Wikipedia

Draft:Center squeeze

Part of the Politics and Economics series
Electoral systems
Ballot box
Single-winner methods
Single vote-runoff methods

Condorcet methods

Positional voting

Cardinal voting

Proportional representation
Party-list

Quota-remainder methods

Approval-based committees

Fractional social choice

Mixed systems
By type of representation

Non-compensatory mixed systems

Compensatory mixed systems

Voting system criteria
Spoiler-resistance

Strategy-resistance

Rational response

Social and collective choice
Impossibility theorems

Positive results

Tournament sets

icon Politics portal icon Economics portal

Center-squeezes are a class of elections where the majority-preferred and socially-best candidate tends to be eliminated by plurality rule and ranked-choice runoff (ranked-choice voting).[1][2] In a center-squeeze, the candidates are arranged along an ideological spectrum. By the median voter theorem, the candidate who wins over the voter closest to the median will always be the majority-preferred candidate in this scenario.[2][3][4]

However, in methods that strongly prioritize first preferences, majority-preferred candidates are often eliminated because they appeal to a broad coalition of voters, rather than to narrowly appealing to their party's base.[2][4] Voting systems that suffer from the center-squeeze effect have a bias in favor of more extreme candidates, leading to unrepresentative winners and political polarization in the long run.[1][5] Candidates in such systems are incentivized to avoid the political center.[6]

Despite use of the term "center", the term does not refer to any particular political spectrum (such as the left-right spectrum). The effect is visible whenever voters prefer candidates who are similar to them along some trait (i.e. when they have single peaked preferences).[7]

Election systems that exhibit center-squeeze candidates tend to elect leaders who are unrepresentative of the voting population. Candidates who draw support from across the voting population tend to perform worse in these elections, lacking enough staunch support to outcompete extreme candidates whose voters like fewer of the available options. Repeated poor results from consensus candidates discourages them from running in subsequent elections and voters abandon these candidates in order to form voting blocks with more extreme leaders.

Voting systems that have serious problems with center squeeze include first-preference plurality, two-round runoff,[2] and ranked-choice runoff voting (RCV).[2] By contrast, Condorcet and rated voting methods are not affected by such pathologies. Condorcet methods are insulated from center-squeezes by the median voter theorem, which shows that if candidates are arranged along a one-dimensional ideological spectrum, all Condorcet methods will select the candidate closest to the median voter. Rated voting systems like score or approval voting are also insulated from the pathology by closely-related results.[8]

Examples

edit
 
Top: 1031 Mid-top: 532 Mid-end: 415 End: 1108

Say there is a country using a three-letter alphabet. Voters are divided by alphabetical order of names. Candidate A thinks names should always be in alphabetical order; Candidate C believes they should be in reverse-alphabetical order; and Candidate B is in the middle, and thinks both sides should take turns alternating. Candidates and voters are therefore polarized along a political spectrum, as seen in the diagram left.

Voters with names near the beginning of the alphabet vote for A first, but are willing to accept B as a second choice. Similarly, voters who support C are willing to accept A as a second choice.

Because candidate B is preferred to both candidate A and candidate C in head-to-head matchups, candidate B is the majority-preferred (Condorcet) winner. If voters' utility falls linearly with respect to distance, the median minimizes the mean absolute error, making B the socially-optimal winner as well.[9] Alternatively, this also holds true if the score for each candidate is a decreasing function of distance and the distribution of voters is roughly symmetric, in which case the median are equal. However, candidate B is experiencing a center-squeeze, losing first-preference votes to candidates A and C on either side.

First-past-the-post

edit
 
Vote totals of an example first-past-the-post election if all voters supported their favorite candidate.

Candidate C wins under a single-round of FPTP, with 1108 voters choosing them as their absolute preference. However, significantly more voters considered candidate C to be their least preferred candidate, with 1563 out of a total voters preferring either candidates A and B. With majority opposition, and a core group of supporters so far from the median voter, candidate C should be considered rather unrepresentative of the voting population.

Instant-runoff (Alternative vote, Ranked-choice voting)

edit

Ranked-choice runoff tries to address the vote-splitting of first-past-the-post by replacing it with a series of first-past-the-post elections, where the loser is eliminated in each round.[10] Voters submit ballots ranking their preferences, and each voter's highest-ranked candidate receives their support. The candidate in last place is eliminated and their votes redistributed according to each ballot's next preferred candidate. This repeats until all candidates except one have been eliminated.[11]

The first round of the election proceeds exactly the same as the first-past-the-post election with candidate C having a slight lead. No candidate has a majority of the remaining votes, and so candidate B is eliminated in last place. Their votes are redistributed to both candidates A and C, according to their voter's ballot preferences. In the second round, enough voters who preferred candidate B as their first choice took candidate A as their second choice and candidate A wins the election. With near-majority opposition and a position far to the left of most voters, candidate A is also unrepresentative of the electorate.

 
Vote totals of the second round of an example RCV election where candidate B experienced center-squeeze.

Notable elections

edit

2022 Alaska Special Election

edit
Main article: 2022 Alaska's at-large congressional district special election
Alaska's at-large congressional district
Turnout32.2%[12]
       
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 for the state's single House of Representatives seat was a prominent and conclusive example of a center squeeze. 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, election scientists were able determine that Palin spoiled the race for Begich.

Begich was preferred to both Palin and Peltola in head-to-head matchups, but was eliminated in the first round after pulling slightly fewer first-preference votes than Peltola and Palin.[13][14] Of those who chose to support a second candidate, Begich's supporters were split roughly evenly between Palin and Peltola, whereas Palin's supporter's overwhelmingly preferred Begich to Peltola.[15] The final winner, Peltola, received no support from a majority of voters (having been ranked last on 52%).[13][16]

Many social choice theorists criticized the ranked-choice runoff procedure for its pathological behavior.[17][18] Along with being a center-squeeze, the election was also a negative voting weight event,[16] where a voter's ballot has the opposite of its intended effect (i.e. a candidate being eliminated for having "too many votes").[16][19] In this race, Peltola won as a result of 5,200 ballots that ranked her last (after Palin then Begich),[16][20] and would have lost if she had received more support from Palin voters.[16][21][22][23][24]

2009 Burlington mayoral election

edit
Main article: 2009 Burlington mayoral election

The 2009 Burlington mayoral election was held in March 2009 for the city of Burlington, Vermont. This was the second mayoral election since the city's 2005 change to ranked-choice runoff voting, after the 2006 mayoral election.[25] In the 2009 election, incumbent Burlington mayor (Bob Kiss) won reelection as a member of the Vermont Progressive Party,[26] defeating Kurt Wright in the final round with 48% of the vote (51.5% excluding exhausted ballots).

Some mathematicians and voting theorists criticized the election results as revealing several pathologies associated with ranked-choice runoff voting, including the monotonicity criterion, noting that Kiss was elected as a result of 750 votes cast against him (ranking Kiss in last place).[27][28][29] Several electoral reform advocates branded the election a failure after Kiss was elected despite 54% of voters voting for Montroll over Kiss,[30][31] violating the principle of majority rule.[32][33][34] Later analyses showed the race was spoiled, with Wright acting as a spoiler pulling moderate votes from Montroll, who would have beaten Kiss in a one-on-one race.[35][32]

The resulting controversy culminated in a successful 2010 initiative repealing RCV by a vote of 52% to 48%.[29][36][37][38]

Tournament matrix

edit

The results of every possible one-on-one election can be completed as follows:

Party Candidate vs. Simpson vs. Smith vs. Wright vs. Montroll 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, preferred over Wright by 56% of voters, over Smith by 60%, and over Simpson by 91% of voters.[39][40]

See Also

edit
edit

References

edit

  This article incorporates text from this source, which is available under the CC BY-SA 4.0 license.

  1. ^ a b 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.
  2. ^ a b c d e 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): 23–48. 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.
  4. ^ a b Lewyn, Michael (2012). "Two Cheers for Instant Runoff Voting". 6 Phoenix L. Rev. 117. Rochester, NY. SSRN 2276015. 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
  5. ^ Myerson, Roger B.; Weber, Robert J. (March 1993). "A Theory of Voting Equilibria". American Political Science Review. 87 (1): 102–114. doi:10.2307/2938959. hdl:10419/221141. ISSN 1537-5943. JSTOR 2938959.
  6. ^ Robinette, Robbie (2023-09-01). "Implications of strategic position choices by candidates". Constitutional Political Economy. 34 (3): 445–457. doi:10.1007/s10602-022-09378-6. ISSN 1572-9966.
  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. 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.
  8. ^ Laslier, Jean-François; Sanver, Remzi, eds. (2010). Handbook on Approval Voting. Studies in Choice and Welfare. Heidelberg: Springer Berlin. doi:10.1007/978-3-642-02839-7. ISBN 978-3-642-02839-7.
  9. ^ DeGroot, Morris H. (1970). Optimal Statistical Decisions. McGraw-Hill Book Co., New York-London-Sydney. p. 232. ISBN 9780471680291. MR 0356303.
  10. ^ "Avoid Vote-Splitting and Weak Plurality Results". RCV Resources. Ranked Choice Voting Resource Center. 2020-11-09. Retrieved 2024-07-22.
  11. ^ "Ranked Choice Voting". FairVote. FairVote. Retrieved 2024-07-22.
  12. ^ "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.
  13. ^ a b 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
  14. ^ 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.
  15. ^ 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].
  16. ^ a b c d e 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.
  17. ^ 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.
  18. ^ 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
  19. ^ 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.
  20. ^ 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
  21. ^ 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.
  22. ^ 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
  23. ^ 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].
  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 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.
  25. ^ 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.
  26. ^ "Mayor Bob Kiss". City of Burlington. Archived from the original on November 29, 2007. Retrieved November 16, 2007.
  27. ^ 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.
  28. ^ 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
  29. ^ a b 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.
  30. ^ 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
  31. ^ 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. doi:10.1007/s10602-023-09393-1.
  32. ^ a b Lewyn, Michael (2012). "Two Cheers for Instant Runoff Voting". Phoenix L. Rev. 6: 117. SSRN 2276015. election where Democratic candidate for mayor was Condorcet winner but finished third behind Republican and 'Progressive'
  33. ^ 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.
  34. ^ 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.
  35. ^ Laatu, Juho; Smith, Warren D. (March 2009). "THE RANK-ORDER VOTES IN THE 2009 BURLINGTON MAYORAL ELECTION".
  36. ^ "Burlington voters repeal IRV". Wcax.com. March 2, 2010. Archived from the original on April 9, 2016. Retrieved March 28, 2016.
  37. ^ "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.
  38. ^ "Official Results Of 2010 Annual City Election" (PDF). City of Burlington. March 2, 2010.
  39. ^ 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.
  40. ^ "IRV and Core Support". The Center for Election Science. Retrieved December 4, 2019.
Retrieved from "https://en.wikipedia.org/w/index.php?title=Draft:Center_squeeze&oldid=1235967300"