zbMATH — the first resource for mathematics

The effectiveness of weighted scoring rules when pairwise majority rule cycles exist. (English) Zbl 1069.91024
Summary: Many studies have evaluated the probabilities that weighted scoring rules (WSRs) select the Condorcet winner or match the complete ranking by pairwise majority rule (PMR) in three candidate elections. This study considers situations in which PMR cycles exist, to evaluate the associated probabilities that WSRs select the Condorcet winner or match the complete ranking of a modified PMR relation. This modified relation reverses the PMR relationship on the pair with the smallest majority rule advantage. Evidence indicates that the WSRs that maximize these probabilities when a Condorcet winner exists also maximize the associated probabilities when a PMR cycle exists.

91B12 Voting theory
Full Text: DOI
[1] Berg, S.; Bjurulf, B., A note on the paradox of voting: anonymous preference profiles and may’s formula, Public choice, 40, 307-316, (1983)
[2] Black, D., The theory of committees and elections, (1958), Cambridge University Press Cambridge · Zbl 0091.15706
[3] Cervone, D., Gehrlein, W.V., Zwicker, W., 2002. Which scoring rule maximizes Condorcet efficiency? Unpublished manuscript. · Zbl 1126.91017
[4] Condorcet, Marquis de, 1784. On ballot votes. In: Sommerlad and McLean, 1989, pp. 119-121.
[5] Gehrlein, W.V., A representation for quadrivariate normal positive orthant probabilities, Communications in statistics, 8, 349-358, (1979) · Zbl 0411.62030
[6] Gehrlein, W.V., Condorcet efficiency and constant scoring rules, Mathematical social sciences, 2, 123-130, (1982) · Zbl 0479.90015
[7] Gehrlein, W.V., Condorcet’s paradox and the likelihood of its occurrence: different perspectives on balanced preferences, Theory and decision, 52, 171-199, (2002) · Zbl 1030.91500
[8] Gehrlein, W.V., Obtaining representations for probabilities of voting outcomes with effectively unlimited precision integer arithmetic, Social choice and welfare, 19, 503-512, (2002) · Zbl 1072.91530
[9] Gehrlein, W.V.; Fishburn, P.C., Condorcet’s paradox and anonymous preference profiles, Public choice, 26, 1-18, (1976)
[10] Gehrlein, W.V.; Fishburn, P.C., Coincidence probabilities for simple majority and positional voting rules, Social science research, 7, 272-283, (1978)
[11] Gehrlein, W.V.; Lepelley, D., The Condorcet efficiency of Borda rule with anonymous voters, Mathematical social sciences, 41, 39-50, (2001) · Zbl 0977.91014
[12] Guilbaud, G.T., LES théories de l’intérêt général et le problème logique de l’agrégation, Economie appliquée, 5, 501-584, (1952)
[13] Kendall, M.G.; Stuart, A., The advanced theory of statistics, (1963), Griffin London
[14] Lepelley, D.; Pierron, P.; Valognes, F., Scoring rules, Condorcet efficiency, and social homogeneity, Theory and decision, 49, 175-196, (2000) · Zbl 0989.91024
[15] Saari, D.G., Explaining all three-alternative voting outcomes, Journal of economic theory, 87, 313-355, (1999) · Zbl 1016.91029
[16] Slepian, D., The one sided barrier problem for Gaussian noise, Bell systems technical journal, 41, 463-501, (1962)
[17] Sommerlad, F., McLean, I., 1989. The political theory of Condorcet. University of Oxford Working Paper.
[18] Tovey, C.A., Probabilities of preferences and cycles with supermajority rules, Journal of economic theory, 75, 271-279, (1997) · Zbl 0892.90012
[19] Young, H.P., Extending condorcet’s rule, Journal of economic theory, 16, 335-353, (1977) · Zbl 0399.90006
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.