2013/21 | LEM Working Paper Series | ||||||||||||||||
Decidability in complex social choices |
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Gennaro Amendola, Luigi Marengo, Davide Pirino, Simona Settepanella, Akimichi Takemura |
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Keywords | |||||||||||||||||
Social choice, object construction, hyperplane arrangement, probability, tournament, algorithm
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JEL Classifications | |||||||||||||||||
D03, D71, D72
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Abstract | |||||||||||||||||
In this paper we develop on a geometric model of social choice among
bundles of interdependent elements (objects). Social choice can be
seen as a process of search for optima in a complex multi-dimensional
space and objects determine a decomposition of such a space into
subspaces. We present a series of numerical and probabilistic
results which show that such decompositions in objects can greatly
increase decidability, as new kind of optima (called local and
u-local) are very likely to appear also in cases in which no
generalized Condorcet winner exists in the original search space.
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