The Burr Dilemma in Approval Voting

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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“…The winner is the candidate who receives (approval) votes on the most ballots. (For one critique of approval voting, see Nagel, 2007).…”

Section: Use Of Feeling-thermometer Data To Project Results Under Dif...mentioning

confidence: 99%

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

Potthoff

Munger

2021

American Politics Research

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“…Hence, her preferred reaction is to vote sincerely and reveal her signal.Pure double voting has been termed the Burr dilemma byNagel (2007), who argues that approval voting is inherently biased towards such ties. He documents this with the "[approval] experiment [that] ended disastrously in 1800 with the infamous Electoral College tie between Je¤ erson and Burr ".…”

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confidence: 99%

Divided majority and information aggregation: Theory and experiment

Bouton

Castanheira

Llorente-Saguer

2016

Journal of Public Economics

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This paper both theoretically and experimentally studies the properties of plurality and approval voting when the majority is divided as a result of information imperfections. The minority backs a third alternative, which the majority views as strictly inferior. The majority thus faces two problems: aggregating information and coordinating to defeat the minority candidate. Two types of equilibria coexist under plurality: either voters aggregate information, but this requires splitting their votes, or they coordinate but cannot aggregate information. With approval voting, expected welfare is strictly higher, because some voters multiple vote to achieve both goals at once. In the laboratory, we observe both types of equilibrium under plurality. Which one is selected depends on the size of the minority. Approval voting vastly outperforms plurality. Finally, subject behavior suggests the need to study asymmetric equilibria.

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“…However, if one BC|A or one CB|A voter alters their ballot to approve only their favorite candidate, that candidate wins. As Nagel (2007) shows, this example creates a strategic dynamic between the BC|A and CB|A voters analogous to a game of chicken, in which approving both candidates is analogous to swerving, approving only one candidate is analogous to driving straight ahead, and the election of A is analogous to the car crash. Such a dynamic lacks an obvious practical resolution; and since it does not require an exact tie in the sincere outcome, it may not be uncommon.…”

Section: Borda Approval and Rangementioning

confidence: 99%

A Dodgson-Hare Synthesis

Green-Armytage

2022

Preprint

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In 1876, Charles Dodgson (better known as Lewis Carroll) proposed a committee election procedure that chooses the Condorcet winner when one exists and otherwise eliminates candidates outside the Smith set, then allows for re-votes until a Condorcet winner emerges. The present paper discusses Dodgson’s work in the context of strategic election behavior and suggests a “Dodgson-Hare” method, a variation on Dodgson’s procedure, for use in public elections. This method allows for candidate withdrawal and employs Hare’s plurality-loser-elimination method to resolve persistent cycles. Given plausible assumptions about how candidates decide whether to withdraw when there is a cycle, Dodgson-Hare outperforms Hare, Condorcet-Hare, and 12 other voting rules in a series of spatial-model simulations that count how often each rule is vulnerable to coalitional manipulation. In the case of a one-dimensional spatial model, all coalitional voting strategies that are possible under Condorcet-Hare can be undone in Dodgson-Hare, by the withdrawal of candidates who have incentive to withdraw. JEL Classifications: D71, D72

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The Burr Dilemma in Approval Voting

Cited by 24 publications

References 24 publications

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

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

Divided majority and information aggregation: Theory and experiment

A Dodgson-Hare Synthesis

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