Proportional representation: An empirical evaluation of single-stage,non-ranked voting procedures

Rapoport, Felsenthal and Maoz (1988) have proposed three alternative methods to discern the fair proportion of seats that a party in a representative assembly ought to receive as a function of voters' preference orderings. All three methods assume that the ratio between the number of voters preferring party i over j to the number of voters preferring party j over i can be tested for consistency, and, if sufficiently consistent, can be appropriately scaled to discover the proportion of seats each party ought to receive. Using these methods as standards, we use exit-poll data gathered during the 1985 elections to the general convention of the Israeli General Federation of Labor (Histadrut) to examine the extent to which plurality- and approval-voting procedures provide a fair allocation of seats. The findings indicate that: (a) all three methods yield sufficiently consistent matrices of preference ratios; (b) the plurality- and the approval-voting procedures yielded significantly different proportional representations; (c) the proposed proportion of seats according to the three aggregation methods fall midway between the proportion of seats that the plurality and the approval procedures allocate. We discuss practical implications of these findings. Requests for reprints should be sent to: Professor Amnon Rapoport, Department of Psychology, University of North Carolina, Davie Hall 013A, Chapel Hill, NC 27514.