Universal and Symmetric Scoring Rules for Binary Relations

نویسنده

  • William S. Zwicker
چکیده

Are Plurality voting, the Kemeny rule, Approval voting, and the Borda Mean Dichotomy rule all versions of the same voting rule? Yes, in a sense. In an extension of work by Barthélemy and Monjardet [3], we consider functions F that assign real number scoring weights F (R1, R2) to pairs of binary relations on a finite set A of alternatives, serving as symmetric measures of similarity between R1 and R2. Any such F induces a symmetric binary relational scoring rule F – an abstract aggregation rule with arbitrary binary relations as ballots R1 and as aggregated outcomes R2. The level of generality is surprisingly effective. By restricting the classes of relations allowed as ballots and elections outcomes, F yields more familiar and concrete scoring rules. The symmetric assignment F , for example, arises from an inner product in a simple and natural way, and restrictions of the induced scoring rule F yield all the aformentioned familiar voting rules. Moreover, the inner product formulation yields a Euclidean form of distance rationalization for F , resulting in a universal distance rationalization for all concrete scoring rules obtained as restrictions.

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تاریخ انتشار 2014