Abstract
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.
Similar content being viewed by others
References
Black, D. (1958). The theory of committees and elections. Cambridge: Cambridge University Press.
Brams, S.J. (1987). Approval voting and proportional representation. Paper presented at the European Consortium of Political Research Workshop, Amsterdam, April 10–15.
Brams, S.J., and Fishburn, P.C. (1983). Approval voting. Boston: Birkhauser.
Dummett, M. (1984). Voting procedures. Oxford: Clarendon Press.
Jensen, R.E. (1984). An alternative scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology 28(2): 317–332.
Joslyn, R.A. (1976). The impact of decision rules in multi-candidate campaigns: The case of the 1972 democratic presidential elections. Public Choice 25(1): 1–18.
Lampert, S.I., Nitzan, S., and Paroush, J. (1984). The sensitivity of political outcomes to electoral decision rules. Political Methodology 10(2): 337–356.
Ludwin, W.G. (1976). Voting methods: A simulation. Public Choice 25(1): 19–30.
Rapoport, A., Felsenthal, D.S., and Maoz, Z. (1988). Microcosms and macrocosms: Seat allocation in proportional representation systems. Theory and Decision 24(1): 11–33.
Saaty, T.L. (1977). A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology 15(2): 234–281.
Saaty, T.L. (1980). The analytic hierarchy process. New York: McGraw Hill.
Saaty, T.L., and Vargas, L.G. (1984). Comparison of eigenvalue, logarithmic least squares, and least squares methods in estimating ratios. Mathematical Modelling 5(2): 309–324.
Williams, C., and Crawford, G. (1985). A note on the analysis of subjective judgment matrices. Journal of Mathematical Psychology 29(3): 387–405.
Additional information
University of Haifa
This research was supported by the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel. We wish to thank Eli Nachmias and his staff at the Haifa Workers' Council for their assistance in conducting the exit poll and Steven Brams for many helpful comments.
Rights and permissions
About this article
Cite this article
Rapoport, A., Felsenthal, D.S. & Maoz, Z. Proportional representation: An empirical evaluation of single-stage, non-ranked voting procedures. Public Choice 59, 151–165 (1988). https://doi.org/10.1007/BF00054451
Issue Date:
DOI: https://doi.org/10.1007/BF00054451