A REPRESENTATION THEOREM FOR VOTING WITH LOGICAL CONSEQUENCES

Peter Gärdenfors

Economics and Philosophy, 2006, vol. 22, issue 2, 181-190

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.

Date: 2006
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