kenneth arrow's impossibility theorem essentially states that in the presence of three or more candidates there is no way to hold a fair election. that this statement is true in practice should not be a surprise to anyone familiar with our current electoral system. it is a little more surprising that it holds even in the abstract world of mathematics. \vskip .1in \noindent in this talk we shall define social welfare functions, discuss a reasonable set of fairness criteria, and sketch a proof of arrow's theorem. along the way we shall touch on topics in combinatorics, geometry, logic, and set theory. to end on a positive note, we shall show that fair voting methods do exist when the number of voters is infinite. \vskip .1in \noindent prerequisites: a small amount of basic set theory and linear algebra will be assumed, but all important terms will be defined as we go. \vskip .1in \noindent refreshments will be provided!