A note of Arrow impossibility theorem in choice function forms

The paper is a study of Impossibility Theorem in social choice. First, it gives the definition of social choice function and defines the normative forms of rational social choice function. Then it gives the definition of Pareto Principle, Independence of Irrelevant alternative and Non-dictatorial Condition in choice function forms. On the basis of this analysis, it investigates the impossibility theorem in choice function forms, and gives Arrow Impossibility Theorem in choice function forms and Sen Oligarchy Impossibility Theorem in choice function forms.