Spline methods for degressive proportionality in the composition of the European Parliament

Abstract

This paper contains a proposal to determine the distribution of seats of the European Parliament among the member states by using linear spline functions. The Lisbon Treaty establishes that such an allotment must be done under degressive proportion to the population, and that every member state must receive no less than 6 and no more than 96 seats. A definition of degressive proportion was given in 2007 by Lamassoure and Severin as that, the ratio between population and assigned seats should not increase when population decreases. In addition, the Parliament size cannot surpass 751 seats.With these limitations, we first study some linear spline functions leading to allotments verifying limitations on minimum, maximum and size, and unrounded degressive proportionality (before rounding to integers). Next, restricted linear spline functions are used to obtain allotments verifying all four properties including rounded degressive proportionality, although sometimes a slightly smaller EP size must be considered.