2590:
expenditures for and against candidates. In this analysis, I found that negative spending increased significantly in Maine following the implementation of ranked-choice voting, casting doubt on the claim that RCV makes campaigns more civil. To provide more evidence, I also created a dataset of all
Facebook advertisements that mentioned any congressional candidates for 2018, the first year that RCV was used in Maine. I then conducted a sentiment analysis to find each advertisement's sentiment (whether it was negative or not). I then used genetic matching to approximate an experiment to find the impact of RCV on civility. In doing so, I found that the 2018 campaign was even more negative than in paired districts around the country.
1313:
1299:
1306:
956:
91:
931:
31:
1594:
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1649:
3599:
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.
943:
1767:
3390:
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.
2843:
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.
1978:
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.
3389:
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
2842:
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
1977:
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
2670:
The idea was that by opening up primaries to all voters, regardless of party, a flood of new centrist voters would arrive. That would give moderate candidates a route to victory .. Candidates did not represent voters any better after the reforms, taking positions just as polarized as they did before
2226:
third place
Candidate C is a centrist who is 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
3598:
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
1083:
Voting systems that suffer from the center-squeeze effect incentivize candidates to avoid the political center, creating political polarization in the long run. As a result, rules like RCV can lead to extreme winners even if center-squeezes seem empirically rare, because the rules disincentivize
3851:
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
3120:
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
2589:
One of the main claims made by reformers about RCV is that it will make campaigns more civil, as campaigns will have the incentive to seek the second-place vote of supporters of different candidates. To study this claim, I first conducted a difference-in-differences analysis on independent
3802:
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
1895:
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
2133:
third place C is a centrist who is the second choice of
Candidate A's left-wing supporters and Candidate B's right-wing supporters. ... In such a situation, C would prevail over both Candidates A ... and B ... in a one-on-one runoff election. Yet, C would not prevail under
1241:
The opposite situation—a bias toward "bland" or inoffensive candidates, and against polarizing ones—does not appear for any common rules. However, it can occur for bottom-heavy or negative voting methods that elect candidates with the least opposition, such as
3662:
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
1446:
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
4151:
2713:
Fiji's objective of ameliorating ethnic divisions by the adoption of AV was not successful. In elections in 1999 and 2001, moderate parties would have fared better under a proportional representation system
2642:
neither the Citizens Redistricting Commission nor the top-two primary immediately halted the continuing partisan polarization of California's elected lawmakers or their drift away from the average voter
1229:
of the voter distribution. As a result, while score voting does not always elect the candidate closest to the median voter, it often behaves like methods that do. Under most models of strategic voting,
1474:
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,
2099:
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.
1478:
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
2987:
Instant Runoff Voting, however, achieves the most centripetal result (when it does) only by happenstance, not intrinsically, and fails to do so when the electorate is especially polarized
914:
3915:
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.
1264:
1112:
1561:
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:
598:
3768:
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".
1512:, 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
3635:
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.
3322:
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.
617:
1076:. However, in methods that strongly prioritize first preferences, these candidates are often eliminated early on because they aim for broad appeal rather than strong
3623:
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
3523:
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
3417:
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
3358:
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
3305:
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
2814:
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
2241:"How an Ideologically Concentrated Minority Can Trump a Dispersed Majority: Nonmedian Voter Results for Plurality, Run-off, and Sequential Elimination Elections"
1992:"How an Ideologically Concentrated Minority Can Trump a Dispersed Majority: Nonmedian Voter Results for Plurality, Run-off, and Sequential Elimination Elections"
4155:
3704:
3268:
3121:
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.
3864:
Bristow-Johnson, Robert (2023). "The failure of Instant Runoff to accomplish the purpose for which it was adopted: a case study from Burlington Vermont".
984:
821:
4201:
4022:
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1554:. 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.
2065:
Davis, Otto A.; Hinich, Melvin J.; Ordeshook, Peter C. (1970-01-01). "An Expository Development of a Mathematical Model of the Electoral Process".
3756:
A display of non-monotonicity under the Alternative Vote method was reported recently, for the March 2009 mayoral election in Burlington, Vermont.
2408:
1820:
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.
2655:
3730:
Felsenthal, Dan S.; Tideman, Nicolaus (2014). "Interacting double monotonicity failure with direction of impact under five voting methods".
4651:
4419:
1274:
675:
3611:
Graham-Squire, Adam; McCune, David (2022-09-11). "A Mathematical Analysis of the 2022 Alaska Special Election for US House". p. 2.
3511:
Graham-Squire, Adam; McCune, David (2022-09-11). "A Mathematical Analysis of the 2022 Alaska Special Election for US House". p. 2.
3405:
Graham-Squire, Adam; McCune, David (2022-09-11). "A Mathematical Analysis of the 2022 Alaska Special Election for US House". p. 2.
3346:
Graham-Squire, Adam; McCune, David (2022-09-11). "A Mathematical Analysis of the 2022 Alaska Special Election for US House". p. 2.
3293:
Graham-Squire, Adam; McCune, David (2022-09-11). "A Mathematical Analysis of the 2022 Alaska Special Election for US House". p. 2.
2802:
Graham-Squire, Adam; McCune, David (2022-09-11). "A Mathematical Analysis of the 2022 Alaska Special Election for US House". p. 2.
3374:
2827:
1962:
3479:
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2384:
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1550:
advocates branded the election a failure after Kiss was elected despite 54% of voters voting for Montroll over Kiss, violating the
1128:
707:
569:
564:
1415:
The 2022 Alaska special election seat was an infamous example of a center squeeze. The ranked-choice runoff election involved one
4646:
4424:
1834:
977:
670:
2371:
However, squeezed by surrounding opponents, a centrist candidate may receive few first-place votes and be eliminated under Hare.
1949:
However, squeezed by surrounding opponents, a centrist candidate may receive few first-place votes and be eliminated under Hare.
4409:
4194:
352:
3113:
2550:
1517:
4773:
3817:"Voting Paradoxes and Perverse Outcomes: Political Scientist Tony Gierzynski Lays Out A Case Against Instant Runoff Voting"
876:
127:
2277:
As with simple plurality elections, it is apparent the outcome will be highly sensitive to the distribution of candidates.
2028:
As with simple plurality elections, it is apparent the outcome will be highly sensitive to the distribution of candidates.
38:, showing how center-squeeze extends to more complex or multi-dimensional models. The number of winners is displayed as a
4456:
3948:
election where Democratic candidate for mayor was Condorcet winner but finished third behind Republican and 'Progressive
4816:
970:
4187:
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871:
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1503:
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1416:
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522:
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were able to confirm that Palin spoiled the race for Begich, with Peltola winning the race as a result of several
4768:
4439:
1479:
1463:
1440:
1127:, despite a majority of voters preferring Begich to either one of his opponents. Another possible example is the
593:
118:
3708:
3258:"State of Alaska | 2022 Special General Election | Election Summary Report | August 16, 2022 | Official Results"
3257:
1455:
of their candidacy. In this case, ballots ranking Palin first and Begich second instead allowed Peltola to win.
4791:
4567:
656:
17:
2766:"Electoral Institutions and Substantive Representation in Local Politics: The Effects of Ranked Choice Voting"
720:
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346:
328:
169:
1312:
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methods are not affected by this pathology. Condorcet methods are insulated from center-squeezes by the
4626:
4317:
1539:
790:
773:
740:
504:
492:
462:
263:
221:
154:
43:
2727:"The Failure of the Alternative Vote as a Tool for Ethnic Moderation in Fiji: A Rejoinder to Horowitz"
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639:
123:
1470:, where a voter's ballot has the opposite of its intended effect (e.g. where a candidate would need
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480:
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1867:"A statistical model for Condorcet efficiency based on simulation under spatial model assumptions"
909:
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1298:
826:
680:
363:
4114:
3900:
2685:"Does the Alternative Vote Foster Moderation in Ethnically Divided Societies?: The Case of Fiji"
2040:
795:
4811:
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or other multiple-round systems. In these methods, candidates must focus on appealing to their
1042:
855:
735:
665:
472:
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3990:
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2221:
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2135:
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1022:
763:
603:
487:
293:
272:
204:
182:
55:
3995:
K was elected even though M was a clear Condorcet winner and W was a clear Plurality winner.
3100:. Studies in Choice and Welfare. Berlin, Heidelberg: Springer Berlin Heidelberg. p. 2.
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1048:
The term "center squeeze" refers to candidates who are close to the center of public opinion
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3204:
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under IRV because he or she finished third and thus would be the first candidate eliminated
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1305:
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113:
8:
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4150:. The copyright holder has licensed the content in a manner that permits reuse under the
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can thus "squeeze" broadly-popular candidates trapped between them, starving them of the
800:
634:
287:
1084:
moderates from running for office in the first place. The effect was first predicted by
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2090:
2082:
2019:
1940:
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442:
226:
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2011:
1932:
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to ensure they can make it past the first round, where only first-preferences count.
955:
866:
836:
758:
695:
529:
256:
231:
214:
82:
35:
3797:
2940:
Igersheim, Herrade; Durand, François; Hamlin, Aaron; Laslier, Jean-François (2022).
2182:
4737:
4369:
4225:
4210:
4086:
4078:
4023:"Instant run-off voting experiment ends in Burlington : Rutland Herald Online"
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3015:
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2307:
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2074:
2003:
1924:
1878:
1547:
1546:, where Kiss won only as a result of 750 votes ranking Kiss in last place. Several
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159:
147:
108:
70:
51:
47:
3453:
2157:"Candidate incentive distributions: How voting methods shape electoral incentives"
2138:
because he or she finished third and thus would be the first candidate eliminated.
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4253:
4243:
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3200:
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1199:
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1116:
935:
768:
623:
588:
509:
420:
323:
246:
188:
66:
4174:
1088:
in the 1940s and has since been confirmed empirically by studies of politics in
4600:
4305:
4265:
3877:
3235:
2311:
1829:
1779:
1754:
1726:
1685:
1638:
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1132:
1077:
1038:
1006:
805:
730:
541:
410:
385:
236:
3781:
3105:
2917:
2900:
2604:"Reform and Representation: A New Method Applied to Recent Electoral Changes*"
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4344:
4100:
3789:
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3019:
3004:"The Leader Rule: A Model of Strategic Approval Voting in a Large Electorate"
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2708:
2700:
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2015:
1936:
1890:
1535:
1105:
814:
514:
302:
140:
103:
78:
3537:"Single Transferrable Vote: An Example of a Perverse Social Choice Function"
2656:"California's jungle primary sets up polarized governor's race for November"
1508:
The 2009 Burlington mayoral election was held in March 2009 for the city of
1060:. Center squeezes can occur in any situation where voters prefer candidates
4359:
4300:
3480:"Opinion: Alaska's ranked-choice voting is flawed. But there's an easy fix"
2901:"Condorcet Loser in 2016: Apparently Trump; Condorcet Winner: Not Clinton?"
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318:
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90:
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333:
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2272:
2240:
2086:
2023:
1991:
1944:
1882:
1120:
1097:
2409:"Munger: "If you have a dumb incentive system, you get dumb outcomes""
30:
4752:
4747:
3963:
Stensholt, Eivind (October 7, 2015). "What Happened in Burlington?".
3852:
Montroll over every other candidate ... Montroll is the most-approved
3658:
3641:
3617:
3517:
3411:
3352:
3328:
3299:
2808:
2334:
1912:
1221:
If voters assign scores to candidates based on ideological distance,
1089:
1034:
400:
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4179:
3552:
3153:
3061:
2350:
2256:
2078:
2007:
1928:
4572:
3834:
Gierzynski, Anthony; Hamilton, Wes; Smith, Warren D. (March 2009).
2453:
2173:
1648:
1520:
1053:
651:
58:(center-left column) towards extreme candidates is clearly visible.
39:
2865:"Alaska's ranked-choice voting is flawed. But there's an easy fix"
1697:
1593:
4434:
1804:– defeats all candidates below, including Wright (4,313 to 4,061)
1527:, defeating Kurt Wright in the final round with 48% of the vote.
1068:, the candidate who appeals most to the median voter will be the
437:
3089:
3087:
2671:
the top two. We detected no shift toward the ideological middle.
2575:"The Effect of Ranked-Choice Voting in Maine | MIT Election Lab"
2335:"A Comparison of Efficiency of Multicandidate Electoral Systems"
1913:"A Comparison of Efficiency of Multicandidate Electoral Systems"
1810:– defeats all candidates below, including Smith (3,971 to 3,793)
1166:
The voting systems most strongly affected by center squeeze are
4722:
3930:
Lewyn, Michael (2012). "Two Cheers for Instant Runoff Voting".
2942:"Comparing Voting Methods : 2016 US Presidential Election"
2485:"Australia: No party convergence where we would most expect it"
2239:
McGann, Anthony J.; Koetzle, William; Grofman, Bernard (2002).
1990:
McGann, Anthony J.; Koetzle, William; Grofman, Bernard (2002).
1798:– defeats all candidates below, including Kiss (4,064 to 3,476)
1451:, where a candidate is eliminated as a result of votes cast in
942:
4009:"The Rank-Order Votes in the 2009 Burlington Mayoral Election"
1443:
behaviors that tend to characterize center-squeeze elections.
1265:
2022 Alaska's at-large congressional district special election
3584:"RCV Fools Palin Voters into Electing a Progressive Democrat"
3189:. McGraw-Hill Book Co., New York-London-Sydney. p. 232.
3084:
1766:
1210:
Center squeeze is a major feature of two-party systems using
1093:
2939:
1816:– defeats Simpson (5,570 to 721) and the write-in candidates
4175:
The Center for Range Voting: IRV "center squeeze" pathology
1435:). Because the full ballot data for the race was released,
1101:
4073:
Stensholt, Eivind (2015). "What Happened in Burlington?".
3705:"ChoicePlus Pro 2009 Burlington Mayor Round Detail Report"
2899:
Potthoff, Richard F.; Munger, Michael C. (November 2021).
2797:
2795:
2296:"Implications of strategic position choices by candidates"
3375:"The flaw in ranked-choice voting: rewarding extremists"
2828:"The flaw in ranked-choice voting: rewarding extremists"
1963:"The flaw in ranked-choice voting: rewarding extremists"
1466:. Along with being a center-squeeze, the election was a
3895:
How Not to Be Wrong: The Power of Mathematical Thinking
3833:
3094:
Laslier, Jean-François; Sanver, M. Remzi, eds. (2010).
2792:
3341:
3339:
1462:
criticized the ranked-choice runoff procedure for its
3654:
3652:
3604:
3400:
3398:
2602:
Kousser, Thad; Phillips, Justin; Shor, Boris (2016).
1037:
alternative. Extreme candidates who focus on a small
4148:
https://electowiki.org/Center_squeeze?action=history
3504:
2238:
2064:
1989:
1860:
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1850:
1848:
4140:, this article is derived in whole or in part from
3610:
3510:
3435:
3404:
3345:
3336:
3292:
2801:
2601:
2483:Mussel, Johanan D.; Schlechta, Henry (2023-07-21).
1497:
1131:, where polls found several alternatives including
3892:
3808:
3649:
3395:
3286:
2973:"What is "Centripetalism" and Why Does It Matter?"
1906:
1904:
3729:
3436:Graham-Squire, Adam; McCune, David (2024-01-02).
2150:
2148:
2146:
1845:
1273:
1225:will always select the candidate closest to some
4803:
4015:
3827:
2197:
1791:This leads to an overall preference ranking of:
1557:The controversy culminated in a successful 2010
4053:"Official Results Of 2010 Annual City Election"
3925:
3923:
3863:
3373:Atkinson, Nathan; Ganz, Scott C. (2022-10-30).
3220:"Normed Negative Voting to Depolarize Politics"
2855:
2853:
2851:
2826:Atkinson, Nathan; Ganz, Scott C. (2022-10-30).
2724:
2682:
2482:
2104:
1961:Atkinson, Nathan; Ganz, Scott C. (2022-10-30).
1901:
1258:
1111:Famous examples of center-squeezes include the
3836:"Burlington Vermont 2009 IRV mayoral election"
3767:
3468:
2898:
2725:Fraenkel, Jon; Grofman, Bernard (2006-06-01).
2683:Fraenkel, Jon; Grofman, Bernard (2006-06-01).
2143:
4195:
4045:
3093:
3046:"Electoral Equilibrium under Approval Voting"
2058:
978:
4652:Independence of Smith-dominated alternatives
4007:Laatu, Juho; Smith, Warren D. (March 2009).
4000:
3965:NHH Dept. Of Business and Management Science
3920:
3534:
3372:
3136:Myerson, Roger B.; Weber, Robert J. (1993).
3135:
2848:
2825:
2385:"The primordial election that is never held"
1960:
4170:Center for Election Science: Vote Splitting
4066:
3474:
2859:
2438:"On the Rationale of Group Decision-making"
1238:and thus converge on the Condorcet winner.
1205:
1033:candidate is eliminated in favor of a more
4202:
4188:
4006:
2763:
2289:
2287:
2285:
1202:are protected by closely-related results.
985:
971:
4090:
4072:
3980:
3962:
3890:
3659:4. How did this change to IRV come about?
3640:
3616:
3516:
3410:
3368:
3366:
3351:
3327:
3298:
2916:
2807:
2647:
2619:
2293:
2172:
3819:. Vermont Daily Briefing. Archived from
3634:
3535:Doron, Gideon; Kronick, Richard (1977).
3431:
3429:
3427:
3425:
3321:
3039:
3037:
2997:
2995:
2819:
1530:The election results were criticized by
1275:Alaska's at-large congressional district
1129:2016 United States presidential election
1074:any method compatible with majority-rule
29:
4647:Independence of irrelevant alternatives
4425:Sequential proportional approval voting
3317:
3315:
3313:
3217:
3182:
3002:Laslier, Jean-François (January 2009).
3001:
2332:
2326:
2282:
2232:
1983:
1910:
1864:
1835:Independence of irrelevant alternatives
34:Distribution of winners on a simulated
14:
4804:
4158:. All relevant terms must be followed.
3814:
3628:
3581:
3363:
3250:
3131:
3129:
2894:
2892:
2608:Political Science Research and Methods
2520:"Two Cheers for Instant Runoff Voting"
2476:
2431:
2429:
2206:"Two Cheers for Instant Runoff Voting"
2113:"Two Cheers for Instant Runoff Voting"
1954:
1542:associated with RCV. These included a
1072:, which means they will be elected by
4209:
4183:
3929:
3541:American Journal of Political Science
3422:
3142:The American Political Science Review
3050:American Journal of Political Science
3034:
2992:
2970:
2946:European Journal of Political Economy
2551:"RCV in the 2022 Australian Election"
2548:
2517:
2435:
2382:
2339:American Journal of Political Science
2245:American Journal of Political Science
2203:
2154:
2110:
2067:The American Political Science Review
1996:American Journal of Political Science
1917:American Journal of Political Science
1234:cardinal methods tend to behave like
1155:, but being squeezed out by both the
1119:was eliminated in the first round by
27:Pro-extremist bias in RCV and runoffs
4107:
3857:
3761:
3310:
3274:from the original on August 17, 2022
2718:
2033:
1480:alternatives without these behaviors
4457:Indirect single transferable voting
3438:"Ranked Choice Wackiness in Alaska"
3126:
3043:
2964:
2889:
2653:
2426:
1062:who hold views similar to their own
1045:they need to survive early rounds.
24:
3891:Ellenberg, Jordan (May 29, 2014).
3218:Shankar, Karthik H. (2022-12-01).
1523:won reelection as a member of the
1516:. In the 2009 election, incumbent
1052:and as a result is not limited to
89:
25:
4828:
4163:
3815:Baruth, Philip (March 12, 2009).
3478:; Foley, Edward B. (2022-11-01).
2863:; Foley, Edward B. (2022-11-01).
4029:. April 27, 2010. Archived from
3967:. Discussion Paper No. 2015/26.
3866:Constitutional Political Economy
3744:10.1016/j.mathsocsci.2013.08.001
2300:Constitutional Political Economy
2294:Robinette, Robbie (2023-09-01).
1765:
1696:
1647:
1592:
1504:2009 Burlington mayoral election
1498:2009 Burlington mayoral election
1311:
1304:
1297:
954:
941:
929:
877:McKelvey–Schofield chaos theorem
523:Semi-proportional representation
155:First preference plurality (FPP)
4119:The Center for Election Science
3956:
3884:
3723:
3707:. July 25, 2011. Archived from
3697:
3667:
3588:The Center for Election Science
3575:
3528:
3211:
3176:
3138:"A Theory of Voting Equilibria"
3008:Journal of Theoretical Politics
2971:Foley, Edward B. (2024-08-17).
2933:
2757:
2676:
2595:
2567:
2542:
2511:
2401:
2376:
2183:10.1016/j.electstud.2024.102799
2045:The Center for Election Science
4568:Mixed ballot transferable vote
3224:Group Decision and Negotiation
2958:10.1016/j.ejpoleco.2021.102057
915:Harsanyi's utilitarian theorem
872:Moulin's impossibility theorem
837:Conflicting majorities paradox
13:
1:
3454:10.1080/10724117.2023.2224675
3186:Optimal Statistical Decisions
2731:Comparative Political Studies
2689:Comparative Political Studies
1840:
741:Frustrated majorities paradox
4769:Comparison of voting systems
4611:Satisfaction approval voting
4596:Single non-transferable vote
4415:Proportional approval voting
3732:Mathematical Social Sciences
3582:Hamlin, Aaron (2022-09-16).
3265:Alaska Division of Elections
2549:Ogren, Marcus (2022-11-16).
2442:Journal of Political Economy
2383:Ogren, Marcus (2024-05-08).
2155:Ogren, Marcus (2024-08-01).
1468:negative voting weight event
1259:2022 Alaska special election
1113:2022 Alaska special election
1070:majority-preferred candidate
910:Condorcet dominance theorems
850:Social and collective choice
7:
4375:Graduated majority judgment
3183:DeGroot, Morris H. (1970).
3097:Handbook on Approval Voting
1823:
1253:
576:By mechanism of combination
347:Proportional representation
10:
4833:
4627:Condorcet winner criterion
4318:First-past-the-post voting
3878:10.1007/s10602-023-09393-1
3236:10.1007/s10726-022-09799-6
2905:American Politics Research
2764:Vishwanath, Arjun (2021).
2312:10.1007/s10602-022-09378-6
1501:
1262:
1176:ranked-choice voting (RCV)
1023:ranked-choice voting (RCV)
774:Multiple districts paradox
505:Fractional approval voting
493:Interactive representation
4817:Electoral system criteria
4782:
4774:Voting systems by country
4761:
4715:
4677:Mutual majority criterion
4632:Condorcet loser criterion
4619:
4586:
4578:Vote linkage mixed system
4533:
4498:
4490:Largest remainders method
4465:
4392:
4383:
4234:
4217:
3782:10.1007/s11127-013-0118-2
3106:10.1007/978-3-642-02839-7
2918:10.1177/1532673X211009499
2497:10.1177/13540688231189363
1785:
1760:
1732:
1525:Vermont Progressive Party
1289:
1281:
1271:
1025:. In a center squeeze, a
721:Paradoxes and pathologies
570:Mixed-member proportional
565:Mixed-member majoritarian
560:By results of combination
451:Approval-based committees
4667:Majority loser criterion
4553:Additional member system
4511:Hagenbach-Bischoff quota
4430:Single transferable vote
4355:Positional voting system
4291:Minimax Condorcet method
4249:Combined approval voting
3020:10.1177/0951629808097286
2743:10.1177/0010414005285035
2701:10.1177/0010414005285032
2333:Merrill, Samuel (1984).
1911:Merrill, Samuel (1984).
1865:Merrill, Samuel (1985).
1206:Susceptibility by system
1168:plurality-with-primaries
1019:plurality-with-primaries
900:Condorcet's jury theorem
701:Double simultaneous vote
676:Rural–urban proportional
671:Dual-member proportional
633:
622:
589:Parallel (superposition)
481:Fractional social choice
468:Expanding approvals rule
297:
282:
267:
198:
187:
163:
4692:Resolvability criterion
4682:Participation criterion
4657:Later-no-harm criterion
4473:Highest averages method
4075:SSRN Electronic Journal
2977:Common Ground Democracy
2770:SSRN Electronic Journal
2518:Lewyn, Michael (2012).
2204:Lewyn, Michael (2012).
2111:Lewyn, Michael (2012).
1552:majority-rule principle
1476:social choice theorists
1460:social choice theorists
1437:social choice theorists
1086:social choice theorists
1039:base of core supporters
827:Tyranny of the majority
604:Fusion (majority bonus)
421:Quota-remainder methods
4733:First-preference votes
4672:Monotonicity criterion
4642:Independence of clones
4345:Simple majoritarianism
4115:"IRV and Core Support"
4077:. Elsevier BV: 10–12.
2436:Black, Duncan (1948).
2041:"IRV and Core Support"
1056:along the traditional
961:Mathematics portal
867:Majority impossibility
856:Impossibility theorems
652:Negative vote transfer
473:Method of equal shares
94:
59:
4637:Consistency criterion
4558:Alternative vote plus
4323:Instant-runoff voting
3267:. September 2, 2022.
3044:Cox, Gary W. (1985).
1514:2006 mayoral election
1464:pathological behavior
1244:anti-plurality voting
1011:plurality-elimination
764:Best-is-worst paradox
753:Pathological response
488:Direct representation
141:Single-winner methods
93:
33:
4707:Seats-to-votes ratio
4478:Webster/Sainte-Laguë
4083:10.2139/ssrn.2670462
3973:10.2139/ssrn.2670462
3685:on November 29, 2007
2778:10.2139/ssrn.3802566
2621:10.1017/psrm.2016.43
1192:rated voting systems
1188:median voter theorem
948:Economics portal
895:Median voter theorem
114:Comparative politics
4687:Plurality criterion
4286:Kemeny–Young method
3899:. Penguin. p.
2579:electionlab.mit.edu
1510:Burlington, Vermont
936:Politics portal
647:Vote linkage system
618:Seat linkage system
205:Ranked-choice (RCV)
4728:Election threshold
4662:Majority criterion
4338:Supplementary vote
4060:City of Burlington
3679:City of Burlington
1883:10.1007/bf00127534
1153:rated-voting rules
1058:political spectrum
1027:majority-preferred
832:Discursive dilemma
791:Lesser evil voting
666:Supermixed systems
369:Largest remainders
227:Round-robin voting
95:
60:
4799:
4798:
4697:Reversal symmetry
4606:Cumulative voting
4588:Semi-proportional
4563:Mixed single vote
4529:
4528:
4405:Mixed single vote
4313:Exhaustive ballot
4276:Copeland's method
4271:Condorcet methods
4211:Electoral systems
4027:Rutlandherald.com
3823:on July 26, 2011.
3115:978-3-642-02838-0
2530:. Rochester, NY.
2216:. Rochester, NY.
2161:Electoral Studies
2123:. Rochester, NY.
1789:
1788:
1631:4064 (Montroll) –
1623:4597 (Montroll) –
1615:4570 (Montroll) –
1607:6262 (Montroll) –
1413:
1412:
1409:
1408:
1043:first preferences
995:
994:
882:Gibbard's theorem
822:Dominance paradox
759:Perverse response
463:Phragmen's method
329:Majority judgment
257:Positional voting
215:Condorcet methods
83:electoral systems
36:political compass
16:(Redirected from
4824:
4738:Liquid democracy
4390:
4389:
4370:Two-round system
4281:Dodgson's method
4204:
4197:
4190:
4181:
4180:
4143:"Center squeeze"
4130:
4129:
4127:
4125:
4111:
4105:
4104:
4094:
4070:
4064:
4063:
4062:. March 2, 2010.
4057:
4049:
4043:
4042:
4040:
4038:
4033:on March 4, 2016
4019:
4013:
4012:
4004:
3998:
3997:
3984:
3960:
3954:
3953:
3951:
3927:
3918:
3917:
3898:
3888:
3882:
3881:
3861:
3855:
3854:
3848:
3846:
3831:
3825:
3824:
3812:
3806:
3805:
3765:
3759:
3758:
3727:
3721:
3720:
3718:
3716:
3711:on July 25, 2011
3701:
3695:
3694:
3692:
3690:
3681:. Archived from
3675:"Mayor Bob Kiss"
3671:
3665:
3656:
3647:
3646:
3644:
3632:
3626:
3625:
3620:
3608:
3602:
3601:
3595:
3594:
3579:
3573:
3572:
3532:
3526:
3525:
3520:
3508:
3502:
3501:
3499:
3498:
3472:
3466:
3465:
3433:
3420:
3419:
3414:
3402:
3393:
3392:
3386:
3385:
3370:
3361:
3360:
3355:
3343:
3334:
3333:
3331:
3319:
3308:
3307:
3302:
3290:
3284:
3283:
3281:
3279:
3273:
3262:
3254:
3248:
3247:
3230:(6): 1097–1120.
3215:
3209:
3208:
3180:
3174:
3173:
3133:
3124:
3123:
3091:
3082:
3081:
3041:
3032:
3031:
2999:
2990:
2989:
2984:
2983:
2968:
2962:
2961:
2937:
2931:
2930:
2920:
2896:
2887:
2886:
2884:
2883:
2857:
2846:
2845:
2839:
2838:
2823:
2817:
2816:
2811:
2799:
2790:
2789:
2761:
2755:
2754:
2722:
2716:
2715:
2680:
2674:
2673:
2667:
2666:
2660:The Conversation
2651:
2645:
2644:
2623:
2599:
2593:
2592:
2586:
2585:
2571:
2565:
2564:
2562:
2561:
2546:
2540:
2539:
2524:6 Phoenix L. Rev
2515:
2509:
2508:
2480:
2474:
2473:
2433:
2424:
2423:
2421:
2420:
2413:buffett.cnbc.com
2405:
2399:
2398:
2396:
2395:
2380:
2374:
2373:
2330:
2324:
2323:
2291:
2280:
2279:
2236:
2230:
2229:
2210:6 Phoenix L. Rev
2201:
2195:
2194:
2176:
2152:
2141:
2140:
2117:6 Phoenix L. Rev
2108:
2102:
2101:
2062:
2056:
2055:
2053:
2051:
2037:
2031:
2030:
1987:
1981:
1980:
1974:
1973:
1958:
1952:
1951:
1908:
1899:
1898:
1862:
1769:
1700:
1651:
1596:
1564:
1563:
1548:electoral reform
1536:voting theorists
1518:Burlington mayor
1492:Condorcet voting
1335:Nick Begich III
1315:
1308:
1301:
1291:
1290:
1277:
1269:
1268:
1227:central tendency
1172:two-round runoff
1161:primary election
1031:socially-optimal
1015:two-round system
987:
980:
973:
959:
958:
946:
945:
934:
933:
889:Positive results
784:Strategic voting
681:Majority jackpot
638:
627:
498:Liquid democracy
374:National remnant
364:Highest averages
301:
286:
271:
203:
194:Alternative vote
192:
176:Partisan primary
168:
109:Mechanism design
62:
61:
21:
4832:
4831:
4827:
4826:
4825:
4823:
4822:
4821:
4802:
4801:
4800:
4795:
4778:
4757:
4711:
4702:Smith criterion
4615:
4582:
4543:Parallel voting
4525:
4521:Imperiali quota
4494:
4461:
4379:
4333:Contingent vote
4296:Nanson's method
4254:Unified primary
4244:Approval voting
4230:
4213:
4208:
4166:
4123:
4121:
4113:
4112:
4108:
4071:
4067:
4055:
4051:
4050:
4046:
4036:
4034:
4021:
4020:
4016:
4005:
4001:
3961:
3957:
3949:
3928:
3921:
3911:
3889:
3885:
3862:
3858:
3844:
3842:
3840:RangeVoting.org
3832:
3828:
3813:
3809:
3766:
3762:
3728:
3724:
3714:
3712:
3703:
3702:
3698:
3688:
3686:
3673:
3672:
3668:
3657:
3650:
3633:
3629:
3609:
3605:
3592:
3590:
3580:
3576:
3553:10.2307/2110496
3533:
3529:
3509:
3505:
3496:
3494:
3484:Washington Post
3473:
3469:
3434:
3423:
3403:
3396:
3383:
3381:
3371:
3364:
3344:
3337:
3320:
3311:
3291:
3287:
3277:
3275:
3271:
3260:
3256:
3255:
3251:
3216:
3212:
3197:
3181:
3177:
3154:10.2307/2938959
3134:
3127:
3116:
3092:
3085:
3062:10.2307/2111214
3042:
3035:
3000:
2993:
2981:
2979:
2969:
2965:
2938:
2934:
2897:
2890:
2881:
2879:
2869:Washington Post
2858:
2849:
2836:
2834:
2824:
2820:
2800:
2793:
2762:
2758:
2723:
2719:
2681:
2677:
2664:
2662:
2654:Kousser, Thad.
2652:
2648:
2600:
2596:
2583:
2581:
2573:
2572:
2568:
2559:
2557:
2547:
2543:
2516:
2512:
2481:
2477:
2434:
2427:
2418:
2416:
2407:
2406:
2402:
2393:
2391:
2381:
2377:
2351:10.2307/2110786
2331:
2327:
2292:
2283:
2257:10.2307/3088418
2237:
2233:
2202:
2198:
2153:
2144:
2109:
2105:
2079:10.2307/1953842
2063:
2059:
2049:
2047:
2039:
2038:
2034:
2008:10.2307/3088418
1988:
1984:
1971:
1969:
1959:
1955:
1929:10.2307/2110786
1909:
1902:
1863:
1846:
1843:
1826:
1772:James Simpson (
1719:3971 (Wright) –
1714:1310 (Simpson)
1711:5270 (Wright) –
1599:Andy Montroll (
1586:Win : Loss
1544:no-show paradox
1506:
1500:
1449:no-show paradox
1433:Nick Begich III
1399:
1393:
1379:
1372:
1365:
1272:
1267:
1261:
1256:
1236:approval voting
1216:core supporters
1208:
1200:approval voting
1178:. By contrast,
1145:Hillary Clinton
1139:defeating both
1117:Nick Begich III
1066:Black's theorem
1013:rules like the
991:
953:
952:
940:
928:
920:
919:
886:
862:Arrow's theorem
852:
842:
841:
810:
780:
769:No-show paradox
750:
736:Cloning paradox
726:Spoiler effects
723:
713:
712:
687:
574:
557:
547:
546:
519:
510:Maximal lottery
477:
458:Thiele's method
447:
417:
349:
339:
338:
324:Approval voting
312:Cardinal voting
308:
253:
247:Maximal lottery
211:
143:
133:
28:
23:
22:
15:
12:
11:
5:
4830:
4820:
4819:
4814:
4797:
4796:
4783:
4780:
4779:
4777:
4776:
4771:
4765:
4763:
4759:
4758:
4756:
4755:
4750:
4745:
4740:
4735:
4730:
4725:
4719:
4717:
4713:
4712:
4710:
4709:
4704:
4699:
4694:
4689:
4684:
4679:
4674:
4669:
4664:
4659:
4654:
4649:
4644:
4639:
4634:
4629:
4623:
4621:
4617:
4616:
4614:
4613:
4608:
4603:
4601:Limited voting
4598:
4592:
4590:
4584:
4583:
4581:
4580:
4575:
4570:
4565:
4560:
4555:
4550:
4545:
4539:
4537:
4531:
4530:
4527:
4526:
4524:
4523:
4518:
4513:
4508:
4502:
4500:
4496:
4495:
4493:
4492:
4487:
4486:
4485:
4480:
4469:
4467:
4463:
4462:
4460:
4459:
4454:
4449:
4448:
4447:
4442:
4437:
4427:
4422:
4417:
4412:
4407:
4402:
4396:
4394:
4387:
4381:
4380:
4378:
4377:
4372:
4367:
4362:
4357:
4352:
4347:
4342:
4341:
4340:
4335:
4330:
4328:Coombs' method
4320:
4315:
4310:
4309:
4308:
4306:Schulze method
4303:
4298:
4293:
4288:
4283:
4278:
4268:
4266:Bucklin voting
4263:
4258:
4257:
4256:
4251:
4240:
4238:
4232:
4231:
4218:
4215:
4214:
4207:
4206:
4199:
4192:
4184:
4178:
4177:
4172:
4165:
4164:External links
4162:
4161:
4160:
4146:, authored by
4132:
4131:
4106:
4065:
4044:
4014:
3999:
3955:
3932:Phoenix L. Rev
3919:
3909:
3883:
3872:(3): 378–389.
3856:
3826:
3807:
3760:
3722:
3696:
3666:
3648:
3627:
3603:
3574:
3547:(2): 303–311.
3527:
3503:
3467:
3421:
3394:
3362:
3335:
3309:
3285:
3249:
3210:
3195:
3175:
3148:(1): 102–114.
3125:
3114:
3083:
3056:(1): 112–118.
3033:
3014:(1): 113–136.
2991:
2963:
2932:
2911:(6): 618–636.
2888:
2847:
2818:
2791:
2756:
2737:(5): 663–666.
2717:
2695:(5): 623–651.
2675:
2646:
2614:(4): 809–827.
2594:
2566:
2541:
2510:
2489:Party Politics
2475:
2454:10.1086/256633
2425:
2400:
2375:
2325:
2306:(3): 445–457.
2281:
2251:(1): 134–147.
2231:
2196:
2142:
2103:
2073:(2): 426–448.
2057:
2032:
2002:(1): 134–147.
1982:
1953:
1900:
1877:(2): 389–403.
1842:
1839:
1838:
1837:
1832:
1830:Vote splitting
1825:
1822:
1818:
1817:
1811:
1805:
1799:
1787:
1786:
1784:
1781:0 W : 4 L
1777:
1770:
1762:
1761:
1759:
1756:1 W : 3 L
1752:
1750:721 (Simpson)
1747:5570 (Smith) –
1744:
1737:
1734:
1733:
1731:
1728:2 W : 2 L
1724:
1716:
1708:
1701:
1693:
1692:
1690:
1687:3 W : 1 L
1683:
1681:4061 (Wright)
1675:
1667:
1665:844 (Simpson)
1659:
1652:
1644:
1643:
1640:4 W : 0 L
1636:
1628:
1626:3664 (Wright)
1620:
1612:
1610:591 (Simpson)
1604:
1597:
1589:
1588:
1583:
1580:
1577:
1574:
1571:
1568:
1532:mathematicians
1502:Main article:
1499:
1496:
1411:
1410:
1407:
1406:
1401:
1396:
1389:
1383:
1382:
1375:
1368:
1361:
1357:
1356:
1351:
1346:
1341:
1337:
1336:
1333:
1328:
1321:
1317:
1316:
1309:
1302:
1295:
1287:
1286:
1283:
1279:
1278:
1263:Main article:
1260:
1257:
1255:
1252:
1248:Coombs' method
1207:
1204:
1133:Bernie Sanders
1104:, and various
1007:spoiler effect
1003:center squeeze
993:
992:
990:
989:
982:
975:
967:
964:
963:
951:
950:
938:
925:
922:
921:
918:
917:
912:
907:
902:
897:
885:
884:
879:
874:
869:
864:
853:
848:
847:
844:
843:
840:
839:
834:
829:
824:
809:
808:
806:Turkey-raising
803:
798:
793:
779:
778:
777:
776:
766:
761:
749:
748:
746:Center squeeze
743:
738:
733:
731:Spoiler effect
724:
719:
718:
715:
714:
711:
710:
705:
704:
703:
690:By ballot type
686:
685:
684:
683:
678:
673:
663:
662:
661:
660:
659:
654:
644:
643:
642:
631:
608:
607:
606:
601:
596:
591:
573:
572:
567:
558:
553:
552:
549:
548:
545:
544:
542:Limited voting
539:
538:
537:
518:
517:
512:
507:
502:
501:
500:
495:
476:
475:
470:
465:
460:
446:
445:
440:
435:
430:
416:
415:
414:
413:
411:Localized list
408:
403:
398:
393:
383:
382:
381:
379:Biproportional
376:
371:
366:
350:
345:
344:
341:
340:
337:
336:
331:
326:
321:
307:
306:
291:
276:
252:
251:
250:
249:
244:
239:
234:
224:
210:
209:
208:
207:
196:
183:Instant-runoff
180:
179:
178:
170:Jungle primary
157:
146:Single vote -
144:
139:
138:
135:
134:
132:
131:
121:
116:
111:
106:
100:
97:
96:
86:
85:
75:
74:
42:. The bias of
26:
18:Center-squeeze
9:
6:
4:
3:
2:
4829:
4818:
4815:
4813:
4812:Voting theory
4810:
4809:
4807:
4794:
4793:
4788:
4787:
4781:
4775:
4772:
4770:
4767:
4766:
4764:
4760:
4754:
4751:
4749:
4746:
4744:
4741:
4739:
4736:
4734:
4731:
4729:
4726:
4724:
4721:
4720:
4718:
4714:
4708:
4705:
4703:
4700:
4698:
4695:
4693:
4690:
4688:
4685:
4683:
4680:
4678:
4675:
4673:
4670:
4668:
4665:
4663:
4660:
4658:
4655:
4653:
4650:
4648:
4645:
4643:
4640:
4638:
4635:
4633:
4630:
4628:
4625:
4624:
4622:
4618:
4612:
4609:
4607:
4604:
4602:
4599:
4597:
4594:
4593:
4591:
4589:
4585:
4579:
4576:
4574:
4571:
4569:
4566:
4564:
4561:
4559:
4556:
4554:
4551:
4549:
4546:
4544:
4541:
4540:
4538:
4536:
4532:
4522:
4519:
4517:
4514:
4512:
4509:
4507:
4504:
4503:
4501:
4497:
4491:
4488:
4484:
4481:
4479:
4476:
4475:
4474:
4471:
4470:
4468:
4464:
4458:
4455:
4453:
4450:
4446:
4443:
4441:
4438:
4436:
4433:
4432:
4431:
4428:
4426:
4423:
4421:
4418:
4416:
4413:
4411:
4408:
4406:
4403:
4401:
4398:
4397:
4395:
4391:
4388:
4386:
4382:
4376:
4373:
4371:
4368:
4366:
4363:
4361:
4358:
4356:
4353:
4351:
4348:
4346:
4343:
4339:
4336:
4334:
4331:
4329:
4326:
4325:
4324:
4321:
4319:
4316:
4314:
4311:
4307:
4304:
4302:
4299:
4297:
4294:
4292:
4289:
4287:
4284:
4282:
4279:
4277:
4274:
4273:
4272:
4269:
4267:
4264:
4262:
4259:
4255:
4252:
4250:
4247:
4246:
4245:
4242:
4241:
4239:
4237:
4236:Single-winner
4233:
4229:
4227:
4223:
4216:
4212:
4205:
4200:
4198:
4193:
4191:
4186:
4185:
4182:
4176:
4173:
4171:
4168:
4167:
4159:
4157:
4153:
4149:
4144:
4141:
4139:
4134:
4133:
4120:
4116:
4110:
4102:
4098:
4093:
4092:11250/2356264
4088:
4084:
4080:
4076:
4069:
4061:
4054:
4048:
4032:
4028:
4024:
4018:
4010:
4003:
3996:
3992:
3988:
3983:
3982:11250/2356264
3978:
3974:
3970:
3966:
3959:
3952:
3945:
3941:
3937:
3933:
3926:
3924:
3916:
3912:
3910:9780698163843
3906:
3902:
3897:
3896:
3887:
3879:
3875:
3871:
3867:
3860:
3853:
3841:
3837:
3830:
3822:
3818:
3811:
3804:
3799:
3795:
3791:
3787:
3783:
3779:
3775:
3771:
3770:Public Choice
3764:
3757:
3753:
3749:
3745:
3741:
3737:
3733:
3726:
3710:
3706:
3700:
3684:
3680:
3676:
3670:
3664:
3660:
3655:
3653:
3643:
3638:
3631:
3624:
3619:
3614:
3607:
3600:
3589:
3585:
3578:
3570:
3566:
3562:
3558:
3554:
3550:
3546:
3542:
3538:
3531:
3524:
3519:
3514:
3507:
3493:
3489:
3485:
3481:
3477:
3471:
3463:
3459:
3455:
3451:
3447:
3443:
3442:Math Horizons
3439:
3432:
3430:
3428:
3426:
3418:
3413:
3408:
3401:
3399:
3391:
3380:
3376:
3369:
3367:
3359:
3354:
3349:
3342:
3340:
3330:
3325:
3318:
3316:
3314:
3306:
3301:
3296:
3289:
3270:
3266:
3259:
3253:
3245:
3241:
3237:
3233:
3229:
3225:
3221:
3214:
3206:
3202:
3198:
3196:9780471680291
3192:
3188:
3187:
3179:
3171:
3167:
3163:
3159:
3155:
3151:
3147:
3143:
3139:
3132:
3130:
3122:
3117:
3111:
3107:
3103:
3099:
3098:
3090:
3088:
3079:
3075:
3071:
3067:
3063:
3059:
3055:
3051:
3047:
3040:
3038:
3029:
3025:
3021:
3017:
3013:
3009:
3005:
2998:
2996:
2988:
2978:
2974:
2967:
2959:
2955:
2951:
2947:
2943:
2936:
2928:
2924:
2919:
2914:
2910:
2906:
2902:
2895:
2893:
2878:
2874:
2870:
2866:
2862:
2856:
2854:
2852:
2844:
2833:
2829:
2822:
2815:
2810:
2805:
2798:
2796:
2787:
2783:
2779:
2775:
2771:
2767:
2760:
2752:
2748:
2744:
2740:
2736:
2732:
2728:
2721:
2714:
2710:
2706:
2702:
2698:
2694:
2690:
2686:
2679:
2672:
2661:
2657:
2650:
2643:
2639:
2635:
2631:
2627:
2622:
2617:
2613:
2609:
2605:
2598:
2591:
2580:
2576:
2570:
2556:
2552:
2545:
2537:
2533:
2529:
2525:
2521:
2514:
2506:
2502:
2498:
2494:
2490:
2486:
2479:
2471:
2467:
2463:
2459:
2455:
2451:
2447:
2443:
2439:
2432:
2430:
2414:
2410:
2404:
2390:
2386:
2379:
2372:
2368:
2364:
2360:
2356:
2352:
2348:
2344:
2340:
2336:
2329:
2321:
2317:
2313:
2309:
2305:
2301:
2297:
2290:
2288:
2286:
2278:
2274:
2270:
2266:
2262:
2258:
2254:
2250:
2246:
2242:
2235:
2228:
2223:
2219:
2215:
2211:
2207:
2200:
2192:
2188:
2184:
2180:
2175:
2170:
2166:
2162:
2158:
2151:
2149:
2147:
2139:
2137:
2130:
2126:
2122:
2118:
2114:
2107:
2100:
2096:
2092:
2088:
2084:
2080:
2076:
2072:
2068:
2061:
2046:
2042:
2036:
2029:
2025:
2021:
2017:
2013:
2009:
2005:
2001:
1997:
1993:
1986:
1979:
1968:
1964:
1957:
1950:
1946:
1942:
1938:
1934:
1930:
1926:
1922:
1918:
1914:
1907:
1905:
1897:
1892:
1888:
1884:
1880:
1876:
1872:
1871:Public Choice
1868:
1861:
1859:
1857:
1855:
1853:
1851:
1849:
1844:
1836:
1833:
1831:
1828:
1827:
1821:
1815:
1812:
1809:
1806:
1803:
1800:
1797:
1794:
1793:
1792:
1783:
1782:
1778:
1775:
1771:
1768:
1764:
1763:
1758:
1757:
1753:
1751:
1748:
1745:
1742:
1738:
1736:
1735:
1730:
1729:
1725:
1723:
1722:3793 (Smith)
1720:
1717:
1715:
1712:
1709:
1706:
1703:Kurt Wright (
1702:
1699:
1695:
1694:
1691:
1689:
1688:
1684:
1682:
1679:
1678:4313 (Kiss) –
1676:
1674:
1673:3576 (Smith)
1671:
1670:3944 (Kiss) –
1668:
1666:
1663:
1662:5514 (Kiss) –
1660:
1657:
1653:
1650:
1646:
1645:
1642:
1641:
1637:
1635:
1632:
1629:
1627:
1624:
1621:
1619:
1618:2997 (Smith)
1616:
1613:
1611:
1608:
1605:
1602:
1598:
1595:
1591:
1590:
1587:
1584:
1581:
1578:
1575:
1572:
1569:
1566:
1565:
1562:
1560:
1555:
1553:
1549:
1545:
1541:
1537:
1533:
1528:
1526:
1522:
1519:
1515:
1511:
1505:
1495:
1493:
1489:
1485:
1481:
1477:
1473:
1469:
1465:
1461:
1456:
1454:
1450:
1444:
1442:
1438:
1434:
1430:
1426:
1422:
1418:
1405:
1402:
1397:
1395:
1390:
1388:
1385:
1384:
1381:
1376:
1374:
1369:
1367:
1362:
1359:
1358:
1355:
1352:
1350:
1347:
1345:
1342:
1339:
1338:
1334:
1332:
1329:
1327:
1326:
1322:
1319:
1318:
1314:
1310:
1307:
1303:
1300:
1296:
1293:
1292:
1288:
1284:
1280:
1276:
1270:
1266:
1251:
1249:
1245:
1239:
1237:
1233:
1228:
1224:
1219:
1217:
1213:
1203:
1201:
1197:
1193:
1189:
1185:
1181:
1177:
1173:
1169:
1164:
1162:
1158:
1154:
1150:
1146:
1142:
1138:
1134:
1130:
1126:
1122:
1118:
1114:
1109:
1107:
1103:
1099:
1095:
1091:
1087:
1081:
1079:
1075:
1071:
1067:
1063:
1059:
1055:
1051:
1046:
1044:
1040:
1036:
1032:
1028:
1024:
1020:
1016:
1012:
1008:
1005:is a kind of
1004:
1000:
999:social choice
988:
983:
981:
976:
974:
969:
968:
966:
965:
962:
957:
949:
944:
939:
937:
932:
927:
926:
924:
923:
916:
913:
911:
908:
906:
905:May's theorem
903:
901:
898:
896:
893:
892:
891:
890:
883:
880:
878:
875:
873:
870:
868:
865:
863:
860:
859:
858:
857:
851:
846:
845:
838:
835:
833:
830:
828:
825:
823:
820:
819:
818:
817:
816:
815:majority rule
813:Paradoxes of
807:
804:
802:
799:
797:
794:
792:
789:
788:
787:
786:
785:
775:
772:
771:
770:
767:
765:
762:
760:
757:
756:
755:
754:
747:
744:
742:
739:
737:
734:
732:
729:
728:
727:
722:
717:
716:
709:
706:
702:
699:
698:
697:
694:
693:
692:
691:
682:
679:
677:
674:
672:
669:
668:
667:
664:
658:
655:
653:
650:
649:
648:
645:
641:
636:
632:
630:
625:
621:
620:
619:
616:
615:
614:
613:
609:
605:
602:
600:
597:
595:
592:
590:
587:
586:
585:
584:
579:
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577:
571:
568:
566:
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1325:Mary Peltola
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242:Ranked pairs
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4743:Spoilt vote
4506:Droop quota
4445:Schulze STV
4420:Rural–urban
4365:STAR voting
4261:Borda count
4124:December 4,
2050:December 4,
1739:Dan Smith (
1579:vs. Wright
1540:pathologies
1429:Sarah Palin
1425:Republicans
1387:Final round
1331:Sarah Palin
1125:Sarah Palin
696:Single vote
599:Conditional
594:Coexistence
443:Quota Borda
433:Schulze STV
391:Closed list
334:STAR voting
279:Borda count
4806:Categories
4762:Comparison
4516:Hare quota
4466:Allocation
4452:Spare vote
4440:Hare-Clark
4410:Party-list
3845:October 1,
3715:January 3,
3593:2024-07-11
3497:2024-02-09
3384:2023-05-14
2982:2024-08-18
2882:2024-02-09
2837:2023-05-14
2665:2018-06-23
2584:2024-07-25
2560:2024-09-05
2419:2024-09-30
2394:2024-09-05
2174:2306.07147
2167:: 102799.
1972:2023-05-14
1841:References
1654:Bob Kiss (
1576:vs. Smith
1570:Candidate
1559:initiative
1482:, such as
1423:) and two
1404:Eliminated
1354:Republican
1349:Republican
1344:Democratic
1320:Candidate
1121:right-wing
1098:California
1009:common to
801:Truncation
530:Cumulative
353:Party-list
128:By country
119:Comparison
4753:Unseating
4748:Sortition
4350:Plurality
4226:Economics
4138:this edit
4101:1556-5068
3790:0048-5829
3752:0165-4896
3738:: 57–66.
3561:0092-5853
3492:0190-8286
3462:1072-4117
3244:1572-9907
3162:0003-0554
3070:0092-5853
3028:0951-6298
2927:1532-673X
2877:0190-8286
2786:1556-5068
2751:0010-4140
2709:0010-4140
2630:2049-8470
2505:1354-0688
2462:0022-3808
2359:0092-5853
2320:1572-9966
2265:0092-5853
2191:0261-3794
2016:0092-5853
1937:0092-5853
1891:0048-5829
1582:vs. Kiss
1212:primaries
1180:Condorcet
1149:majority-
1090:Australia
1054:centrists
708:Dual-vote
401:Panachage
396:Open list
386:List type
264:Plurality
160:Two-round
148:plurality
71:Economics
52:primaries
4620:Criteria
4573:Scorporo
4222:politics
4037:April 1,
3798:30833409
3379:The Hill
3269:Archived
2832:The Hill
1967:The Hill
1824:See also
1796:Montroll
1521:Bob Kiss
1488:approval
1417:Democrat
1254:Examples
1190:, while
1147:under a
1123:spoiler
1115:, where
1108:cities.
428:Hare STV
67:Politics
65:A joint
4792:Project
4483:D'Hondt
4435:CPO-STV
4393:Systems
3991:2670462
3944:2276015
3938:: 117.
3803:failure
3663:Senate.
3569:2110496
3205:0356303
3170:2938959
3078:2111214
2638:2260083
2536:2276015
2470:1825026
2367:2110786
2273:3088418
2222:2276015
2129:2276015
2095:1161006
2087:1953842
2024:3088418
1945:2110786
1896:winning
1453:support
1294:
1282:Turnout
1163:rules.
1035:extreme
438:CPO-STV
288:Baldwin
237:Schulze
232:Minimax
150:methods
48:runoffs
40:heatmap
4786:Portal
4723:Ballot
4499:Quotas
4228:series
4136:As of
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1567:Party
1400:48.5%
1398:86,026
1392:91,266
1378:52,536
1371:58,339
1364:74,817
1340:Party
1174:, and
1021:, and
303:Coombs
73:series
54:, and
4716:Other
4535:Mixed
4056:(PDF)
3950:'
3794:S2CID
3637:arXiv
3613:arXiv
3565:JSTOR
3513:arXiv
3407:arXiv
3348:arXiv
3324:arXiv
3295:arXiv
3272:(PDF)
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3166:JSTOR
3074:JSTOR
2804:arXiv
2466:JSTOR
2363:JSTOR
2269:JSTOR
2169:arXiv
2091:S2CID
2083:JSTOR
2020:JSTOR
1941:JSTOR
1814:Smith
1490:, or
1458:Many
1394:51.5%
1380:27.8%
1373:30.9%
1366:39.7%
1285:32.2%
1196:score
1194:like
1094:Maine
1064:. By
640:'MMP'
629:'AMS'
4224:and
4156:GFDL
4154:and
4126:2019
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4039:2016
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1484:STAR
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