Center squeeze

Example

In Alphabet Land, voters want their name to be placed close to the start of a list. Candidate ${\displaystyle A}$ thinks names should be listed in alphabetical order, and Candidate ${\displaystyle Z}$ thinks they should be in reverse-alphabetical order. Candidate ${\displaystyle M}$ thinks the order should be random.

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, and if voters' unhappiness with the result is equal to their ideological distance from the winner, ${\displaystyle M}$ will be the socially-optimal winner as well. Thus, ${\displaystyle M}$ is the "best" or "most popular" candidate under both common metrics of candidate quality in social choice.

First-preference plurality

If we use a single-round of first-preference plurality (FPP) then ${\displaystyle Z}$ wins, with 35.9% of voters choosing them as their favorite. However, most voters considered ${\displaystyle Z}$ their least-favorite candidate, and almost two-thirds (63.1%) of the voters preferred ${\displaystyle M}$ to ${\displaystyle Z}$.

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.

If we use RCV instead of FPP then the first round of the election is the same as the FPP election. But then ${\displaystyle M}$, because they have the least first preferences, is eliminated. Their votes are then 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 only causing a swing from one extreme to the other.

Real-world occurrences

1991 Louisiana gubernatorial election

Buddy Roemer was squeezed out of the election, leaving corrupt Edwin Edwards and white supremacist David Duke in the runoff.

2007 French presidential election

The 2007 French presidential election was seen as an example of a center squeeze. The second round saw Nicolas Sarkozy, a conservative, face off against Ségolène Royal, a socialist. Moderate liberal François Bayrou was eliminated in the first round, despite polls showing a majority of voters preferred Bayrou in a one-on-one match with either of his opponents.

2012 Egyptian presidential election

In the 2012 Egyptian presidential election, held using the two-round system, vote-splitting among three leading moderate, non-Islamist candidates caused them all to be eliminated in the first round. This allowed the two more polarizing candidates, Mohamed Morsi and Ahmed Shafik, to advance to the runoff, despite pre-election polls suggesting the eliminated moderates would have defeated either finalist in a head-to-head contest. This led to the June 2013 Egyptian protests and 2013 Egyptian coup d'état.

2022 Alaska special election

The 2022 Alaska special election seat was seen as an example of a center squeeze, where Nick Begich III was eliminated in the first round by right-wing spoiler Sarah Palin, despite a majority of voters preferring Begich to either one of his opponents. 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.

The election produced a winner opposed by a majority of voters, with a majority of voters ranking Begich above Peltola and Palin, and more than half giving Peltola no support at all. 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.

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

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

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. Several electoral reform advocates branded the election a failure after Kiss was elected despite 54% of voters voting for Montroll over Kiss, violating the majority-rule principle. 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.

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

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.

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.

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, for creating a center squeeze in the 2024 presidential election and thus contributing to political polarization. Foley stated that both the existing primary system and a hypothetical election instant-runoff system would have led to the election of Donald Trump by eliminating Nikki Haley. He claimed that Haley would have been the majority-preferred (Condorcet) candidate according to polling, but he only quoted polls on Haley beating Biden, but none on Haley beating either Trump or Harris.