Marshall University Math Colloquium

April 2, 2004

“Arrow's Theorem, or: Why we all just can't get along”

John Drost

Marshall University

Abstract

In every election involving at least three choices, there must be a method of translating the individual voter's preferences into a global or societal preference. More specifically, suppose every voter ranks his or her choices in some order. Then a societal preference must somehow reflect the will of the individual voters. For example, if every voter prefers choice x to choice y, then the society should also. Arrow's theorem, proven by Kenneth Arrow in 1951, shows that there is no method of translating individual preferences into a societal preference that satisfies each of several seemingly reasonable requirements, other than a 'dictatorship' where one individual's preferences are that of the entire society.