Political Economy and Social Welfare with Voting Procedure

Mathematical Economics, Social Science and Political Science are inter-related. In this paper, an attempt has been made to describe aspects of these subjects by introducing examples, definitions, mathematical calculations and discussions. Game Theory is included in this paper to study mathematical models in economics and political science especially to study Nash equilibrium. Success and failure of democracy are interpreted as different equilibria of a dynamic political game with cost of changing leadership. Unitary democracy can be frustrated when voters do not replace corrupt leaders. Federal democracy cannot be consistently frustrated at both national and provincial levels. Arrow’s theorem indicates that the aggregate of individuals’ preferences will not satisfy transitivity, indifference to irrelevant alternatives and non-dictatorship, simultaneously to enable one of the individuals becomes a dictator. In this paper both social welfare functions and social choice correspondence are considered in economical environments.