Impossibility theorems in multiple von Wright’s preference logic

Abstract

By using the standard combining logics technique (D. M. Gabbay 1999) we define a generalization of von Wright?s preference logic (G. H. von Wright 1963) enabling to express, on an almost propositional level, the individual and the social preference relations simultaneously. In this context we present and prove the counterparts of crucial results of the Arrow-Sen social choice theory, including impossibility theorems (K. Arrow 1951 and A. K. Sen 1970b), as well as some logical interdependencies between the dictatorship condition and the Pareto rule, and thus demonstrate the power and applicability of combining logics method in mathematical economics.