Arrow's Impossibility Theorem

Statistical Physics and Complexity Group meeting

Arrow's Impossibility Theorem

Event details

There are a few little corners of Maths which everyone should know, but don't really belong in any topic, and so never get taught. Arrow's paradox is one of these. The issue is what system can be employed to decide the choice of a group of more than three people, based on individual rankings, under the conditions that.

a) If all the group favour A over B, then the group will also favour A. b) The system is deterministic - for the same set of votes, it always gives the same outcome. c) No voter can improve the chance of achieving his desired outcome by changing their rank order. d) The group preference between A and B in unaffected by their ranking of unrelated option C.

Arrow proves that the only consistent system is to have a dictator, whose view always prevails.