Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Description

Abstract: Economist Kenneth Arrow proved in the 1951 the much celebrated "Arrow's Impossibility Theory". This theorem essentially says that there can never be a "fair" election with three or more candidated when one makes certain mathematically necessary assumptions. Given the predominately two-party political system in the United States, it doesn't seem overly surprising that this result is not better known to Americans. However, the content of the theorem has perhaps never before been so important to Californians as during the recent Gubernatorial Recall Election. In this intentionally light-hearted talk, we will first examine what reasonably constitutes a fair election in so-called Arrovian Social Choice Theory. This will natually include a brief discussion of various voting systems and in particular an examination of just how poor the Plurality system currently employed in political election is in this respect. Then we will closely examine Arrow's assumptions and consider several ways of both trying to weaken these conditions and how one can try to prove the theorem in such contexts. Finally, we will illustrate this somewhat surprising result by showing how certain example elections can be modified via a careful examination of a graphical representation of voter preference so that any one of the three or more candidates becomes the winner. These examples will, of course, include the 2000 US Presidental Election (in which we will show, e.g., how Ralph Nader could have won) and the 2003 California Gubinatorial Recall Election (in which we will show, e.g., how any of the leading candidates could have won).