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Modularity and Optimality in Social Choice

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  • Gennaro Amendola
  • Simona Settepanella
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    Abstract

    Marengo and the second author have developed in the last years a geometric model of social choice when this takes place among bundles of interdependent elements, showing that by bundling and unbundling the same set of constituent elements an authority has the power of determining the social outcome. In this paper we will tie the model above to tournament theory, solving some of the mathematical problems arising in their work and opening new questions which are interesting not only from a mathematical and a social choice point of view, but also from an economic and a genetic one. In particular, we will introduce the notion of u-local optima and we will study it from both a theoretical and a numerical/probabilistic point of view; we will also describe an algorithm that computes the universal basin of attraction of a social outcome in O(M^3 log M) time (where M is the number of social outcomes).

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    Bibliographic Info

    Paper provided by Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy in its series LEM Papers Series with number 2010/05.

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    Date of creation: 22 Apr 2010
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    Handle: RePEc:ssa:lemwps:2010/05

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    Related research

    Keywords: Social rule; modularity; object; optimum; hyperplane arrangement; tournament; algorithm;

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    1. Weinberger, Shmuel, 2004. "On the topological social choice model," Journal of Economic Theory, Elsevier, vol. 115(2), pages 377-384, April.
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