# 80 KAM Mathematical Colloquium

## DON'T VOTE!: JUDGE

patek 10. unora 2012 ve 14:00, poslucharna S5, druhe patro
KAM MFF UK
Malostranske nam. 25
118 00 Praha 1

## Abstract

Voting mechanisms used throughout the world are in deep trouble. People are slowly but surely becoming aware that they do not work properly. The outputs---winners and orders-of-finish of candidates---are not the true choices of electorates.

Why? Voters' inputs do not permit an adequate expression of their opinions. More fundamentally, the theory of voting (or ``social choice'') has hypothesized an inadequate model that leads to paradoxes and impossibility theorems (notably, Arrow's). That model assumes that voters' inputs are rank-orders of the candidates.

What can be done? It suffices to formulate a new model in which voters' inputs are evaluations of candidates. Instead of ranking candidates, or of naming one (``first-past-the-post'') or several (``approval voting''), they are given grades. A candidate's final grade---her majority-grade---is the grade that a majority of the electorate prefers to any other grade. The order-of-finish---the majority-ranking---is determined by the candidates' majority-grades.

This change in paradigm leads to a method---majority judgment---that avoids the important traditional paradoxes and impossibilities, elicits honest opinions, resists manipulation, is meaningful in measurement, and gives voters the right to truly express their opinions. It may be characterized in several ways as the only method that meets different subsets of these properties.

The method has been used and/or tested in various spheres: political elections, judging wines, discerning an international prize, ranking applicants for university positions, electing members of the British Academy.

This talk will give an overview of the method and theory via concrete examples.

Reference: Michel Balinski and Rida Laraki, Majority Judgment: Measuring, Ranking, and Electing, Cambridge, MA: MIT Press, 2010.

## O přednášejícím

Michel Balinski studoval v USA, MSc v oboru ekonomie ziskal na MIT v roce 1956 a doktorat v oboru matematika v Princetonu v roce 1959 (pod vedenim Johna Tukeyho), pracoval posleze na rade prednich americkych universit a instituci (Princeton, Penn, CUNY, Yale, SUNY Stony Brook, kde zalozil a vedl Institut for decision sciences). Od roku 1980 zije prevazne ve Francii, kde pracoval na Ecole Polytechnique jako reditel Ekonometricke laboratore. Za svou praci ziskal radu oceneni vcetne Lancaster Prize (OR Society) a Ford Prize (MAA). Byly mu udeleny dva cestne doktoraty na universitach v Augsburgu a Yale. V osobe prof. Balinskeho vitame jednu z klasickych osobnosti matematickeho programovani, operacniho vyzkumu a ekonometie: prof. Balinski je napriklad zakladajicim editorem casopisu Mathematical Programming a byvalym presidentem Mathematical Programming Society. Je autorem nekolika knih, vcetne nedavne vyse zminene uspesne knihy s R. Laraki. Poslednich 40 let se intenzivne zabyva pouzitim matematickych metod pro reseni problemu vzniklych v politickych souvislostech, zejmena problematikou navrhu volebnich systemu. Teto oblasti se venuje ve svem prazskem kolokviu.