Center squeeze

A center squeeze is a kind of spoiler effect shared by rules like the two-round system, plurality-with-primaries, and instant-runoff voting (IRV).^[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]

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.

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]

Overview

Center squeezes are a kind of spoiler effect in which the majority-preferred candidate is eliminated before the final round of an election.^[10][11] 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.^[12][13]

By Black's median-voter 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][10] 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][14][15]

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.^[16] A center squeeze can occur in any situation where voters prefer candidates who hold views similar to their own.^[15]

Indirect effects

Voting systems that suffer from the center-squeeze effect incentivize candidates to avoid the political center,^[13][17][14] creating political polarization in the long run.^[17][14][10] As a result, rules like RCV can lead to polarization even if center squeezes seem empirically rare, because the electoral system provides few incentives encouraging moderates to run for office in the first place.^[17][14][18]

Center-squeeze has been observed in Australia,^[19][20][21] Maine,^[22] Fiji,^[23][24] and various US cities,^[25] all of which use ranked-choice voting, in addition to California (which uses nonpartisan primaries).^[26][27]

Susceptibility by system

Center squeeze is a major feature of two-party systems using primaries or other multiple-round systems.^[12] 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.^[12]

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.^[28][29] Under most models of strategic voting, spoilerproof cardinal methods tend to behave like approval voting and thus converge on the Condorcet winner.^{[30][31][32][33]}

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.^[34]

Example

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. ${\displaystyle A}$ 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.^[29] Thus, ${\displaystyle M}$ is the "best" or "most popular" candidate under both common metrics of candidate quality in social choice.^[10]

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.^[35][36]

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.^[37]

Real-world occurrences

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%[38]
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,^[7][39] despite a majority of voters preferring Begich to either one of his opponents.^[7][40] 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 counter-intuitive behaviors that tend to characterize center-squeeze elections.^[40][7]

The election produced a winner opposed by a majority of voters, with a majority of voters ranking Begich above Peltola and Palin,^[41][7][39] and more than half giving Peltola no support at all.^[41][7] 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.^[7][42][39]

Many social choice theorists criticized the ranked-choice runoff procedure for its pathological behavior.^[43][7] Along with being a center squeeze, the election was a negative voting weight event,^[42] where a voter's ballot has the opposite of its intended effect (e.g. where a candidate would need more votes to lose).^[42][44] In this race, Peltola would have lost if she had received more support from Palin voters,^[45][7][41] and won as a result of 5,200 ballots that ranked her last (after Palin then Begich).^[42][7] 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.^[40][41]

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.^[46] In the 2009 election, incumbent Burlington mayor Bob Kiss won reelection as a member of the Vermont Progressive Party,^[47] defeating Kurt Wright in the final round with 48% of the vote.^[48]

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.^[49][50][51] Several electoral reform advocates branded the election a failure after Kiss was elected despite 54% of voters voting for Montroll over Kiss,^[52][53] violating the majority-rule principle.^[54][55][56] 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.^[55][57]

The controversy culminated in a successful 2010 initiative that repealed RCV by a vote of 52% to 48%,^[58][59] a 16-point shift from the 64% who had supported the 2005 ratification.^[46] 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.^[60][61]

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.^[28][62]

2024 United States presidential election

Main article: 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,^[63][64] for creating a center squeeze in the 2024 presidential election and thus contributing to political polarization. Foley noted both the existing primary system and a hypothetical election instant-runoff system would lead to the election of Donald Trump by eliminating Nikki Haley, the majority-preferred (Condorcet) candidate according to polling.^[65][66]

See also

• Vote splitting
• Wasted vote