No Show Paradox and the Golden Number in Generalized Condorcet Voting Methods

Pérez, Joaquín; Jimeno, José L.; García, Estefanía

doi:10.1007/s10726-014-9416-4

Cited by 2 publications

(2 citation statements)

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“…Both of these questions are addressed in our paper. Pérez, Jimeno, and García (2010) and Pérez, Jimeno, and García (2015) revisited participation for the optimist extension with varying notions of Condorcet-consistency. Pérez et al (2010) derived incompatibilities using a set-valued variant of Condorcet-consistency for irresolute SCFs that always select exactly k alternatives.…”

Section: Related Workmentioning

confidence: 99%

“…Pérez et al (2010) derived incompatibilities using a set-valued variant of Condorcet-consistency for irresolute SCFs that always select exactly k alternatives. Inspired by early work by Holzman (1988) on resolute SCFs, Pérez et al (2015) showed that participation is compatible with Condorcet-consistency if Condorcet winners need the support of a supermajority rather than a simple majority. Brandt (2015) mainly focused on strategyproofness for Kelly's extension but in Remark 9 also gave a simple argument connecting strategyproofness and participation.…”

Section: Related Workmentioning

confidence: 99%

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Strategic Abstention based on Preference Extensions: Positive Results and Computer-Generated Impossibilities

Brandl

Brandt

Geist

et al. 2019

jair

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Voting rules allow multiple agents to aggregate their preferences in order to reach joint decisions. A common flaw of some voting rules, known as the no-show paradox, is that agents may obtain a more preferred outcome by abstaining from an election. We study strategic abstention for set-valued voting rules based on Kelly's and Fishburn's preference extensions. Our contribution is twofold. First, we show that, whenever there are at least five alternatives and seven agents, every Pareto-optimal majoritarian voting rule suffers from the no-show paradox with respect to Fishburn's extension. This is achieved by reducing the statement to a finite - yet very large - problem, which is encoded as a formula in propositional logic and then shown to be unsatisfiable by a SAT solver. We also provide a human-readable proof which we extracted from a minimal unsatisfiable core of the formula. Secondly, we prove that every voting rule that satisfies two natural conditions cannot be manipulated by strategic abstention with respect to Kelly's extension and give examples of well-known Pareto-optimal majoritarian voting rules that meet these requirements.

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Section: Related Workmentioning

confidence: 99%