Minimal determining set and the Arrow impossibility theorem

The unique existence condition of minimal determining set in social choice theory is researched, and the relation between minimal determining set and choice function is analyzed. The unique existence condition of minimal determining set of complete rational choice function is obtained, and its sufficient condition is used to show a very simple proof of Arrow impossibility theorem. By analyzing the impossibility of choice function, it shows that a good method to construct a more rational choice function may be to weaken the uniqueness of minimal determining set.