Abstract
The Ostrogorski paradox refers to the fact that, facing finitely many dichotomous issues, choosing issue-wise according to the majority rule may lead to a majority defeated overall outcome. This paper investigates the possibility for a similar paradox to occur under alternative specifications of the collective preference relation. The generalized Ostrogorski paradox occurs when the issue-wise majority rule leads to an outcome which is not maximal according to some binary relation φ defined over pairs of alternatives. We focus on three possible definitions of φ, whose sets of maximal elements are respectively the Uncovered Set, the Top-Cycle, and the Pareto Set. We prove that a generalized paradox may prevail for the Uncovered Set. Moreover, it may be avoided for the same issue-wise majority margins as for the Ostrogorski paradox. However, the issue-wise majority rule always selects a Pareto-optimal alternative in the Top-Cycle.
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References
Anscombe GEM (1976) On frustration of the majority by fulfillment of the majority’s will. Analysis 36: 161–168
Banks J, Bordes G (1988) Voting games, indifferences, and consistent choice rules. Soc Choice Welf 5: 31–44
Bezembinder T, Van Acker P (1985) The Ostrogorski paradox and its relation to nontransitive choice. J Math Psychol 11: 131–158
Black D (1972) Partial justification of the Borda count. Public Choice 28: 1–15
Bordes G (1983) On the possibility of reasonable majoritarian choices: some positive results. J Econ Theory 31: 122–132
Brams SJ, Kilgour DM, Sanver MR (2007a) A minimax procedure for negotiating multilateral treaties. In: Avenhaus R, Zartman IW (eds) Diplomacy games, formal models and international negotiations. Springer, Berlin, pp 265–282
Brams SJ, Kilgour DM, Sanver MR (2007) A minimax procedure for electing committees. Public Choice 132: 401–420
Brams SJ, Kilgour DM, Zwicker WS (1998) The paradox of multiple elections. Soc Choice Welf 15: 211–236
Cuhadaroglu T, Lainé J (2008) On the Pareto Efficiency of the Issue-wise Majority Rule. Bilgi University Istanbul, Istanbul
Daudt H, Rae D (1976) The Ostrogorski paradox: a peculiarity of compound majority decision. Eur J Polit Res 4: 391–398
Deb R, Kelsey D (1987) On constructing a generalized Ostrogorski paradox: necessary and sufficient conditions. Math Soc Sci 14: 161–174
Dutta B, Laslier JF (1999) Comparison functions and choice correspondences. Soc Choice Welf 16: 513–532
Kornhauser LA, Sager LG (2004) Group choice in paradoxical cases. Philos Public Affairs 32: 249–276
Kelly JS (1989) The Ostrogorski paradox. Soc Choice Welf 6: 71–76
Lacy D, Niou EMS (2000) A problem with referendums. J Theoret Polit 12: 5–31
Laffond G, Lainé J (1994) On weak covering relations in tournaments. Theory Decis 37: 245–265
Laffond G, Lainé J (2000a) Majority voting on orders. Theory Decis 49: 251–289
Laffond G, Lainé J (2000b) Representation in majority tournaments. Math Soc Sci 39: 35–53
Laffond G, Lainé J (2006) Single-switch preferences and the Ostrogorski paradox. Math Soc Sci 52(1): 49–66
Laffond G, Lainé J, Laslier JF (1996) Composition-consistent tournament solutions and social choice functions. Soc Choice Welf 13: 75–93
Laffond G, Laslier JF, Le Breton M (1995) Condorcet choice correspondences: a set-theoretical comparison. Math Soc Sci 30: 23–35
Laslier JF (1997) Tournament solutions and majority voting. Springer, Berlin
List C (2003) A possibility theorem on decisions over multiple interconnected propositions. Math Soc Sci 45: 1–13
List C (2006) Corrigendum to a possibility theorem on decisions over multiple interconnected propositions. Math Soc Sci (forthcoming)
List C, Pettit P (2002) Aggregating sets of judgments: an impossibility result. Econ Philos 18: 89–110
List C, Pettit P (2004) Aggregating sets of judgments: two impossibility results compared. Synthese 140: 207–235
Merlin V, Valognes F (2004) The impact of indifferent voters on the likelihood of some voting paradoxes. Math Soc Sci 48: 343–361
Miller NR (1977) Graph–theoretical approaches to the theory of voting. Am J Polit Sci 24: 769–803
Moulin H (1986) Choosing from a tournament. Soc Choice Welf 2: 271–291
Nurmi H (1999) Voting paradoxes and how to deal with them. Springer, Berlin
Özkal-Sanver I, Sanver RM (2006) Ensuring pareto optimality by referendum voting. Soc Choice Welf 27: 211–219
Peris JE, Subiza B (1999) Condorcet choice correspondences for weak tournaments. Soc Choice Welf 16: 217–231
Ratliff TC (2006) Selecting committees. Public Choice 126: 343–355
Scarsini M (1998) A strong paradox of multiple elections. Soc Choice Welf 15: 237–238
Schwartz T (1972) Rationality and the myth of the maximum. Noûs 6: 97–117
Shelley FM (1994) Notes on Ostrogorski paradox. Theory Decis 17: 267–273
Subiza B, Peris JE (2005) Condorcet choice functions and maximal elements. Soc Choice Welf 24: 497–508
Smith JH (1973) Aggregation of preferences with variable electorate. Econometrica 41: 1027–1041
Wagner C (1983) Anscombe’s paradox and the rule of three–fourth. Theory Decis 15: 303–308
Wagner C (1984) Avoiding the Anscombe’s paradox. Theory Decis 16: 233–238
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Gilbert Laffond and Jean Lainé are grateful to two anonymous referees for their helpful comments and suggestions.
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Laffond, G., Lainé, J. Condorcet choice and the Ostrogorski paradox. Soc Choice Welf 32, 317–333 (2009). https://doi.org/10.1007/s00355-008-0325-9
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DOI: https://doi.org/10.1007/s00355-008-0325-9