Preference of Social Choice in Mathematical Economics

Mathematical Economics is closely related with Social Choice Theory. In this paper, an attempt has been made to show this relation by introducing utility functions, preference relations and Arrow’s impossibility theorem with easier mathematical calculations. The paper begins with some definitions which are easy but will be helpful to those who are new in this field. The preference relations will give idea in individual’s and social choices according to their budget. Economists want to create maximum utility in society and the paper indicates how the maximum utility can be obtained. Arrow’s theorem indicates that the aggregate of individuals’ preferences will not satisfy transitivity, indifference to irrelevant alternatives and non-dictatorship simultaneously so that one of the individuals becomes a dictator. The Combinatorial and Geometrical approach facilitate understanding of Arrow’s theorem in an elegant manner.