2008/28 | LEM Working Paper Series | |
Social choice on complex objects: A geometric approach |
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Luigi Marengo, Simona Settepanella |
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Keywords | ||
Social choice; object construction power; agenda power; intransitive cycles; arrangements; graph theory.
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JEL Classifications | ||
D71, D72
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Abstract | ||
Marengo and Pasquali (2008) present a model of object construction in
majority voting and show that, in general, by appropriate changes of
such bundles, different social outcomes may be obtained. In this paper
we extend and generalize this approach by providing a geometric model
of individual preferences and social aggregation based on hyperplanes
and their arrangements. As an application of this model we give a
necessary condition for existence of a local social optimum.
Moreover we address the question if a social decision rule depends also upon the number of voting agents. More precisely: are there social decision rules that can be obtained by an odd (even) number of voting agent which cannot be obtained by only three (two) voting agent? The answer is negative. Indeed three (or two) voting agent can produce all possible social decision rules. |
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