engleski

Total optimization of the divergence from the compromise

The term ”compromise” is mostly used casually within the social choice theory. It is usually used as a mere result of social choice function, and this omits its deeper meaning and ramifications. This paper is based on a mathematical model for description of a compromise as a version of the Sorites paradox. It introduces a formal definition of p-divergence from a compromise, and models a notion of compromise that is often used only colloquially. Such model for vagueness phenomenon which lies at the core of the notion of compromise, enables introduction of new mathematical structures. In order to maximize compromise, different methods can be used. In this paper we explore properties of a social welfare function TDM (from Total Divergence Measure), which is defined as a function which minimizes the total sum of p-divergences over all possible linear orderings. We prove that TDM satisfies strict Pareto principle and behaves well asymptotically. Furthermore, we show that for certain domain restrictions, TDM satisfies positive responsiveness and IIIA (intense independence of irrelevant alternatives) thus being equivalent to Borda count on such restricted domain. This result gives new opportunities in social choice, especially when there is emphasis on compromise in decision making process.

Social choice function ; Social welfare function ; Strict preferential voting ; Compromise ; Borda count ; Divergence

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