a member of the Vermont Progressive Party, ^[32] defeating Kurt Wright in the final round with 48% of the vote. ^[33]

The election results were criticized by mathematicians and voting theorists for several pathologies associated with RCV. These included a no-show paradox, where Kiss won only as a result of 750 votes ranking Kiss in last place. ^{[34] [35] [36]} Several electoral reform advocates branded the election a failure after Kiss was elected despite 54% of voters voting for Montroll over Kiss, ^{[37] [38]} violating the majority-rule principle. ^{[39] [40] [41]} 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. ^{[40] [42]}

The controversy culminated in a successful 2010 initiative that repealed RCV by a vote of 52% to 48%, ^{[43] [44]} a 16-point shift from the 64% who had supported the 2005 ratification. ^[31] The results of every possible one-on-one election are as follows:

Party	Candidate	vs. Simpson	vs. Smith	vs. Wright	vs. Kiss	Win : Loss
	Andy Montroll (D)	6262 (Montroll) – 591 (Simpson)	4570 (Montroll) – 2997 (Smith)	4597 (Montroll) – 3664 (Wright)	4064 (Montroll) – 3476 (Kiss)	4 W : 0 L
	Bob Kiss (P)	5514 (Kiss) – 844 (Simpson)	3944 (Kiss) – 3576 (Smith)	4313 (Kiss) – 4061 (Wright)	3 W : 1 L
	Kurt Wright (R)	5270 (Wright) – 1310 (Simpson)	3971 (Wright) – 3793 (Smith)	2 W : 2 L
	Dan Smith (I)	5570 (Smith) – 721 (Simpson)	1 W : 3 L
	James Simpson (G)	0 W : 4 L

This leads to an overall preference ranking of:

1. Montroll – defeats all candidates below, including Kiss (4,064 to 3,476)
2. Kiss – defeats all candidates below, including Wright (4,313 to 4,061)
3. Wright – defeats all candidates below, including Smith (3,971 to 3,793)
4. 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. ^[45]

2016 United States presidential election

Main article: 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 majority- or rated-voting rules, but being squeezed out by both RCV and the primary election rules. ^{[13] [46]}

See also

• Vote splitting
• Wasted vote
• Independence of irrelevant alternatives
• Centripetalism

References

1. 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
2. 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
3. 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.
4. 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.
5. 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.
6. 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
7. 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.
8. 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.
9. 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"
10. 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.
11. Lewyn, Michael (2012). "Two Cheers for Instant Runoff Voting". 6 Phoenix L. Rev. 117. Rochester, NY. SSRN   2276015.
12. Vishwanath, Arjun (2021). "Electoral Institutions and Substantive Representation in Local Politics: The Effects of Ranked Choice Voting". SSRN Electronic Journal. doi:10.2139/ssrn.3802566. ISSN   1556-5068.
13. 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.
14. DeGroot, Morris H. (1970). Optimal Statistical Decisions. McGraw-Hill Book Co., New York-London-Sydney. p. 232. ISBN   9780471680291. MR   0356303.
15. 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.
16. 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.
17. 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.
18. Myerson, Roger B.; Weber, Robert J. (1993). "A Theory of Voting Equilibria". The American Political Science Review. 87 (1): 102–114. doi:10.2307/2938959. ISSN   0003-0554. JSTOR   2938959.
19. Shankar, Karthik H. (2022-12-01). "Normed Negative Voting to Depolarize Politics". Group Decision and Negotiation. 31 (6): 1097–1120. doi:10.1007/s10726-022-09799-6. ISSN   1572-9907.
20. "Ranked Choice Voting". FairVote. Retrieved 2024-07-22.
21. "Avoid Vote-Splitting and Weak Plurality Results". RCV Resources. Ranked Choice Voting Resource Center. 2020-11-09. Retrieved 2024-07-22.
22. 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.
23. "State of Alaska | 2022 Special General Election | Election Summary Report | August 16, 2022 | Official Results" (PDF). Alaska Division of Elections. September 2, 2022. Archived (PDF) from the original on August 17, 2022. Retrieved September 2, 2022.
24. 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.
25. 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.
26. Clelland, Jeanne N. (2023-02-28). "Ranked Choice Voting And the Center Squeeze in the Alaska 2022 Special Election: How Might Other Voting Methods Compare?". p. 6. arXiv: 2303.00108v1 [cs.CY].
27. Graham-Squire, Adam; McCune, David (2024-01-02). "Ranked Choice Wackiness in Alaska". Math Horizons. 31 (1): 24–27. doi:10.1080/10724117.2023.2224675. ISSN   1072-4117.
28. Maskin, Eric; Foley, Edward B. (2022-11-01). "Opinion: Alaska's ranked-choice voting is flawed. But there's an easy fix". Washington Post. ISSN   0190-8286 . Retrieved 2024-02-09.
29. Doron, Gideon; Kronick, Richard (1977). "Single Transferrable Vote: An Example of a Perverse Social Choice Function". American Journal of Political Science. 21 (2): 303–311. doi:10.2307/2110496. ISSN   0092-5853. JSTOR   2110496.
30. Hamlin, Aaron (2022-09-16). "RCV Fools Palin Voters into Electing a Progressive Democrat". The Center for Election Science. Retrieved 2024-07-11. 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.
31. "Frequently Asked Questions about Burlington's use of Instant Runoff Voting". Archived from the original on January 30, 2008. Retrieved July 21, 2024. 4. How did this change to IRV come about?
    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.
32. "Mayor Bob Kiss". City of Burlington. Archived from the original on November 29, 2007. Retrieved November 16, 2007.
33. "ChoicePlus Pro 2009 Burlington Mayor Round Detail Report". July 25, 2011. Archived from the original on July 25, 2011. Retrieved January 3, 2018.
34. Felsenthal, Dan S.; Tideman, Nicolaus (2014). "Interacting double monotonicity failure with direction of impact under five voting methods". Mathematical Social Sciences. 67: 57–66. doi:10.1016/j.mathsocsci.2013.08.001. ISSN   0165-4896. A display of non-monotonicity under the Alternative Vote method was reported recently, for the March 2009 mayoral election in Burlington, Vermont.
35. Ornstein, Joseph T.; Norman, Robert Z. (October 1, 2014). "Frequency of monotonicity failure under Instant Runoff Voting: estimates based on a spatial model of elections". Public Choice. 161 (1–2): 1–9. doi:10.1007/s11127-013-0118-2. ISSN   0048-5829. S2CID   30833409. 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
36. Baruth, Philip (March 12, 2009). "Voting Paradoxes and Perverse Outcomes: Political Scientist Tony Gierzynski Lays Out A Case Against Instant Runoff Voting". Vermont Daily Briefing. Archived from the original on July 26, 2011.
37. Gierzynski, Anthony; Hamilton, Wes; Smith, Warren D. (March 2009). "Burlington Vermont 2009 IRV mayoral election". RangeVoting.org. Retrieved October 1, 2017. 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
38. Bristow-Johnson, Robert (2023). "The failure of Instant Runoff to accomplish the purpose for which it was adopted: a case study from Burlington Vermont". Constitutional Political Economy. 34 (3): 378–389. doi:10.1007/s10602-023-09393-1.
39. Ellenberg, Jordan (May 29, 2014). How Not to Be Wrong: The Power of Mathematical Thinking . Penguin. p.  385. ISBN   9780698163843. 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.
40. Lewyn 2012 , p. 122, note 19: "election where Democratic candidate for mayor was Condorcet winner but finished third behind Republican and 'Progressive,'"
41. Stensholt, Eivind (October 7, 2015). "What Happened in Burlington?". NHH Dept. Of Business and Management Science. Discussion Paper No. 2015/26. doi:10.2139/ssrn.2670462. hdl: 11250/2356264 . SSRN   2670462. K was elected even though M was a clear Condorcet winner and W was a clear Plurality winner.
42. Laatu, Juho; Smith, Warren D. (March 2009). "The Rank-Order Votes in the 2009 Burlington Mayoral Election".
43. "Instant run-off voting experiment ends in Burlington : Rutland Herald Online". Rutlandherald.com. April 27, 2010. Archived from the original on March 4, 2016. Retrieved April 1, 2016.
44. "Official Results Of 2010 Annual City Election" (PDF). City of Burlington. March 2, 2010.
45. Stensholt, Eivind (2015). "What Happened in Burlington?". SSRN Electronic Journal. Elsevier BV: 10–12. doi:10.2139/ssrn.2670462. hdl: 11250/2356264 . ISSN   1556-5068.
46. 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.

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External links

• Center for Election Science: Vote Splitting
• The Center for Range Voting: IRV "center squeeze" pathology