Center squeeze: Difference between revisions

Alaska's at-large congressional district
Turnout	32.2%

Browse history interactively

← Previous edit Next edit →

Content deleted Content added

VisualWikitext

Inline

Revision as of 18:05, 21 July 2024

Center-squeezes are a class of elections where the majority-preferred and socially-best candidate tends to be eliminated by plurality rule and instant-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 instant-runoff (ranked-choice) voting.^[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

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 ranked along a one-dimensional spectrum, which can be seen in the diagram. 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.

All voters who prefer candidate A as their true favorite take candidate B as their second favorite. All voters who prefer candidate C as their true favorite also take candidate B as their second favorite. Voters who prefer candidate B as their true favorite are split, with a slight majority preferring candidate A.

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. 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

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.

Candidate C would win 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 or ranked-choice voting)

In this context, instant-runoff can be thought of as an attempt to mitigate the issues caused by vote-splitting under first-past-the-post. Voters submit ballots containing their ranked ordered preferences but only their highest ranked candidate receives their vote. The candidate in last place is eliminated and their votes redistributed according to each ballot's next preferred candidate. This repeats until a candidate obtains more than half the remaining votes.

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.

Systems that generally do well in center-squeeze elections include both Condorcet (majority) voting and rated voting. Methods based on plurality rule such as first-past-the-post, instant-runoff voting, and two-round runoff tend to do poorly.

Cardinal methods

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 pass the median voter theorem per se, it tends to behave much like methods that do. The specific measure of central tendency minimized by the method depends on the exact way voters score candidates. different measures of central tendency minimize different distance metrics. This corresponds to the geometric median when each candidate's score falls off linearly with respect to ideological distance.

Under most common models of strategic voting, all spoilerproof cardinal methods will tend to behave like approval voting, and tend to converge on the Condorcet winner.

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.

Notable elections

2022 Alaska Special Election

The 2022 Alaska special election for the state's single House of Representatives seat was a prominent and conclusive example of a center-squeeze election. The race use instant-runoff voting to choose between the Democratic Party candidate Mary Peltola and the two Republican Party candidates, Sarah Palin and Nick Begich III. Because only three candidates were in the race, and the full ballot data for the race was released, election scientists were able determine that Palin acted as a spoiler for Begich.

Begich was preferred to both Palin and Peltola in head-to-head matchups, but was eliminated in the first round with 28% of the votes, three percentage points behind Palin.^[10]^[11] Of those who chose to support a second candidate, Begich's supporters were split farily evenly between Palin and Peltola with slightly more supporting Palin. Palin's supporter's overwhelmingly preferred Begich, to Peltola.^[12] The final winner, Peltola, received no meaningful support on a majority of ballots.^[10]^[13]

Many social choice theorists criticized the instant-runoff procedure for its pathological behavior.^[14]^[15] Along with being a center-squeeze, the election was also a negative voting weight event,^[13] where a voter's ballot has the opposite of its intended effect (e.g. a candidate being eliminated for having "too many votes").^[13]^[16] In this race, Peltola won as a result of 5,200 ballots that ranked her last (after Palin then Begich),^[13]^[17] and would have lost if she had received more support from Palin voters.^[13]^[18]^[19]^[20]^[21]

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 instant-runoff voting (IRV), after the 2006 mayoral election.^[22] In the 2009 election, incumbent Burlington mayor (Bob Kiss) won reelection as a member of the Vermont Progressive Party,^[23] 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 instant-runoff voting, noting that Kiss was elected as a result of 750 votes cast against him (ranking Kiss in last place).^[24]^[25]

Several electoral reform advocates branded the election a failure after Kiss was elected, despite 54% of voters voting for Montroll over Kiss,^[26]^[27] violating the principle of majority rule.^[28]^[29]^[30]

The election created a controversy as a result of several election pathologies, after Kiss was declared winner as a result of 750 votes cast against his candidacy (ranking him last), over the objections of the 54% of Burlington voters who had preferred Andy Montroll.^[31]Later analyses showed the race was still spoiled, however, with Wright acting as a spoiler pulling moderate votes from Montroll, who otherwise would have been able to defeat Kiss in a one-on-one race.^[32]^[28]

Unlike the city's first IRV election three years prior, however, Kiss was neither the plurality winner (Republican Kurt Wright) nor the majority vote winner (Democrat Andy Montroll).^[33]^[34] This led to a controversy about the use of IRV in mayoral elections,^[31] culminating in a successful 2010 citizen's initiative repealing IRV's use by a vote of 52% to 48%.^[35]^[36]^[37]

External links

References

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

^ ^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.
^ ^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
^ 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.
^ ^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
^ 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.
^ 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.
^ 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.
^ 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.
^ "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.
^ ^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
^ 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.
^ 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].
^ ^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.
^ 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.
^ 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
^ 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.
^ 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
^ 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.
^ 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
^ 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].
^ 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.
^ 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.
^ "Mayor Bob Kiss". City of Burlington. Archived from the original on November 29, 2007. Retrieved November 16, 2007.
^ 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.
^ 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
^ 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
^ 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.
^ ^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'
^ 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.
^ 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.
^ ^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.
^ Laatu, Juho; Smith, Warren D. (March 2009). "THE RANK-ORDER VOTES IN THE 2009 BURLINGTON MAYORAL ELECTION".
^ "Point/Counterpoint: Terry Bouricius Attempts To Rip Professor Gierzynski A New One Over Instant Runoff Voting Controversy (Now With All New Gierzynski Update!)". Archived from the original on July 26, 2011. Retrieved December 30, 2010.
^ 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.
^ "Burlington voters repeal IRV". Wcax.com. March 2, 2010. Archived from the original on April 9, 2016. Retrieved March 28, 2016.
^ "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.
^ "Official Results Of 2010 Annual City Election" (PDF). City of Burlington. March 2, 2010.

[Merrill_1984-1] 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.

[Merril_198522-2] 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.

[Lewyn_201222-4] 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

[Mverson_1993-5] 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.

[Davis_1970-7] 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.

[Laslier_2010-8] 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.

[akdoe1-9] "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.

[Analysis_Alaska2222-10] 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

[:022-11] 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.

[:122-12] 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].

[:3-13] 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.

[easy_fix222-14] 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.

[Analysis_Alaska32-15] 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

[16] 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.

[Analysis_Alaska-17] 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

[18] 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.

[Analysis_Alaska223-19] 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

[:13-20] 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].

[:03-21] 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.

[burlington_votes-22] 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.

[23] "Mayor Bob Kiss". City of Burlington. Archived from the original on November 29, 2007. Retrieved November 16, 2007.

[24] 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.

[:8-25] 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

[ScoreVotingNet-26] 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

[27] 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.

[Lewyn_2012-28] 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'

[29] 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.

[30] 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.

[Voting_Paradoxes-31] 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.

[Laatu_2009-32] Laatu, Juho; Smith, Warren D. (March 2009). "THE RANK-ORDER VOTES IN THE 2009 BURLINGTON MAYORAL ELECTION".

[VermontDaily-33] "Point/Counterpoint: Terry Bouricius Attempts To Rip Professor Gierzynski A New One Over Instant Runoff Voting Controversy (Now With All New Gierzynski Update!)". Archived from the original on July 26, 2011. Retrieved December 30, 2010.

[Stensholt-34] 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.

[repeal2-35] "Burlington voters repeal IRV". Wcax.com. March 2, 2010. Archived from the original on April 9, 2016. Retrieved March 28, 2016.

[rutland_herald-36] "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.

[BVT20100302-37] "Official Results Of 2010 Annual City Election" (PDF). City of Burlington. March 2, 2010.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

[24]

[25]

[26]

[27]

[28]

[29]

[30]

[31]

[32]

[33]

[34]

[35]

[36]

[37]

@@ Line 128: / Line 128: @@
 Many [[Social choice theory|social choice theorists]] criticized the instant-runoff procedure for its [[Pathological (mathematics)#In voting|pathological behavior]].<ref name="easy fix222">{{Cite news |last1=Maskin |first1=Eric |author-link=Eric Maskin |last2=Foley |first2=Edward B. |date=2022-11-01 |title=Opinion: Alaska's ranked-choice voting is flawed. But there's an easy fix. |url=https://www.washingtonpost.com/opinions/2022/11/01/alaska-final-four-primary-begich-palin-peltola/ |access-date=2024-02-09 |newspaper=Washington Post |language=en-US |issn=0190-8286}}</ref><ref name="Analysis Alaska32">{{Cite arXiv |eprint=2209.04764v3 |class=econ.GN |first1=Adam |last1=Graham-Squire |first2=David |last2=McCune |title=A Mathematical Analysis of the 2022 Alaska Special Election for US House |date=2022-09-11 |language=en |page=2 |quote=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}}</ref> Along with being a center-squeeze, the election was also a [[Monotonicity criterion|negative voting weight event]],<ref name=":3" /> where a voter's ballot has the opposite of its intended effect (e.g. a candidate being eliminated for having "too ''many'' votes").<ref name=":3" /><ref>{{Cite journal |last1=Doron |first1=Gideon |last2=Kronick |first2=Richard |date=1977 |title=Single Transferrable Vote: An Example of a Perverse Social Choice Function |url=https://www.jstor.org/stable/2110496 |journal=American Journal of Political Science |volume=21 |issue=2 |pages=303–311 |doi=10.2307/2110496 |jstor=2110496 |issn=0092-5853}}</ref> In this race, Peltola won as a result of 5,200 ballots that ranked her last (after Palin then Begich),<ref name=":3" /><ref name="Analysis Alaska">{{Cite arXiv |last1=Graham-Squire |first1=Adam |last2=McCune |first2=David |date=2022-09-11 |title=A Mathematical Analysis of the 2022 Alaska Special Election for US House |page=2 |class=econ.GN |eprint=2209.04764v3 |language=en |quote=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}}</ref> and would have lost if she had received more support from Palin voters.<ref name=":3" /><ref>{{Cite web |last=Hamlin |first=Aaron |date=2022-09-16 |title=RCV Fools Palin Voters into Electing a Progressive Democrat |url=https://electionscience.org/archive/rcv-fools-palin-voters-into-electing-a-progressive-democrat/ |access-date=2024-07-11 |website=The Center for Election Science |language=en-US |quote=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.}}</ref><ref name="Analysis Alaska223">{{Cite arXiv |eprint=2209.04764v3 |class=econ.GN |first1=Adam |last1=Graham-Squire |first2=David |last2=McCune |title=A Mathematical Analysis of the 2022 Alaska Special Election for US House |date=2022-09-11 |language=en |page=2 |quote=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}}</ref><ref name=":13">{{Cite arXiv |eprint=2303.00108v1 |class=cs.CY |first=Jeanne N. |last=Clelland |title=Ranked Choice Voting And the Center Squeeze in the Alaska 2022 Special Election: How Might Other Voting Methods Compare? |date=2023-02-28 |language=en |page=6}}</ref><ref name=":03">{{Cite web |last1=Atkinson |first1=Nathan |last2=Ganz |first2=Scott C. |date=2022-10-30 |title=The flaw in ranked-choice voting: rewarding extremists |url=https://thehill.com/opinion/campaign/3711206-the-flaw-in-ranked-choice-voting-rewarding-extremists/ |access-date=2023-05-14 |website=The Hill |language=en-US |quote=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.}}</ref>
-=== SECOND EXAMPLE ===
+=== 2009 Burlington mayoral election ===
+{{main |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 [[instant-runoff voting]] (IRV), after the [[2006 Burlington mayoral election|2006 mayoral election]].<ref name="burlington_votes">[http://www.burlingtonvotes.org/faq 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.''</ref> In the 2009 election, incumbent [[List of mayors of Burlington, Vermont|Burlington mayor]] ([[Bob Kiss]]) won reelection as a member of the [[Vermont Progressive Party]],<ref>{{cite web|url=http://www.ci.burlington.vt.us/mayor/|title=Mayor Bob Kiss|website=City of Burlington|archive-url=https://web.archive.org/web/20071129081028/http://www.ci.burlington.vt.us/mayor/|archive-date=November 29, 2007|url-status=dead|access-date=November 16, 2007}}</ref> defeating Kurt Wright in the final round with 48% of the vote (51.5% excluding [[Exhausted ballot|exhausted ballots]]).
+Some [[mathematicians]] and [[Voting theory|voting theorists]] criticized the election results as revealing several [[Pathological (mathematics)|pathologies]] associated with [[instant-runoff voting]], noting that Kiss was elected as a result of 750 votes [[Participation criterion|cast against him]] (ranking Kiss in last place).<ref>{{Cite journal |last1=Felsenthal |first1=Dan S. |last2=Tideman |first2=Nicolaus |date=2014 |title=Interacting double monotonicity failure with direction of impact under five voting methods |journal=Mathematical Social Sciences |volume=67 |pages=57–66 |doi=10.1016/j.mathsocsci.2013.08.001 |issn=0165-4896 |quote=A display of non-monotonicity under the Alternative Vote method was reported recently, for the March 2009 mayoral election in Burlington, Vermont.}}</ref><ref name=":8">{{Cite journal |last1=Ornstein |first1=Joseph T. |last2=Norman |first2=Robert Z. |date=October 1, 2014 |title=Frequency of monotonicity failure under Instant Runoff Voting: estimates based on a spatial model of elections |journal=Public Choice |language=en |volume=161 |issue=1–2 |pages=1–9 |doi=10.1007/s11127-013-0118-2 |issn=0048-5829 |s2cid=30833409 |quote=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}}</ref>
+Several [[electoral reform]] advocates branded the election a failure after Kiss was elected, despite 54% of voters voting for Montroll over Kiss,<ref name="ScoreVotingNet">{{Cite web|url=http://scorevoting.net/Burlington.html|title=Burlington Vermont 2009 IRV mayoral election|last1=Gierzynski|first1=Anthony|last2=Hamilton|first2=Wes|date=March 2009|website=RangeVoting.org|access-date=October 1, 2017|quote=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|last3=Smith|first3=Warren D.}}</ref><ref>{{Cite journal|last1=Bristow-Johnson|first1=Robert|date=2023|title=The failure of Instant Runoff to accomplish the purpose for which it was adopted: a case study from Burlington Vermont|journal=Constitutional Political Economy|doi=10.1007/s10602-023-09393-1}}</ref> violating the principle of [[Condorcet winner|majority rule]].<ref name="Lewyn 2012" /><ref>{{Cite book |last=Ellenberg |first=Jordan |url=https://archive.org/details/hownottobewrongp0000elle |title=How Not to Be Wrong: The Power of Mathematical Thinking |date=May 29, 2014 |publisher=Penguin |isbn=9780698163843 |page=[https://archive.org/details/hownottobewrongp0000elle/page/385 385] |language=en |quote=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. |url-access=registration}}</ref><ref>{{Cite journal |last=Stensholt |first=Eivind |date=October 7, 2015 |title=What Happened in Burlington? |journal=NHH Dept. Of Business and Management Science |language=en |volume=Discussion Paper No. 2015/26 |doi=10.2139/ssrn.2670462 |ssrn=2670462 |quote=K was elected even though M was a clear Condorcet winner and W was a clear Plurality winner. |hdl-access=free |hdl=11250/2356264}}</ref>
+The election created a controversy as a result of several [[List of pathological elections|election pathologies]], after Kiss was declared winner as a result of 750 votes cast against his candidacy (ranking him last), over the objections of the 54% of Burlington voters who had preferred Andy Montroll.<ref name="Voting Paradoxes" />Later analyses showed the race was still spoiled, however, with Wright acting as a spoiler pulling moderate votes from Montroll, who otherwise would have been able to defeat Kiss in a one-on-one race.<ref name="Laatu 2009">{{Cite web |last1=Laatu |first1=Juho |last2=Smith |first2=Warren D. |date=March 2009 |title=THE RANK-ORDER VOTES IN THE 2009 BURLINGTON MAYORAL ELECTION |url=https://rangevoting.org/JLburl09.txt}}</ref><ref name="Lewyn 2012">{{Cite journal |last=Lewyn |first=Michael |date=2012 |title=Two Cheers for Instant Runoff Voting |journal=Phoenix L. Rev. |language=en |volume=6 |page=117 |ssrn=2276015 |quote=election where Democratic candidate for mayor was Condorcet winner but finished third behind Republican and 'Progressive{{'-}}}}</ref>
+Unlike the city's first IRV election three years prior, however, Kiss was neither the [[Plurality voting system|plurality]] winner ([[Republican Party (United States)|Republican]] [[Kurt Wright]]) nor the [[Condorcet winner|majority vote winner]] ([[Democratic Party (United States)|Democrat]] Andy Montroll).<ref name="VermontDaily">{{cite web|url=http://vermontdailybriefing.com/?p%3D1215|title=Point/Counterpoint: Terry Bouricius Attempts To Rip Professor Gierzynski A New One Over Instant Runoff Voting Controversy (Now With All New Gierzynski Update!) |archive-url=https://web.archive.org/web/20110726125759/http://vermontdailybriefing.com/?p=1215|archive-date=July 26, 2011|url-status=dead|access-date=December 30, 2010}}</ref><ref name="Stensholt">{{cite journal | last=Stensholt | first=Eivind | title=What Happened in Burlington? | journal=SSRN Electronic Journal | publisher=Elsevier BV | year=2015 | issn=1556-5068 | doi=10.2139/ssrn.2670462 | pages=10-12| hdl=11250/2356264 | hdl-access=free }}</ref> This led to a controversy about the use of IRV in mayoral elections,<ref name="Voting Paradoxes">{{cite web|url=http://vermontdailybriefing.com/?p=1213|title=Voting Paradoxes and Perverse Outcomes: Political Scientist Tony Gierzynski Lays Out A Case Against Instant Runoff Voting|last=Baruth|first=Philip|date=March 12, 2009|publisher=Vermont Daily Briefing|archive-url=https://web.archive.org/web/20110726125814/http://vermontdailybriefing.com/?p=1213|archive-date=July 26, 2011|url-status=dead}}</ref> culminating in a successful 2010 citizen's [[Popular initiative|initiative]] repealing IRV's use by a vote of 52% to 48%.<ref name="repeal2">{{cite web|url=http://www.wcax.com/story/12074080/burlington-voters-repeal-irv|title=Burlington voters repeal IRV|date=March 2, 2010|publisher=[[WCAX-TV|Wcax.com]]|archive-url=https://web.archive.org/web/20160409132306/http://www.wcax.com/story/12074080/burlington-voters-repeal-irv|archive-date=April 9, 2016|access-date=March 28, 2016}}</ref><ref name="rutland_herald">{{cite web|url=http://www.rutlandherald.com/article/20100427/NEWS03/4270339/1004/NEWS03|title=Instant run-off voting experiment ends in Burlington : Rutland Herald Online|date=April 27, 2010|website=Rutlandherald.com|access-date=April 1, 2016|archive-url=https://web.archive.org/web/20160304055602/http://www.rutlandherald.com/article/20100427/NEWS03/4270339/1004/NEWS03#|archive-date=March 4, 2016|url-status=dead}}</ref><ref name="BVT20100302">{{cite web|url=https://www.burlingtonvt.gov/sites/default/files/CT/ElectionResults/20100302/election_summary_report_20100302.pdf|title=Official Results Of 2010 Annual City Election|date=March 2, 2010|work=City of Burlington}}</ref>
 == See Also ==

Far-west:	1031
Center-west:	532
Center-east:	415
Far-east:	1108