The Desired Political Entropy

In an article published in the December 30, 1967 issue of the Dutch weekly magazine Vrij Nederland , Mr. Frans Grosfeld suggested the following modification of the procedure of parliamentary representation of political parties. Instead of the conventional method of allocating to each party a number of representatives proportional to the number of votes cast for the party, he proposed to allocate a number of representatives which is proportional to the square of the number of votes. Thus, when there are n parties and when p 1 , …, p n are the proportions of the total number of votes obtained by these parties, the idea is to allocate a fraction q i of the representatives to the i th party determined by Mr. Grosfeld made this suggestion for the Dutch political system, because in his view n is so large and even the largest p i belongs to a minority party, so that on many occasions several months of negotiations were necessary to obtain a coalition cabinet of one form or another. By squaring the p i 's one obtains much larger relative differences between the larger and the smaller parties, and one party or a pair of politically related parties then has a much better chance of obtaining a parliamentary majority. Also, the system (1.1) provides an incentive for parties to merge, which contributes to a reduction of the degree to which the country is politically divided. This system should be contrasted with another system which is applied on a rather large scale, viz., that of declining any seat to those parties whose p i is less than a pre-assigned fraction θ (for example, θ = .03).