The net-outdegree social choice correspondence
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In a variable electorate framework, we introduce and study the net-outdegree social choice correspondence (scc), a procedure that allows to determine some alternatives among the ones in a given set for any given preference profile, that is, a complete description of the individual preferences of a group of voters. No property is in principle required to individual preferences. We show that well-known voting rules, i.e. the Borda rule, the Approval Voting, the Plurality rule, the anti-Plurality rule, coincide with the restriction of the net-outdegree scc to suitable sets of preference profiles. We prove then that, when a set of preference profiles satisfies suitable conditions, the restriction of the net-outdegree scc to that set is the unique scc satisfying four properties, among which the well-known property of consistency. That allows to get as consequences Young's characterization of the Borda rule and Fishburn's characterization of the Approval Voting as well as other characterization results present in the literature. Such results are all based on a preliminary analysis and a general characterization theorem of the so-called net-outdegree network solution.
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