2015/03/13 by Daniela Bubboloni, Bubboloni, Daniela, Michele Gori +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #Complexity and Algorithms in Graphs #Game Theory and Voting Systems #math.GR #msc:20B35 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1503.04028
arxiv created 2015/03/13 · arxiv updated 2015/03/16
In the standard arrovian framework and under the assumption that individual preferences and social outcomes are linear orders on the set of alternatives, we study the rules which satisfy suitable symmetries and obey the majority principle. In particular, supposing that individuals and alternatives are exogenously partitioned into subcommittees and subclasses, we provide necessary and sufficient conditions for the existence of reversal symmetric majority rules that are anonymous and neutral with respect to the considered partitions. We also determine a general method for constructing and counting those rules and we explicitly apply it to some simple cases.