ON THE UNBIASEDNESS OF THE PARAMETRIC DIVISOR METHOD FOR THE APPORTIONMENT PROBLEM

Abstract

Apportionment problem has a very long history of more than 200 years and has been challenged actively by many applied mathematicians and operations researchers. In the last 200 years many appor­ tionment methods have been proposed and various types of properties, which they should desirably satisfy, have been proposed and investigated although the apportionment problem itself has not been completely solved yet. Unbiasedness is an important property for the apportJionment method, and has been studied intensively by Balinski and Young and others. In this paper we investigate the unbiasedness of parametric divisor method, comparing with that of most traditional apportionment methods. First we characterize parametric divisor method by explicitly showing the corresponding loeal measure of bias and deriving several useful facts concerning the unbiasedness of apportionment methods. Then we show the numerical results using Japan's House of Representatives data and exhibit parametric divisor method is preferable to other apportionment methods from the viewpoint of the unbiasedness by adJusting the parameter value appropriately in the certain range. Finally we discuss the possibility for the parametric divisor method to be accepted by our society in the future.