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.