Biproportional Delegations

Abstract

This paper deals with the problem of two-dimensional proportional representation most commonly encountered when seats are to be allocated in a region where voters are classified according to the double cleavage of the constituency in which they vote and the party of their choice. A priority is set here on marginal proportionality: seats are dealt out to constituencies and to parties at the global level first. It is proven that, under a very weak condition, a biproportional delegation always exists, i.e. a representation matrix matching imposed margins and which is a controlled rounding of the corresponding solution to the well-known biproportional problem. Two versions of a construction process for such a biproportional delegation are proposed and they are simulated on Belgian electoral data covering the last four general elections. Though no perfect system exists for this type of representation, comparisons with the current system plead in favor of the use of biproportional delegations.