2010/05  LEM Working Paper Series  
Modularity and Optimality in Social Choice 

Gennaro Amendola, Simona Settepanella 

Keywords  
Social rule, modularity, object, optimum, hyperplane arrangement, tournament, algorithm.


JEL Classifications  
D03, D71, D72


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 ulocal 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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