The proportional representation problem in the Second Chamber: an approach via minimal distances

Abstract  The purpose of this paper is to discuss the proportional representation problem in the Second Chamber of Dutch Parliament. Firstly, the present procedure for solving this problem is described, together with a possible alternative procedure, recently proposed by F. J. L isman . Next, the problem is formulated as that of minimizing some distance coefficient between the distribution of the votes of the electorate and that of the seats in the Second Chamber. For distances which satisfy a specific convexity condition a simple and straight forward algorithm is given for computing a distance minimizing seat distribution. The procedure of L isman is shown to have three attractive properties by which it is distinguished from the other usual procedures for solving the proportional representation problem. Finally, the principle of the weighted vote is introduced as a means of breaking the deadlock which always comes into being, because of the inevitable discrepancy between the vote distribution and the actual seat distribution.