Stability, Coalitions and Schisms in Proportional Representation Systems

Abstract

Methods to allocate seats in proportional representation systems are investigated in terms of underlying common-sense properties. Important among these are concepts of stability, coalition encouragement and schism encouragement. In addition, a new concept of uniformity is introduced which seems inherent in the very idea of the word “method, ” and it is shown that this concept is essentially equivalent to a previously investigated property called consistency. These and other criteria are shown to uniquely determine certain methods. In particular, the Jefferson method (incorrectly credited to d'Hondt) and the Quota method are given characterizations which commend them as the principal candidates for use in PR systems.