Scoring rules, ballot truncation, and the truncation paradox

Kamwa, Éric

doi:10.1007/s11127-022-00972-8

Cited by 8 publications

(4 citation statements)

References 37 publications

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“…This matter has been studied from a computational angle as the possible winners problem, which asks, given a collection of partial ballots, which candidates could become winners as those ballots are filled out (Konczak and Lang 2005;Chevaleyre et al 2010;Baumeister et al 2012;Xia and Conitzer 2011;Ayadi et al 2019). There is also a wide array of research on how partial ballots can be used for strategic voting and campaigning (Baumeister et al 2012;Narodytska and Walsh 2014;Menon and Larson 2017;Kamwa 2022;Fishburn and Brams 1984). On the empirical side, voluntary truncation is a concern since it can lead to ballot exhaustion (Burnett and Kogan 2015).…”

Section: Related Workmentioning

confidence: 99%

Ballot Length in Instant Runoff Voting

Tomlinson

Ugander

Kleinberg

2023

AAAI

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Instant runoff voting (IRV) is an increasingly-popular alternative to traditional plurality voting in which voters submit rankings over the candidates rather than single votes. In practice, elections using IRV often restrict the ballot length, the number of candidates a voter is allowed to rank on their ballot. We theoretically and empirically analyze how ballot length can influence the outcome of an election, given fixed voter preferences. We show that there exist preference profiles over k candidates such that up to k-1 different candidates win at different ballot lengths. We derive exact lower bounds on the number of voters required for such profiles and provide a construction matching the lower bound for unrestricted voter preferences. Additionally, we characterize which sequences of winners are possible over ballot lengths and provide explicit profile constructions achieving any feasible winner sequence. We also examine how classic preference restrictions influence our results—for instance, single-peakedness makes k-1 different winners impossible but still allows at least Ω(√k). Finally, we analyze a collection of 168 real-world elections, where we truncate rankings to simulate shorter ballots. We find that shorter ballots could have changed the outcome in one quarter of these elections. Our results highlight ballot length as a consequential degree of freedom in the design of IRV elections.

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Section: Related Workmentioning

confidence: 99%

Ballot Length in Instant Runoff Voting

Tomlinson

Ugander

Kleinberg

2023

AAAI

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“…This matter has been studied from a computational angle as the possible winners problem, which asks, given a collection of partial ballots, which candidates could become winners as those ballots are filled out [23,11,7,37,6]. There is also a wide array of research on how partial ballots can be used for strategic voting and campaigning [7,29,28,21,18]. On the empirical side, voluntary truncation is a concern since it can lead to ballot exhaustion [10].…”

Section: Related Workmentioning

confidence: 99%

Ballot Length in Instant Runoff Voting

Tomlinson¹,

Ugander²,

Kleinberg³

2022

Preprint

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Instant runoff voting (IRV) is an increasingly-popular alternative to traditional plurality voting in which voters submit rankings over the candidates rather than individual votes. In practice, municipalities often restrict the ballot length, the number of candidates a voter is allowed to rank on their ballot. We theoretically and empirically analyze how ballot length can influence the outcome of an election, given fixed voter preferences. We show that there exist preference profiles over k candidates such that up to k − 1 different candidates win at different ballot lengths. We derive exact lower bounds on the number of voters required for such profiles and provide constructions matching these bounds. Additionally, we fully characterize which sequences of winners are possible over ballot lengths and provide explicit profile constructions achieving any feasible winner sequence. Finally, we analyze a collection of 168 real-world elections, where we truncate rankings to simulate shorter ballots. We find that shorter ballots could have changed the outcome in one quarter of these elections and that longer ballots can favor particular candidates. Our results highlight ballot length as a consequential degree of freedom in the design of IRV elections.

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“…Several studies ( [2], [4], [9]) study the problem of which candidates could become the RCV winner if partial ballots were filled in to create full rankings. Other studies ([2], [5], [7]) consider how partial ballots can be used for strategic voting or strategic campaigning, focusing on issues such as truncation or no-show paradoxes. Our work is most similar to [17], which contains an empirical component addressing the issue of how many different candidates could be the RCV winner as the truncation level varies.…”

Section: Introductionmentioning

confidence: 99%

An Empirical Analysis of the Effect of Ballot Truncation on Ranked-Choice Electoral Outcomes

Dickerson,

Martin,

McCune

2024

PUMP J. Undergrad. Res.

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In ranked-choice elections voters cast preference ballots which provide a voter's ranking of the candidates. The method of ranked-choice voting (RCV) chooses a winner by using voter preferences to simulate a series of runoff elections. Some jurisdictions which use RCV limit the number of candidates that voters can rank on the ballot, imposing what we term a truncation level, which is the number of candidates that voters are allowed to rank. Given fixed voter preferences, the winner of the election can change if we impose different truncation levels. We use a database of 1183 real-world ranked-choice elections to empirically analyze the potential effects of imposing different truncation levels in ranked-choice elections. Our general finding is that if the truncation level is at least three then restricting the number of candidates on the ballot rarely affects the election winner.

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Scoring rules, ballot truncation, and the truncation paradox

Cited by 8 publications

References 37 publications

Ballot Length in Instant Runoff Voting

Ballot Length in Instant Runoff Voting

Ballot Length in Instant Runoff Voting

An Empirical Analysis of the Effect of Ballot Truncation on Ranked-Choice Electoral Outcomes

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