Bi-proportional Apportionments

摘要

An apportionment method is proposed that generalises Hamilton's method for matrices, optimising proportionality in both directions, both for rows and columns. The resulting matrix respects fixed totals for rows and columns even when such totals do not satisfy standard criteria (monotonicity, maximum or minimum Hare), for example following the allocation of majority prizes to parties or coalitions. Optionally, if required, the result can also respect the minimum Hare quotae for rows and columns. The algorithm may easily be expressed on the basis of rules.