Arrow's Impossibility Theorem
Above all, everyone wants voting to be fair. What does fair mean and how can we measure it? Kenneth Arrow posited a simple set of conditions that one would certainly desire in a voting system. For example, unanimity - if everyone picks candidate A, then A should win!
Yet surprisingly, under a few basic assumptions, this theorem demonstrates that no voting system exists which can satisfy all the criteria.
This episode is a discussion about the structure of the proof and some of its implications.