The McGarvey problem in judgement aggregation

Pivato, Marcus and Nehring, Klaus (2010): The McGarvey problem in judgement aggregation.

Abstract

`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).

• Item Type: MPRA Paper
• Language: English
• Keywords: judgement aggregation; majority vote; McGarvey; Stearns; 0/1 polytope; Hamming cube
• Subjects: D - Microeconomics > D7 - Analysis of Collective Decision-Making > D70 - General

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