Approach of the Impossibility Theory of Kenneth Arrow in the Voting System

This paper analyzes the Impossibility theory of Kenneth Arrow and proposes a plausible approach to administrate this issue. The methodology which followed is based on the preferences and on the Euclidean distances. The basic idea comes from the attribute that has the middle value. Finally shows to the example of the vote the second choice is preferable than the second choice, and the third choice is preferable than the second choice. It is showed to that work that the private preference (or utility) which happens the same time by all the voters is lower than the public preference, but not the worst