## What is wrong with majority rule? |

**William Zwicker**

Union College

September 15, 2009

4:00 pm

Bailey Hall 207

Refreshments will be served at 3:45 in Bailey 204

Suppose two candidates are running for election. Should we use “majority rule” to determine the winner? One can prove that with majority rule, honesty is the best policy – no voter will ever do better by lying about which candidate she prefers. On the other hand, with any reasonable alternative to majority rule voters do sometimes gain by lying.How about more than two candidates? The famous Gibbard-Satterthwaite Theorem shows that every reasonable voting method is flawed – voters sometimes gain by lying. Still, one might hope for some voting methods to do better than others.

Perhaps majority rule still does relatively well? Not so! We’ll discuss a recent theorem showing that with four candidates or more, every voting rule built on majority rule occasionally gives voters the incentive not only to lie, but to lie totally. For some other voting rules, though, the situation is slightly better, in that partial honesty is the best policy.

In the talk, we’ll explain we’ll explain what we mean by reasonable, as well as the difference between a lie and a total lie.

This talk is based research I did with M. Remzi Sanver, an economist at Bilgi University in Istanbul, Turkey.

For additional information, send e-mail to math@union.edu or call (518) 388-6246.

Union College Math Department Home PageComments to: math@union.edu Created automatically on: Fri Jul 20 16:33:55 EDT 2018 |