Minimally Disproportional Representation : Generalized Entropy and Stolarsky Mean-Divisor Methods of Apportionment

We study divisor methods, the primary class to solve apportionment problems, based upon Stolarsky means S(alphabeta). These encompass the five traditional methods. We disclose a one-to-one relation between methods of the form S(alpha1) and aggregate measures of seat/vote disproportionality of the generalized entropy family: using a divisor method based upon such a generalized logarithmic mean coincides with minimizing a generalized entropy inequality measure. The Balinski-Young 'favoring small states' - ordering ranks the generalized entropy methods. This framework improves upon an inconsistency in the traditional inequality approach to apportionment problems, which we illustrate by showing that the major rationale of the 'method of equal proportions' is consistently preserved by a non-traditional method