Trump, Condorcet and Borda: Voting paradoxes in the 2016 Republican presidential primaries

Kurrild-Klitgaard, Peter

doi:10.1016/j.ejpoleco.2017.10.003

Cited by 16 publications

(5 citation statements)

References 24 publications

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“…Illustrations of the potential importance of the problem include Van Deemen (2014) and Gehrlein and Lepelley (2017). Important empirical precursors of the approach we take here are Kurrild-Klitgaard (2018) and Woon et al (2020), though the elections in those papers are U.S. party primaries.…”

mentioning

confidence: 99%

Condorcet Loser in 2016: Apparently Trump; Condorcet Winner: Not Clinton?

Potthoff

Munger

2021

American Politics Research

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Using thermometer score data from the ANES, we show that while there may have been no clear-cut Condorcet winner among the 2016 US presidential candidates, there appears to have been a Condorcet loser: Donald Trump. Thus the surprise is that the electorate preferred not only Hillary Clinton, but also the two “minor” candidates, Gary Johnson and Jill Stein, to Trump. Another surprise is that Johnson may have been the Condorcet winner. A minimal normative standard for evaluating voting systems is advanced, privileging those systems that select Condorcet winners if one exists, and critiquing systems that allow the selection of Condorcet losers. A variety of voting mechanisms are evaluated using the 2016 thermometer scores: Condorcet voting, plurality, Borda, (single winner) Hare, Coombs, range voting, and approval voting. We conclude that the essential problem with the existing voting procedure—Electoral College runoff of primary winners of two major parties—is that it (demonstrably) allows the selection of a Condorcet loser.

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confidence: 99%

Condorcet Loser in 2016: Apparently Trump; Condorcet Winner: Not Clinton?

Potthoff

Munger

2021

American Politics Research

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“…the well-known Condorcet paradox [6,7], the Ostrogorski paradox [17,18], and the paradox of multiple elections [5,20]. The occurrence of such paradoxes has also been studied empirically [8,10].…”

Section: Related Workmentioning

confidence: 99%

The Price of Majority Support

Fritsch¹,

Wattenhofer²

2022

Preprint

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We consider the problem of finding a compromise between the opinions of a group of individuals on a number of mutually independent, binary topics. In this paper, we quantify the loss in representativeness that results from requiring the outcome to have majority support, in other words, the "price of majority support". Each individual is assumed to support an outcome if they agree with the outcome on at least as many topics as they disagree on. Our results can also be seen as quantifying Anscombes paradox which states that topic-wise majority outcome may not be supported by a majority. To measure the representativeness of an outcome, we consider two metrics. First, we look for an outcome that agrees with a majority on as many topics as possible. We prove that the maximum number such that there is guaranteed to exist an outcome that agrees with a majority on this number of topics and has majority support, equals ⌈(𝑡 + 1)/2⌉ where 𝑡 is the total number of topics. Second, we count the number of times a voter opinion on a topic matches the outcome on that topic. The goal is to find the outcome with majority support with the largest number of matches. We consider the ratio between this number and the number of matches of the overall best outcome which may not have majority support. We try to find the maximum ratio such that an outcome with majority support and this ratio of matches compared to the overall best is guaranteed to exist. For 3 topics, we show this ratio to be 5/6 ≈ 0.83. In general, we prove an upper bound that comes arbitrarily close to 2 √ 6−4 ≈ 0.90 as 𝑡 tends to infinity. Furthermore, we numerically compute a better upper and a non-matching lower bound in the relevant range for 𝑡.

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“…During the 2016 US presidential primary season, an NBC News/Wall Street Journal poll (3–6 March) asked respondents both for their top choice and their preference between Donald Trump and each of Ted Cruz, John Kasich, and Marco Rubio. Trump was the Plurality winner, receiving 30% of first-place votes, but Cruz, Kasich, and Rubio were each preferred to Trump by 57%, 57%, and 56% of respondents, respectively (see Kurrild-Klitgaard 2018 concerning statistical significance). For further discussion of whether another Republican might have been majority preferred to Trump, see Maskin and Sen 2016, Maskin 2017, Kurrild-Klitgaard 2018, and Woon et al 2020.…”

Section: Introductionmentioning

confidence: 99%

“…Trump was the Plurality winner, receiving 30% of first-place votes, but Cruz, Kasich, and Rubio were each preferred to Trump by 57%, 57%, and 56% of respondents, respectively (see Kurrild-Klitgaard 2018 concerning statistical significance). For further discussion of whether another Republican might have been majority preferred to Trump, see Maskin and Sen 2016, Maskin 2017, Kurrild-Klitgaard 2018, and Woon et al 2020 For related examples outside the US, see, for example, Kaminski 2015, Section 20.3.2 andFeizi et al 2020.…”

Section: Introductionmentioning

confidence: 99%

Axioms for defeat in democratic elections

Holliday

Pacuit

2021

Journal of Theoretical Politics

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We propose six axioms concerning when one candidate should defeat another in a democratic election involving two or more candidates. Five of the axioms are widely satisfied by known voting procedures. The sixth axiom is a weakening of Kenneth Arrow’s famous condition of the Independence of Irrelevant Alternatives (IIA). We call this weakening Coherent IIA. We prove that the five axioms plus Coherent IIA single out a method of determining defeats studied in our recent work: Split Cycle. In particular, Split Cycle provides the most resolute definition of defeat among any satisfying the six axioms for democratic defeat. In addition, we analyze how Split Cycle escapes Arrow’s impossibility theorem and related impossibility results.

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Trump, Condorcet and Borda: Voting paradoxes in the 2016 Republican presidential primaries

Cited by 16 publications

References 24 publications

Condorcet Loser in 2016: Apparently Trump; Condorcet Winner: Not Clinton?

Condorcet Loser in 2016: Apparently Trump; Condorcet Winner: Not Clinton?

The Price of Majority Support

Axioms for defeat in democratic elections

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