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 ith 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).