Abstract:
There are many ways to structure an election besides the familiar
method of plurality, where the winner is whoever has the most first
place votes. There are advantages and disadvantages to each voting
system. Arrow’s Impossibility Theorem shows that there is no perfect
way to structure an election.
A Social Welfare Function (SWF) is a function that takes any
number of rational individual preferences and gives back a rational
preference for the society as a whole. Arrow’s Impossibility Theorem
proves that there is no Social Welfare Function that satisfies
unanimity (U), independence of irrelevant alternatives (IIA),
and is not a dictatorship (ND). I will present a proof of this
important result.