### DIMACS - RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:**
**Brian Nakamura**, Rutgers University, bnaka {at} math [dot] rutgers [dot] edu
** Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: The Mathematics of Three-Candidate Elections

Speaker: **Walter Stromquist**, Swarthmore College

Date: Thursday, March 8, 2012 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

Some observers say that the race between Bush and Gore in 2000 was influenced by the votes Ralph Nader won in Florida, or that Bill Clinton's 1992 election was influenced by the candidacy of Ross Perot. Did Chileans overlook a consensus centrist candidate when they elected Salvador Allende in 1970? What can we learn from John Anderson, Joe Lieberman, Lisa Murkowski, Charlie Crist, John Edwards, Jean-Marie Le Pen, and Vicente Fox? Each of them was involved in a famous three-candidate election. The Republican primaries of March 6 will provide more current examples.

Would we do better if we asked voters to rank all of the candidates? We would then have to decide how to count the votes. Several systems have been proposed, including instant runoffs, Borda counts, approval voting, and Eric Maskin's "true majority" rule (which picks "Condorcet winners" and which has trouble with "Condorcet cycles"). All of them have their advocates, and some are in use in various countries or organizations.

We might want a system that respects the "No Spoilers" rule---formally, the property of "Independence of Irrelevant Alternatives" or "IIA." This says that if X would beat Y in a head-to-head race, then Y should not be the winner of an X-Y-Z race. It seems a simple enough requirement, but the Arrow Impossibility Theorem tells us, essentially, that no such system is possible.

We will review this theorem and its significance and give some real and hypothetical examples. Along the way we will discuss expressive voting (voting for Nader when one prefers Gore), strategic voting (voting for Gore when one prefers Nader), and the kinds of institutions that arise from various rules for vote counting.

See: http://www.math.rutgers.edu/~bnaka/expmath/