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).
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 22600.
Date of creation: 10 May 2010
Date of revision:
judgement aggregation; majority vote; McGarvey; Stearns; 0/1 polytope; Hamming cube;
Find related papers by JEL classification:
- D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-05-22 (All new papers)
- NEP-CDM-2010-05-22 (Collective Decision-Making)
- NEP-POL-2010-05-22 (Positive Political Economics)
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- Nehring, Klaus & Pivato, Marcus & Puppe, Clemens, 2011. "Condorcet admissibility: Indeterminacy and path-dependence under majority voting on interconnected decisions," MPRA Paper 32434, University Library of Munich, Germany.
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