# Center squeeze

The center squeeze effect refers to a class of voting scenarios which are troublesome for many voting systems. In such a scenario, the strongest three candidates can be arranged on a spectrum such as "left", "center", and "right"; and of the three, the "center" candidate is the Condorcet winner or utilitarian winner, but loses the election.[1][2][3]

Most consider that if the center candidate is not too far behind in honest plurality, they should be the winner, as they would beat any other candidate in a head-to-head election, and otherwise, the voting system is encouraging strategy (typically, a favorite betrayal) from one of the other two groups. (Though note that any voting method avoiding center squeeze can also incentivize strategy if one of the wings thinks they can squeeze out victory for their preferred candidate i.e. if the "liberal" wing bullet votes in Approval voting).

(Note that "center" does not refer to an absolute political spectrum, but relative to the ideologies of the candidates. If the Libertarian Party holds an election, for instance, the winner should be near the center of Libertarian ideology, but if there are other candidates to either side, the most-representative candidate cannot win.)

The effect is not limited to 3 candidates: The more candidates there are crowding the center, the less likely they are to win.

## Three-candidate example

For example, consider the following election:

```1031: A>B>C
415: B>A>C
446: B>C>A
1108: C>B>A
```

On a 2-dimensional political compass with 3 candidates, candidate B is the Condorcet winner and utilitarian winner, but is squeezed out by A and C on either side:

C would win under a single-round of FPTP, but if there is a runoff, then more of B's votes transfer to A, making A the winner:

Either way, the winner is not as good of a representative of the electorate as candidate B.

## With more candidates

A 5-candidate FPTP election, where center-squeeze eliminates the 3 center candidates and elects an extremist

Center squeeze can occur under FPTP and two-round runoff with any number of candidates. If the center candidates are close enough together, honest votes will be split between all of them, electing the worst (FPTP) or second-worst (T2R) candidate.

Animation of a 5-candidate IRV election, where center-squeeze eliminates each of the 3 center candidates, in turn, and elects an extremist

A similar effect can occur under IRV, electing the second-worst candidate, though the effect is less extreme, since eliminated candidates transfer votes to nearby candidates, making it harder for them to be eliminated.

## Prevalence

Voting systems that have serious problems with center squeeze include FPTP, two-round runoff voting, and IRV.

Systems that can do either well or poorly in a center squeeze situation include most graded Bucklin systems and score voting.

Systems that generally do well with center squeeze include Condorcet systems (although in some cases, a center squeeze scenario could become an opportunity for one of the wings to use burial strategy and create an artificial Condorcet cycle).

## Effect of strategy

Some voting methods are not only vulnerable to center squeeze, but in fact, make it difficult for voters to combat the effect with strategy. IRV may be one of these: Suppose the 1st choices of the voters are 25% for the Very Liberal party, 10% for the Liberal party, and 20% for the Center party, with the rest going to the Conservative party. Putting the Center party strategically 1st in IRV risks eliminating the Liberal party, at which point their votes may go more towards the Very Liberal party, eliminating the Center party; if a liberal voter desiring consensus instead puts the Liberal party 1st, that makes it more likely the Center party will be eliminated first, and then their voters' 2nd choice may help the Liberal party eliminate the Very Liberal party, resulting in more consensus overall than if the Very Liberal party had won.

## Notes

3-candidate example for center squeeze under Condorcet:

48 A>B

5 B

47 C>B

When ignoring C, the votes become 52 voters preferring B to 48 preferring A. If ignoring A instead, the votes become 53 to 47 B to C. So in both directions, the center candidate is preferred by a majority, and thus is the Condorcet winner.