The McGarvey problem in judgement aggregation
Marcus Pivato () and
MPRA Paper from University Library of Munich, Germany
`Judgement aggregation' is a model of social choice where the space of social alternatives is the set of consistent truth-valuations (`judgements') on a family of logically interconnected propositions. It is well-known that propositionwise majority voting can yield logically inconsistent judgements. We show that, for a variety of spaces, propositionwise majority voting can yield any possible judgement. By considering the geometry of sub-polytopes of the Hamming cube, we also estimate the number of voters required to achieve all possible judgements. These results generalize the classic results of McGarvey (1953) and Stearns (1959).
Keywords: judgement aggregation; majority vote; McGarvey; Stearns; 0/1 polytope; Hamming cube (search for similar items in EconPapers)
JEL-codes: D70 (search for similar items in EconPapers)
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