Voting Power and Proportional Representation of Voters ∗ Artyom Jelnov † Yair Tauman ‡ July 3, 2012 Abstract Our paper provides a justification for the proportional representative (PR) elec- tion system for politically diversified societies. We employ the Shapley value con- cept to measure the political power of parties in a parliament. We prove that for the PR system if parties’ size add up to 1 and is uniformly distributed, the ex- pected ratio of a party size to its political power converges to 1, and the variance decreases to 0 as the number of parties increases. The rate of convergence is high. An empirical evidence from the Netherlands elections supports our result. Using the Shapley-Owen index we obtain similar result (this time numerically only) for a voting model that takes into account ideological differences between parties and voters. * The authors thank Abraham Diskin, Pradeep Dubey, David Gilat, Dennis Leech, Abraham Neyman, Ronny Razin and Dov Samet for discussion, comments and assistance. † The Faculty of Management, Tel Aviv University, Israel. E-mail address: artyomje@post.tau.ac.il ‡ Department of Economics, State University of New York, Stony Brook, NY, USA and The Interdis- ciplinary Center, Herzliya, Israel 1