Evaluating Compromise in Social Choice Functions

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We investigate the notion of compromise in the strict preferential voting setting. Weintroduce divergence as an inverse measure of compromise in a collection of strictpreferential votes. Classical functions of social choice theory are analyzed with respectto divergence. New social welfare functions and new social choice functions with theobjective of compromise are defined directly from optimization of divergence and lateranalyzed with respect to the common desiderata of social choice theory. For a verynatural function, a simple divergence minimizer, we prove it satisfies the properties ofanonymity, neutrality, consistence, and continuity. Consequently, according toYoung’s theorem of characterization it follows that this function is a scoring pointfunction. Its scoring point vector is also given. Finally, we discuss the parameter p inthe divergence measure which was introduced to address vagueness and fuzziness ofcompromise and to control for a variety of intended levels of compromise.