Attainable results in committee elections

The committee election problem is to choose from a finite set S of candidat es a nonempty subset T of committee members as the consequence of an electi on in which each voter expresses a preference for a candidate in S. Solutio ns of this problem can be modelled by functions which map each partition of 1 (i.e., normalized vote tallies of candidates who have been ordered canon ically by tally) into a nonempty subset of positive integers (i.e., sizes o f committees). To solve this problem, we recently described a parameterized voting scheme, the ratio-of-sums or ras(p) consensus rule, in which p cont rols the degree to which votes must be concentrated in elected committees. It is desirable to identify the attainable results of such rules so as to u nderstand their properties and to facilitate their comparison. For all p, w e characterize the attainable ras(p) results in the general case where the partition's parts are real, and in the special case where p as well as its parts are rational. (C) 1999 Elsevier Science Ltd. All rights reserved.