The apportionment problem and the European Parliament

A class of allocation rules is introduced for allocating votes in a parliament to parties based on population. A unique feature of the class is that a well-defined objective function is associated with each allocation rule in the class. It is shown that the objective function corresponding to the “square root” allocation rule is of particular interest. This rule attempts to give each party a number of votes proportional to the square root of its size. Also described is an allocation procedure which takes care of the typical situation when the allocation rule results in fractional votes being allocated whereas in fact one allows only whole number votes to be allocated. Allocations for the European Parliament using the above class of rules are compared with the currently proposed allocations for that body.