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A REPRESENTATION THEOREM FOR VOTING WITH LOGICAL CONSEQUENCES

Published online by Cambridge University Press:  11 July 2006

PETER GÄRDENFORS
PETER GÄRDENFORS
Affiliation:
Lund University
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Abstract

This paper concerns voting with logical consequences, which means that anybody voting for an alternative x should vote for the logical consequences of x as well. Similarly, the social choice set is also supposed to be closed under logical consequences. The central result of the paper is that, given a set of fairly natural conditions, the only social choice functions that satisfy social logical closure are oligarchic (where a subset of the voters are decisive for the social choice). The set of conditions needed for the proof include a version of Independence of Irrelevant Alternatives that also plays a central role in Arrow's impossibility theorem.

Type
Essay
Information
Economics & Philosophy , Volume 22 , Issue 2 , July 2006 , pp. 181 - 190
Copyright
2006 Cambridge University Press

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Footnotes

Much of this article was written while the author was a fellow at the Swedish Collegium for Advanced Study in the Social Sciences (SCASSS) in Uppsala. I want to thank the Collegium for providing me with excellent working conditions. Wlodek Rabinowicz and other fellows gave me valuable comments at a seminar at SCASSS when an early version of the paper was presented. I also want to thank Luc Bovens, Franz Dietrich, Christian List and an anonymous referee for their excellent comments on a later version. The final version was prepared during a stay at Oxford University for which I am grateful to the British Academy.