Voting power and proportional representation of voters

The paper provides a justification for the proportional representative (PR) election system for politically diversified societies. We employ the Shapley value concept to measure the political power of parties in a parliament. We prove that for the PR system if parties’ sizes are uniformly distributed on the simplex, the expected ratio of a party size to its political power increases to 1, and the variance converges to 0, as the number n of parties increases. The rate of convergence is high and it is of the magnitude of 1 n . Empirical evidence from the Netherlands elections supports our result.