Abstract
A great deal of evidence has been accumulated to support the Borda Compromise when the goal is to select the winning candidate in an election setting. A significant amount of research has also been conducted to determine how significant the impact might be when different voting rules are used. That is, the issue is addressed as to how much difference it actually makes when a voting rule is being selected. The initial exploration of this problem focused on the likelihood that two different voting rules would elect the same winner.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abramson PR (2007) The French presidential election of 2007: was Sarkozy the Condorcet winner? Fr Polit 5:287–291
Aleskerov F (2005) The history of social choice in Russia and in the Soviet Union. Soc Choice Welfare 25:419–431
Arrington TS, Brenner S (1984) Another look at approval voting. Polity 17:118–134
Bartholdi JJ, Orlin JB (1991) Single transferable vote resists strategic voting. Soc Choice Welfare 8:341–354
Bassett GW, Persky J (1999) Robust voting. Public Choice 99:299–310
Brams SJ, Fishburn PC (1978) Approval voting. Am Polit Sci Rev 72:831–847
Brams SJ, Fishburn PC (1983a) Paradoxes of preferential voting. Math Mag 56:207–214
Brams SJ, Fishburn PC (1988) Does approval voting elect the lowest common denominator? Polit Sci Polit 21:277–284
Brams SJ, Merrill S (1994) Would Ross Perot have won the 1992 presidential election under approval voting? Polit Sci Polit 27:39–45
Brams SJ, Nagel JH (1991) Approval voting in practice. Public Choice 71:1–17
Fedrizzi M, Kacprzyk J, Nurmi H (1996) How different are social choice functions: a rough sets approach. Qual Quant 30:87–99
Fishburn PC (1975) A probabilistic model of social choice: Comment. Rev Econ Stud 42:297–301
Fishburn PC (1983) Dimensions of election procedures: Analysis and comparisons. Theory Decis 15:371–397
Fishburn PC, Brams SJ (1981a) Approval voting, Condorcet’s principle, and runoff elections. Public Choice 36:89–114
Fishburn PC, Gehrlein WV (1976a) An analysis of simple two stage voting systems. Behav Sci 21:1–12
Fishburn PC, Gehrlein WV (1977a) An analysis of voting procedures with nonranked voting. Behav Sci 22:178–185
Fishburn PC, Little JDC (1988) An experiment in approval voting. Manage Sci 34:555–568
Flood MM (1980) Implicit intransitivity under majority rule with mixed motions. Manage Sci 26:312–321
Gehrlein WV (1979) A representation for quadrivariate normal positive orthant probabilities. Commun Stat 8:349–358
Gehrlein WV (1980) Scoring rule sensitivity to weight selection. In: Proceedings of the Southeast Decision Sciences Institute, Orlando, FL, pp 265–267
Gehrlein WV (1986) Weighted scoring rules, the impartial culture condition, and homogeneity. Qual Quant 20: 85–107
Gehrlein WV (1987) The impact of social homogeneity on the Condorcet efficiency of weighted scoring rules. Soc Sci Res 16:361–369
Gehrlein WV (1991) Coincidence probabilities for simple majority and proportional lottery rules. Econ Lett 35:349–353
Gehrlein WV (1998a) The sensitivity of weight selection on the Condorcet efficiency of weighted scoring rules. Soc Choice Welfare 15:351–358
Gehrlein WV (1999a) The Condorcet efficiency of Borda Rule under the dual culture condition. Soc Sci Res 28:36–44
Gehrlein WV (1999b) On the probability that all weighted scoring rules elect the Condorcet winner. Qual Quant 33:77–84
Gehrlein WV (2002a) Condorcet’s Paradox and the likelihood of its occurrence: different perspectives on balanced preferences. Theory Decis 52:171–199
Gehrlein WV (2003a) Weighted scoring rules that maximize Condorcet Efficiency. In: Sertel MR, Koray S (eds) Advances in Economic Design, Springer-Verlag Publishers, Berlin, pp 53–64
Gehrlein WV (2006a) Condorcet’s paradox. Springer Publishing, Berlin
Gehrlein WV (2007) Coincidence of agreement between probabilistic and algebraic choosers. Qual Quant 41:461–487
Gehrlein WV (2010) The impact of forcing preference rankings when indifference exists. In: Van Deemen A, Rusinowska A (eds) Collective decision making: views from social choice and game theory, Springer-Verlag Publishers (in press)
Gehrlein WV, Berg S (1992) The effect of social homogeneity on coincidence probabilities for pairwise proportional lottery and simple majority rules. Soc Choice Welfare 9:361–372
Gehrlein WV, Fishburn PC (1983) Scoring rule sensitivity to weight selection. Public Choice 40:249–261
Gehrlein WV, Lepelley D (1998) The Condorcet efficiency of approval voting and the probability of electing the Condorcet loser. J Math Econ 29:271–283
Gehrlein WV, Lepelley D (2003) On some limitations of the median voting rule. Public Choice 117:177–190
Heckelman JC (2003) Probabilistic Borda voting rule. Soc Choice Welfare 21:455–468
Heckelman JC (2007) On voting by proportional lottery. Korean J Public Choice 2:1–11
Inada K (1964) A note on simple majority decision rule. Econometrica 32:525–531
Intriligator MD (1973) A probabilistic model of social choice. Rev Econ Stud 40:553–560
Kiewiet RW (1979) Approval voting: the case of the 1968 election. Polity 12:170–181
Laslier JF, Van der Straeten K (2003) Approval voting: An experiment during the French 2002 presidential election. Presented at Third International Conference on Logic, Game Theory and Social Choice, SienaV, pp 294–297, September 2003
Laslier JF (2009), A note on choosing the alternative with the best median evaluation. Unpublished paper, Département d’Economie, Ecole Polytechnique, Paris
Lepelley D (1993) On the probability of electing the Condorcet loser. Math Soc Sci 25:105–116
Lepelley D, Gehrlein WV (2010a) The probability that all weighted scoring rules select the pairwise majority rule winner, University of Reunion, unpublished manuscript
Lines M (1986) Approval voting and strategy analysis. Theory Decis 20:155–172
May KO (1954) Intransitivity, utility, and the aggregation of preference patterns. Econometrica 22:1–13
Merlin V, Tataru M, Valognes F (2000). On the probability that all decision rules select the same winner. J Math Econ 33:183–207
Moulin H (1988a) Condorcet’s principle implies the no show paradox. J Econ Theory 45:53–64
Mueller DC (1989) Probabilistic majority rule. Kyklos 42:151–170
Niemi RG (1984) The problem of strategic behavior under approval voting. Am Polit Sci Rev 78:952–958
Nitzan S (1975) Social preference ordering in a probabilistic voting model. Public Choice 24:93–100
Radcliff B (1993) The structure of voter preferences. J Polit 55:714–719
Saari DG (1995b) Basic geometry of voting. Springer, Berlin
Stensholt E (2002) Nonmonotonicity in AV. Voting Matters Issue15:5–10 Paper 2
Tabarrok A (2001) President Perot or fundamentals of voting theory illustrated with the 1992 election. Public Choice 106:275–297
Tangian AS (2003) Historical background of the mathematical theory of democracy. Discussion paper 332, Fern University, Hagen
Weber RJ (1978b) Multiply weighted voting systems. Yale University, unpublished manuscript
Wiseman J (2000) Approval voting in subset elections. Econ Theory 15:477–483
Young P (1995) Optimal voting rules. J Econ Perspect 9:51–64
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Gehrlein, W.V., Lepelley, D. (2011). The Significance of Voting Rule Selection. In: Voting Paradoxes and Group Coherence. Studies in Choice and Welfare. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03107-6_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-03107-6_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03106-9
Online ISBN: 978-3-642-03107-6
eBook Packages: Business and EconomicsEconomics and Finance (R0)