Some Properties of Divisor Methods for Legislative Apportionment and Proportional Representation

Cyril Carter

American Political Science Review, 1982, vol. 76, issue 3, 575-584

Abstract: Some rather elegant properties of linear divisor methods are derived and used to establish upper and lower bounds on the possible variation between apportionment and exact quota entitlement. A probability distribution is derived for this variation, and it is shown that the probability of the variation exceeding one seat is very small with the major fractions linear divisor method. A less rigorous analysis of the nonlinear equal proportions method shows that in practice it is very similar to the major fractions method, but with a very slight bias in favor of small parties (or states). It is concluded that there is no “best” apportionment method, but a knowledge of the properties of the various methods enables a political choice of the most appropriate method.

Date: 1982
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