Center squeeze

From electowiki

The center squeeze effect refers to a class of voting scenarios which are troublesome for many voting systems. In such a scenario, the candidates exist along some spectrum from "left" to "right", with a "center" candidate who is the Condorcet winner and/or utilitarian winner, yet who loses the election.[1][2][3][4]

Many consider that the Condorcet winner (the candidate that would beat any other candidate in a head-to-head election) or utilitarian winner (the candidate rated most highly by the electorate) is the rightful winner of an election. Failing to select this candidate can encourage strategy (typically, favorite betrayal) from one of the other groups. Note, however, 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 "left wing" bullet votes in Approval voting, see Chicken dilemma).

Voting systems that suffer from the center-squeeze effect exhibit a bias in favor of more extreme candidates, which leads to unrepresentative winners and political polarization.[5][6]

(Note that "center" does not refer to an absolute political spectrum, but relative to the ideologies of the voters. 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. This also doesn't imply any particular spectrum, such as the American left-right political spectrum; it could be any attribute on which candidates are evaluated, or multiple such attributes.[7])

While typically illustrated in a simple case with three candidates, the effect can occur with any number of candidates: In systems that suffer from center squeeze, the more candidates there are crowding the center, the less likely a good representative is to win. It may eliminate not just the highest-ranked/rated candidate, but also the 2nd-highest, 3rd-highest, and so on.

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,[2] two-round runoff voting,[2] and IRV.[1][8][6][9]

Systems that can do either well or poorly in a center squeeze situation include most graded Bucklin systems, Approval voting,[5] and Score voting.

Systems that generally do well with center squeeze include Condorcet systems. Some people suggest that a center squeeze scenario could become an opportunity for one of the wings to use burial strategy and create an artificial Condorcet cycle. However, Condorcet cycles are exceedingly rare: only one instance is known for a real-world set of ranked ballots. Furthermore, purposefully trying to inducing a cycle by voting for less-preferred candidates risks getting the less-preferred candidates elected.

Primary system

Center squeeze is also a feature of two-party systems which use a primary to select candidates. In this case, the two parties tend to separate ideologically, and a "center" candidate, ideologically between the two, would find themselves unable to win a primary against another candidate closer to the centroid of the party. The center candidate would win in any one-on-one vote over the whole voting population, but will not win in the subset of the population represented by a party.

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.

External links

References

  1. a b Lewyn, Michael (2012). "Two Cheers for Instant Runoff Voting". 6 Phoenix L. Rev. Rochester, NY. 117. third place Candidate C is a centrist who is in fact 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
  2. a b c 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
  3. Merrill, Samuel (1984). "A Comparison of Efficiency of Multicandidate Electoral Systems". American Journal of Political Science. 28 (1): 23. doi:10.2307/2110786. ISSN 0092-5853. However, squeezed by surrounding opponents, a centrist candidate may receive few first-place votes and be eliminated under Hare.
  4. Stensholt, Eivind (2015-10-07). "What Happened in Burlington?". Discussion Papers: 13. There is a Condorcet ranking according to distance from the center, but Condorcet winner M, the most central candidate, was squeezed between the two others, got the smallest primary support, and was eliminated.
  5. a b 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.
  6. a b 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.
  7. 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. 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.
  8. Verma, Dhruv (2021-01-01). "Reflecting People's Will: Evaluating elections with computer aided simulations". Open Political Science. 4 (1): 228–237. doi:10.1515/openps-2021-0021. ISSN 2543-8042. Instant runoff corrects for the spoiler effect to some extent and reduces strategic voting, however, centre squeeze is a real issue in a three legged race. With two dominant parties, it works well in that it establishes a clearer winner than plurality elections. It has however been observed that the long term end results are likely to be similar, with the same major parties and elimination of smaller parties, similar to plurality voting (but to a lesser extent) as has been witnessed in the Australian elections.
  9. Poundstone, William. (2013). Gaming the vote : why elections aren't fair (and what we can do about it). Farrar, Straus and Giroux. pp. 168, 197, 234. ISBN 9781429957649. OCLC 872601019. IRV is subject to something called the "center squeeze." A popular moderate can receive relatively few first-place votes through no fault of her own but because of vote splitting from candidates to the right and left.