Abstract
We consider the elections of a seat-posted committee, and investigate the propensity of seat-wise majority voting to choose a committee that fulfills the majority will with respect to preferences over committees. Voters have seat-wise preferences and preferences over committees are derived from seat-wise preferences by means of a neutral preference extension. Neutrality means that the names of candidates do not play any role. The majority committee paradox refers to a situation where a Condorcet winner exists for each seat, and a Condorcet winner committee also exists but does not coincide with the combination of seat-wise Condorcet winners. The majority committee weak paradox refers to a situation where the combination of seat-wise Condorcet winners is not a Condorcet winner among committees. We characterize the domains of preference extensions immune to each of the paradoxes.
The first author is grateful to the CNRS PICS program 08001 (Université de Caen Normandie and Istanbul Bilgi University) for its financial support.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Hamming distance criterion in this specific setting simply means that voters prefer the committee(s) agreeing with her ideal on a higher number of seats.
- 2.
Laffond and Lainé (2009) show that Maj always selects a Pareto optimal element in the Top-Cycle of the majority tournament among outcomes (Schwartz 1972) while Maj may select an outcome which does not belong to the Uncovered set (Miller (1977); Moulin (1986)). An overview of compound majority paradoxes in multiple referenda is provided in Laffond and Lainé (2010).
- 3.
Lacy and Niou (2000) show that under a non-separable preference extension rule, Maj may select a Condorcet-loser outcome (i.e., an outcome majority defeated by all other outcomes). However, if separability holds, Maj always chooses the Condorcet winner outcome (i.e., the outcome majority defeating all other outcomes) whenever it exists (Kadane 1972).
- 4.
Within a similar setting, Laffond and Lainé (2012) show that Maj may fail at implementing a compromise, even under strong restrictions upon the seat-wise majority margin.
- 5.
Note that the preference extensions used by the voters are not separable which turns out to be necessary and sufficient to avoid the majority committee paradox as will be shown in Theorem 1.
- 6.
Note that for each voter the preference extension used is either \(\delta ^{1Lex}\) or \(\delta ^{2Lex}\), but voters are not unanimously using one or the other which makes a significant difference as we will show in Theorem 2.
References
Anscombe, G.E.M.: On frustration of the majority by fulfilment of the majority’s will. Analysis 36(4), 161–168 (1976)
Benoît, J.-P., Kornhauser, L.A.: Only a dictatorship is efficient. Games Econ. Behav. 70(2), 261–270 (2010)
Bezembinder, T., Van Acker, P.: The Ostrogorski paradox and its relation to nontransitive choice. J. Math. Soc. 11(2), 131–158 (1985)
Black, D.: On the rationale of group decision-making. J. Polit. Econ. 56(1), 23–34 (1948)
Brams, S.J., Kilgour, D.M., Sanver, M.R.: A minimax procedure for electing committees. Publ. Choice 132(3–4), 401–420 (2007)
Brams, S.J., Kilgour, D.M., Zwicker, W.S.: The paradox of multiple elections. Soc. Choice Welfare 15(2), 211–236 (1998)
Çuhadaroğlu, T., Lainé, J.: Pareto efficiency in multiple referendum. Theory Decis. 72(4), 525–536 (2012)
Deb, R., Kelsey, D.: On constructing a generalized Ostrogorski paradox: necessary and sufficient conditions. Math. Soc. Sci. 14(2), 161–174 (1987)
Hollard, G., Breton, M.: Logrolling and a McGarvey theorem for separable tournaments. Soc. Choice Welfare 13(4), 451–455 (1996)
Kadane, J.B.: On division of the question. Publ. Choice 13(1), 47–54 (1972)
Kelly, J.S.: The Ostrogorski paradox. Soc. Choice Welfare 6(1), 71–76 (1989)
Lacy, D., Niou, E.M.S.: A problem with referendums. J. Theor. Polit. 12(1), 5–31 (2000)
Laffond, G., Lainé, J.: Single-switch preferences and the Ostrogorski paradox. Math. Soc. Sci. 52(1), 49–66 (2006)
Laffond, G., Lainé, J.: Condorcet choice and the Ostrogorski paradox. Soc. Choice Welfare 32(2), 317–333 (2009)
Laffond, G., Lainé, J.: Does choosing committees from approval balloting fulfill the electorate’s will? In: Laslier, J.F., Sanver, M. (eds.) Handbook on Approval Voting. Studies in Choice and Welfare, pp. 125–150. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-02839-7_7
Laffond, G., Lainé, J.: Searching for a compromise in multiple referendum. Group Decis. Negot. 21(4), 551–569 (2012)
Laffond, G., Lainé, J.: Unanimity and the Anscombe’s paradox. Top 21(3), 590–611 (2013)
Miller, N.: Graph theoretical approaches to the theory of voting. Am. J. Pol. Sci. 21, 769–803 (1977)
Moulin, H.: Choosing from a tournament. Soc. Choice Welfare 2, 271–291 (1986)
Ostrogorski, M.: Democracy and the Organization of Political Parties, vol. 2. Macmillan, London (1902)
Özkal-Sanver, I., Sanver, M.R.: Ensuring Pareto optimality by referendum voting. Soc. Choice Welfare 27(1), 211–219 (2006)
Rae, D.W., Daudt, H.: The Ostrogorski paradox: a peculiarity of compound majority decision. Eur. J. Polit. Res. 4(4), 391–398 (1976)
Scarsini, M.: A strong paradox of multiple elections. Soc. Choice Welfare 15(2), 237–238 (1998)
Schwartz, T.: Rationality and the myth of the maximum. Noûs 6, 97–117 (1972)
Sen, A.K.: A possibility theorem on majority decisions. Econometrica: J. Econom. Soc. 34, 491–499 (1966)
Shelley, F.M.: Notes on Ostrogorski’s paradox. Theory Decis. 17(3), 267–273 (1994)
Vidu, L.: An extension of a theorem on the aggregation of separable preferences. Soc. Choice Welfare 16(1), 159–167 (1999)
Vidu, L.: Majority cycles in a multi-dimensional setting. Econ. Theory 20(2), 373–386 (2002)
Wagner, C.: Avoiding Anscombe’s paradox. Theory Decis. 16(3), 233–238 (1984)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Aslan, F., Dindar, H., Lainé, J. (2019). Choosing a Committee Under Majority Voting. In: Morais, D., Carreras, A., de Almeida, A., Vetschera, R. (eds) Group Decision and Negotiation: Behavior, Models, and Support. GDN 2019. Lecture Notes in Business Information Processing, vol 351. Springer, Cham. https://doi.org/10.1007/978-3-030-21711-2_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-21711-2_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-21710-5
Online ISBN: 978-3-030-21711-2
eBook Packages: Computer ScienceComputer Science (R0)