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Social choice and electoral systems |
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Mathematicsportal |
In social choice, a center squeeze is a kind of spoiler effect common to plurality-elimination rules like the two-round system, plurality-with-primaries, and ranked-choice voting (RCV). [1] In a center squeeze, a majority-preferred and socially-optimal candidate is eliminated in favor of a more extreme alternative. [2] [3] Extreme or polarizing candidates who focus on appealing to a small base of core supporters can thus "squeeze" broadly-popular candidates trapped between them, starving them of the first preferences they need to survive early rounds. [1] [4] [5]
The term "center squeeze" refers to candidates who are close to the center of public opinion, and as a result is not limited to centrists along the traditional political spectrum. [6] Center squeezes can occur in any situation where voters prefer candidates who hold views similar to their own. [7] By Black's theorem, the candidate who appeals most to the median voter will be the majority-preferred candidate, which means they will be elected by any method compatible with majority-rule. [1] [2] However, in methods that strongly prioritize first preferences, these candidates are often eliminated early on because they aim for broad appeal rather than strong base support. [1] [8] [9]
Voting systems that suffer from the center-squeeze effect incentivize candidates to avoid the political center, [4] [10] creating political polarization in the long run. [8] [10] [11] As a result, rules like RCV can lead to extreme winners even if center-squeezes seem empirically rare, because the rules disincentivize moderates from running for office in the first place. [10] [12] [13] The effect was first predicted by social choice theorists in the 1940s [14] before being confirmed empirically in Australia, [12] [15] [16] California, [17] [18] and Maine. [19]
Famous examples of center-squeezes include the 2022 Alaska special election, where Nick Begich III was eliminated in the first round by right-wing spoiler Sarah Palin, [20] [21] despite a majority of voters preferring Begich to either one of his opponents. [20] [22] Another possible example is the 2016 United States presidential election, where polls found several alternatives defeating both Donald Trump and Hillary Clinton under majority- or rated-voting rules, but being squeezed out by both the IRV and primary election rules. [23] [24]
Voting systems most strongly affected by center squeeze are first-preference plurality, plurality-with-primaries, two-round runoff, and ranked-choice voting (RCV). [1] By contrast, Condorcet and rated voting methods are not affected by this pathology. Condorcet methods are insulated from center-squeezes by the median voter theorem, [25] [26] while rated voting systems like score or approval voting are protected by closely-related results. [27] [28] [29]
Center squeeze is a major feature of two-party systems using primaries or other multiple-round systems. [1] In all such races, candidates must focus on appealing to their core supporters to ensure they can make it past the first round, where only first-preferences can count. 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. [1] 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 precise way voters score candidates, with different measures of central tendency minimizing different distance metrics; for example, an absolute value. [30] Under the 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. [27] [28] [31] The opposite situation of a bias toward "bland" or inoffensive candidates, and against polarizing ones, does not appear in any rule or method in common use. However, it can occur for bottom-heavy or negative voting methods that elect candidates with the least opposition, such as anti-plurality voting or Coombs' method. [32]
Alaska's at-large congressional district | |||||||||||||||||||||
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Turnout | 32.2% [33] | ||||||||||||||||||||
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The 2022 Alaska special election seat was an infamous example of a center squeeze. The ranked-choice runoff election involved one Democrat (Mary Peltola) and two Republicans (Sarah Palin and Nick Begich III). Because the full ballot data for the race was released, social choice theorists were able to confirm that Palin spoiled the race for Begich, with Peltola winning the race as a result of several pathological behaviors that tend to characterize center-squeeze elections. [22] [34]
The election produced a winner opposed by a majority of voters, with a majority of voters ranking Begich above Peltola and Palin [35] [36] [37] and more than half giving Peltola no support at all. [35] [36] The election was also notable as a no-show paradox, where a candidate is eliminated as a result of votes cast in support of their candidacy. In this case, ballots ranking Palin first and Begich second instead allowed Peltola to win. [38] [39] [37]
Many social choice theorists criticized the ranked-choice runoff procedure for its pathological behavior. [40] [41] Along with being a center-squeeze, the election was a negative voting weight event, [39] where a voter's ballot has the opposite of its intended effect (e.g. where a candidate would need more votes to lose). [39] [42] In this race, Peltola would have lost if she had received more support from Palin voters, [43] [44] [45] and won as a result of 5,200 ballots that ranked her last (after Palin then Begich). [39] [38] However, social choice theorists 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 alternatives without these behaviors, such as STAR, approval, or Condorcet voting. [22] [35]
The 2009 Burlington mayoral election was held in March 2009 for the city of Burlington, Vermont, 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 2006 mayoral election. [46] In the 2009 election, incumbent Burlington mayor (Bob Kiss) won reelection as a member of the Vermont Progressive Party, [47] defeating Kurt Wright in the final round with 48% of the vote. [48]
The election results were criticized by mathematicians and voting theorists for several pathologies associated with RCV. These included a no-show paradox, where Kiss won only as a result of 750 votes ranking Kiss in last place. [49] [50] [51] Several electoral reform advocates branded the election a failure after Kiss was elected despite 54% of voters voting for Montroll over Kiss, [52] [53] violating the majority-rule principle. [54] [55] [56] 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. [55] [57]
The controversy culminated in a successful 2010 initiative that repealed RCV by a vote of 52% to 48%, [58] [59] a 16-point shift from the 64% who had supported the 2005 ratification. [46] The results of every possible one-on-one election are as follows:
Party | Candidate | vs. Simpson | vs. Smith | vs. Wright | vs. Kiss | Win : Loss |
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Andy Montroll (D) | 6262 (Montroll) – 591 (Simpson) | 4570 (Montroll) – 2997 (Smith) | 4597 (Montroll) – 3664 (Wright) | 4064 (Montroll) – 3476 (Kiss) | 4 W : 0 L | |
Bob Kiss (P) | 5514 (Kiss) – 844 (Simpson) | 3944 (Kiss) – 3576 (Smith) | 4313 (Kiss) – 4061 (Wright) | 3 W : 1 L | ||
Kurt Wright (R) | 5270 (Wright) – 1310 (Simpson) | 3971 (Wright) – 3793 (Smith) | 2 W : 2 L | |||
Dan Smith (I) | 5570 (Smith) – 721 (Simpson) | 1 W : 3 L | ||||
James Simpson (G) | 0 W : 4 L |
This leads to an overall preference ranking of:
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. [60] [5]
The two-round system, also called ballotage, top-two runoff, or two-round plurality, is a single winner voting method. It is sometimes called plurality-runoff, although this term can also be used for other, closely-related systems such as ranked-choice voting or the exhaustive ballot. It falls under the class of plurality-based voting rules, together with instant-runoff and first-past-the-post (FPP). In a two-round system, both rounds are held under choose-one voting, where the voter marks a single favorite candidate. The two candidates with the most votes in the first round proceed to a second round, where all other candidates are excluded.
In social choice theory and politics, a spoiler effect is a situation where a losing candidate's performance affects the result of an election. A voting system that is not affected by spoilers satisfies independence of irrelevant alternatives and is called spoilerproof.
A Condorcet method is an election method that elects the candidate who wins a majority of the vote in every head-to-head election against each of the other candidates, whenever there is such a candidate. A candidate with this property, the pairwise champion or beats-all winner, is formally called the Condorcet winner or Pairwise Majority Rule Winner (PMRW). The head-to-head elections need not be done separately; a voter's choice within any given pair can be determined from the ranking.
Coombs' method is a ranked voting system. Like instant-runoff (IRV-RCV), Coombs' method is a sequential-loser method, where the last-place finisher according to one method is eliminated in each round. However, unlike in instant-runoff, each round has electors voting against their least-favorite candidate; the candidate ranked last by the most voters is eliminated.
The positive response, monotonicity, or nonperversitycriterion is a principle of social choice that says increasing a candidate's ranking or rating should not cause them to lose. Positive response rules out cases where a candidate loses an election as a result of receiving too much support from voters. Rules that violate positive response are said to show perverseresponse.
In an election, a candidate is called a majority winner or majority-preferred candidate if more than half of all voters would support them in a one-on-one race against any one of their opponents. Voting systems where a majority winner will always win are said to satisfy the majority-rule principle, because they extend the principle of majority rule to elections with multiple candidates.
In social choice, a no-show paradox is a pathology in some voting rules, where a candidate loses an election as a result of having too many supporters. More formally, a no-show paradox occurs when adding voters who prefer Alice to Bob causes Alice to lose the election to Bob. Voting systems without the no-show paradox are said to satisfy the participation criterion.
The Borda count electoral system can be combined with an instant-runoff procedure to create hybrid election methods that are called Nanson method and Baldwin method. Both methods are designed to satisfy the Condorcet criterion, and allow for incomplete ballots and equal rankings.
Instant-runoff voting (IRV) is a ranked voting method used in single-winner elections. IRV is also known outside the US as the alternative vote (AV). Today it is in use at a national level to elect the Australian House of Representatives, the National Parliament of Papua New Guinea, the President of Ireland and President of India. In Australia it is also used for elections to the legislative assemblies of all states and territories except Tasmania and the Australian Capital Territory, and for the Tasmanian Legislative Council.
Later-no-harm is a property of some ranked-choice voting systems, first described by Douglas Woodall. In later-no-harm systems, increasing the rating or rank of a candidate ranked below the winner of an election cannot cause a higher-ranked candidate to lose.
Ranked-choice voting (RCV) can refer to one of several ranked voting methods used in some cities and states in the United States. The term is not strictly defined, but most often refers to instant-runoff voting (IRV) or single transferable vote (STV), the main difference being whether only one winner or multiple winners are elected.
Mary Sattler Peltola is an American politician and former tribal judge serving as the U.S. representative from Alaska's at-large congressional district since September 2022. A member of the Democratic Party, she previously served as a judge on the Orutsararmiut Native Council's tribal court, executive director of the Kuskokwim River Inter-Tribal Fish Commission, Bethel city councilor, and member of the Alaska House of Representatives.
Instant-runoff voting (IRV), also known as ranked-choice voting (RCV), preferential voting (PV), or the alternative vote (AV), is a multi-round elimination method where the loser of each round is determined by the first-past-the-post method. In academic contexts, the term instant-runoff voting is generally preferred as it does not run the risk of conflating the method with methods of ranked voting in general.
The 2009 Burlington mayoral election was the second mayoral election since the city's 2005 change to instant-runoff voting (IRV), after the 2006 mayoral election. In the 2009 election, incumbent Burlington mayor won reelection as a member of the Vermont Progressive Party, defeating Kurt Wright in the final round with 48% of the vote.
Ranked voting is any voting system that uses voters' orderings (rankings) of candidates to choose a single winner or multiple winners. More formally, a ranked rule is one that depends only on which of two candidates is preferred by a voter, and as such does not incorporate any information about intensity of preferences. Ranked voting systems vary dramatically in how preferences are tabulated and counted, which gives them very different properties.
The November 2022 United States House of Representatives election in Alaska was held on Tuesday, November 8, to elect a member of the United States House of Representatives to represent the state of Alaska. Democratic incumbent Mary Peltola won reelection to a full term in office, defeating Republicans Sarah Palin and Nick Begich III and Libertarian Chris Bye in the runoff count.
The 2022 Alaska at-large congressional district special election was held on August 16 to fill the seat left vacant after the death of Republican incumbent Don Young. Mary Peltola defeated former governor Sarah Palin in the election, becoming the first Alaska Native and woman to represent Alaska in the House.
A final-four or final-five primary is an electoral system using a nonpartisan primary by multi-winner plurality in the first step.
The 2022 Alaska state elections took place on November 8, 2022. The state also held Regional Educational Attendance Area (REAA) elections on the first Tuesday in October.
The 2024 United States House of Representatives election in Alaska will be held on November 5, 2024, to elect a member of the United States House of Representatives to represent the state of Alaska from its at-large congressional district. The election will coincide with the 2024 U.S. presidential election, as well as other elections to the U.S. House, elections to the United States Senate, and various other state and local elections.
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
However, squeezed by surrounding opponents, a centrist candidate may receive few first-place votes and be eliminated under Hare.
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.
As with simple plurality elections, it is apparent the outcome will be highly sensitive to the distribution of candidates.
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.
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 IRV because he or she finished third and thus would be the first candidate eliminated.
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 under IRV because he or she finished third and thus would be the first candidate eliminated
However, squeezed by surrounding opponents, a centrist candidate may receive few first-place votes and be eliminated under Hare.
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
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 the top two. We detected no shift toward the ideological middle.
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 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.
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
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.
By eliminating the squeezing effect, Approval Voting would encourage the election of consensual candidates. The squeezing effect is typically observed in multiparty elections with a runoff. The runoff tends to prevent extremist candidates from winning, but a centrist candidate who would win any pairwise runoff (the "Condorcet winner") is also often "squeezed" between the left-wing and the right-wing candidates and so eliminated in the first round.
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
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
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.
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
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
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.
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
A display of non-monotonicity under the Alternative Vote method was reported recently, for the March 2009 mayoral election in Burlington, Vermont.
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
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
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.
election where Democratic candidate for mayor was Condorcet winner but finished third behind Republican and 'Progressive'
K was elected even though M was a clear Condorcet winner and W was a clear Plurality winner.