On an apportionment method

Abstract

We study here the apportionment of representatives in a parliament and give the problem an integer programming formulation. For some methods of apportionment, it may happen that, when the total number of seats S in the parliament increases, the number of seats of some district decreases (Alabama Paradox). This is the case for the greatest fractional part method of apportionment (GFP) which we study more specifically. For GFP, we give a geometric interpretation and some results the variation for each district when S increases, which permits us to see in which circumstances this paradox can occur.