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Collective Choice for Simple Preferences

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Handbook on Approval Voting

Part of the book series: Studies in Choice and Welfare ((WELFARE))

Abstract

Individual preferences often take simple structures in some restricted environments. The so-called universal domain assumption in the three impossibility results by Arrow (1951), Sen (1970a,b), and Gibbard (1973) and Satterthwaite (1975) have been scrutinized and (partially) abandoned in numerous later studies, which do not intend to identify well-behaved social welfare functions that “would be universal in the sense that it would be applicable to any community” (Arrow 1951, p. 24). Important breakthroughs have been made in this line of research: Gaertner (2002) provides a comprehensive survey of the literature on domain restrictions.

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References

  • Aleskerov, F., Yakuba, V., & Yuzbashev, D. (2007). A ‘threshold aggregation’ of three-graded rankings. Mathematical Social Science, 53, 106–110.

    Article  Google Scholar 

  • Alos-Ferrer, C. (2006). A simple characterization of approval voting. Social Choice and Welfare, 27, 621–625.

    Article  Google Scholar 

  • Arrow, K. J. (1951). Social choice and individual values. Wiley, New York.

    Google Scholar 

  • Aşan, G., & Sanver, M. R. (2002). Another characterization of the majority rule. Economic Letters, 75, 409–413.

    Article  Google Scholar 

  • Banks, J. S. (1995). Acyclic social choice from finite sets. Social Choice and Welfare, 12, 293–310.

    Article  Google Scholar 

  • Baigent, N., & Xu, Y. (1991). Independent necessary and sufficient conditions for approval voting. Mathematical Social Science, 21, 21–29.

    Article  Google Scholar 

  • Barberà, S., Masso, J., & Neme, A. (1997). Voting under Constraints. J Econ Theory, 76, 298–321.

    Article  Google Scholar 

  • Barberà, S., Masso, J., & Neme, A. (2005). Voting by committees under constraints. Journal of Economic Theory, 122, 185–205.

    Article  Google Scholar 

  • Barberà, S., Sonnenschein, H., & Zhou, L. (1991). Voting by committees. Econometrica, 59, 595–609.

    Article  Google Scholar 

  • Barberà, S., Gul, F., & Stacchetti, E. (1993). Generalized median voter schemes and committees. Journal of Economic Theory, 76, 298–321.

    Article  Google Scholar 

  • Blau, J. H. (1975). Liberal values and independence. Review of Economic Studies, 42, 395–402.

    Article  Google Scholar 

  • Bogomolnaia, A., & Moulin, H. (2004). Random matching under dichotomous preferences. Econometrica, 72, 257–279.

    Article  Google Scholar 

  • Bogomolnaia, A., Moulin, H., & Stong, R. (2005). Collective choice under dichotomous preferences. Journal of Economic Theory, 122, 165–184.

    Article  Google Scholar 

  • Brams, S. J., & Fishburn, P. C. (1978). Approval voting. American Political Science Review, 72, 831–847.

    Article  Google Scholar 

  • Brams, S. J., & Fishburn, P. C. (2002). Voting procedures. In K. J. Arrow, A. K. Sen., & K. Suzumura (Eds.), Handbook of social choice of welfare (pp. 173–236). Amsterdam: Elsevier Science B.V.

    Google Scholar 

  • Brown, D. J. (1975). Aggregation of preferences. Quarterly Journal of Economics, 89, 456–469.

    Article  Google Scholar 

  • Campbell, D. E., & Kelly, J. S. (2000). A simple characterization of majority rule. Economic Theory, 15, 689–700.

    Article  Google Scholar 

  • Çengelci, M. A., & Sanver, R. (2010). Simple collective identity functions. Theory and Decision, 68, 417–443.

    Article  Google Scholar 

  • Ching, S. (1996). A simple characterization of plurality rule. Journal of Economic Theory, 71, 298–302.

    Article  Google Scholar 

  • Dimitrov, D., Sung, S. C., & Xu, Y. (2007). Procedural group identification. Mathematical Social Sciences, 54, 137–146.

    Article  Google Scholar 

  • Fishburn, P. C. (1978a). Axioms for approval voting: Direct proof. Journal of Economic Theory, 19, 180–185; Corrigendum 45 (1988), 212.

    Google Scholar 

  • Fishburn, P. C. (1978b). A strategic analysis of nonranked voting systems. SIAM Journal on Applied Mathematics, 35, 488–495.

    Article  Google Scholar 

  • Fishburn, P. C. (1979). Symmetric and consistent aggregation with dichotomous voting. In J.-J. Laffont (Ed.), Aggregation and revelation of preferences (pp. 201–218). Amsterdam: North-Holland.

    Google Scholar 

  • Gaertner, W. (2002). Domain restrictions. In K. J. Arrow, A. K. Sen, & K. Suzumura (Eds.), Handbook of social choice and welfare (Vol. I, pp. 131–170). Amsterdam: Elsevier Science B.V.

    Google Scholar 

  • Gaertner, W., Pattanaik, P. K., & Suzumura, K. (1992). Individual rights revisited. Economica, 59(234), 161–177.

    Article  Google Scholar 

  • Gibbard, A. (1969). Social choice and the Arrow condition. Mimeograph, Harvard University.

    Google Scholar 

  • Gibbard, A. (1973). Manipulation of voting schemes: A general result. Econometrica, 41, 587–602.

    Article  Google Scholar 

  • Gibbard, A. (1974). A Pareto-consistent libertarian claim. Journal of Economic Theory, 7, 388–410.

    Article  Google Scholar 

  • Guha, A. S. (1972). Neutrality, monotonicity, and the right of veto. Econometrica, 40, 821–826.

    Article  Google Scholar 

  • Herzberger, H. G. (1973). Ordinal preference and rational choice. Econometrica, 41, 187–237.

    Article  Google Scholar 

  • Inada, K.-I. (1964). A note on the simple majority decision rule. Econometrica, 32, 525–531.

    Article  Google Scholar 

  • Inada, K.-I. (1969). The simple majority decision rule. Econometrica, 37, 490–506.

    Article  Google Scholar 

  • Inada, K.-I. (1970). Majority rule and rationality. Journal of Economic Theory, 2, 27–40.

    Article  Google Scholar 

  • Ju, B.-G. (2003). A characterization strategy-proof voting rules for separable weak orderings. Social Choice and Welfare, 21(3), 469–499.

    Article  Google Scholar 

  • Ju, B.-G. (2005a). An efficiency characterization of plurality social choice on simple preference domains. Economic Theory, 26(1), 115–128.

    Article  Google Scholar 

  • Ju, B.-G. (2005b). A characterization of plurality-like rules based on non-manipulability, restricted efficiency, and anonymity. International Journal of Game Theory, 33, 335–354.

    Article  Google Scholar 

  • Ju, B.-G. (2008). Individual powers and social consent: Sen’s paradox reconsidered (working paper). Korea University.

    Google Scholar 

  • Ju, B.-G. (2009a). On the characterization of liberalism by Samet and Schmeidler (working paper). Korea University.

    Google Scholar 

  • Ju, B.-G. (2009b). Collectively rational voting rules for simple preferences (working paper). Korea University.

    Google Scholar 

  • Ju, B.-G. (2010). Individual powers and social consent: An axiomatic approach. Social Choice and Welfare, 34, 571–596.

    Article  Google Scholar 

  • Kasher, A., & Rubinstein, A. (1997). On the question ‘Who is a j’, a social choice approach. Logique et Analyse, 160, 385–395.

    Google Scholar 

  • Le Breton, M., & Sen, A. (1995). Strategyproofness and decomposability: weak ordering. Discussion Papers in Economics No. 95–04, Indian Statistical Institute, Delhi Centre.

    Google Scholar 

  • Le Breton, M., & Sen, A. (1999). Separable preferences, strategyproofness, and decomposability. Econometrica 67(3): 605–628.

    Article  Google Scholar 

  • Mas-Colell, A., & Sonnenschein, H. (1972). General possibility theorems for group decisions. Review of Economic Studies, 39, 185–192.

    Article  Google Scholar 

  • Maskin, E. S. (1995). Majority rule, social welfare functions, and game forms. In: Basu, K., Pattanaik, P. K., & Suzumura, K. (Eds.), Choice, welfare, and development. Oxford: The Clarendon Press.

    Google Scholar 

  • May, K. O. (1952). A set of independent necessary and sufficient conditions for simple majority decision. Econometrica, 20, 680–684.

    Article  Google Scholar 

  • Miller, A. D. (2008). Group identification. Games and Economic Behavior, 63, 188–202.

    Article  Google Scholar 

  • Moulin, H. (1980). On strategy-proofness and single peakedness. Public Choice, 35, 437–455.

    Article  Google Scholar 

  • Myerson, R. B. (1995). Axiomatic derivation of scoring rules without the ordering assumption. Social Choice and Welfare, 12, 59–74.

    Article  Google Scholar 

  • Rubinstein, A., & Fishburn, P. C. (1986). Algebraic aggregation theory. Journal of Economic Theory, 38, 63–77.

    Article  Google Scholar 

  • Sakai, T., & Shimoji, M. (2006). Dichotomous preferences and the possibility of Arrovian social choice. Social Choice and Welfare, 26, 435–445.

    Article  Google Scholar 

  • Samet, D., & Schmeidler, D. (2003). Between liberalism and democracy. Journal of Economic Theory, 110(2), 213–233.

    Article  Google Scholar 

  • Sanver, M. R. (2009). Characterizations of majoritarianism: A unified approach. Social Choice and Welfare, 33, 159–171.

    Article  Google Scholar 

  • Satterthwaite, M. A. (1975). Strategy-proofness and Arrow’s condition: Existence and correspondence theorems for voting procedures and social welfare functions. Journal of Economic Theory, 10, 187–217.

    Article  Google Scholar 

  • Sen, A. K. (1970a). Collective choice and social welfare. San Francisco: Holden-Day.

    Google Scholar 

  • Sen, A. K. (1970b). The impossibility of a Paretian Liberal. Journal of Political Economy, 78, 152–157.

    Article  Google Scholar 

  • Sen, A. K. (1976). Liberty, unanimity and rights. Economica, 43, 217–245.

    Article  Google Scholar 

  • Sen, A. K. (1977). Social Choice Theory: A Re-Examination. Econometrica, 45, 53–89.

    Article  Google Scholar 

  • Sen, A. K. (1983). Liberty and social choice. Journal of Philosophy, 80(1), 5–28.

    Article  Google Scholar 

  • Serizawa, S. (1995). Power of voters and domain of preferences where voting by committees is strategy-proof. J Econ Theory, 67, 599–608.

    Article  Google Scholar 

  • Sertel, M. R. (1988). Characterizing approval voting. Journal of Economic Theory, 45, 207–211.

    Article  Google Scholar 

  • Shapley, L. S., & Shubik, M. (1954). A method for evaluating the distribution of power in a committee system. American Political Science Review, 48, 787–792.

    Article  Google Scholar 

  • Shimomura, K-I. (1996). Partially efficient voting by committees, Social Choice and Welfare, 13, 327–342.

    Article  Google Scholar 

  • Sprumont, Y. (1991). The division problem with single-peaked preferences: A characterization of the uniform allocation rule. Econometrica, 59, 509–519.

    Article  Google Scholar 

  • Sung, S. C., & Dimitrov, D. (2003). On the axiomatic characterization of “Who is a J?” (working paper). Tilburg University.

    Google Scholar 

  • Thomson, W. (2001). On the axiomatic method and its recent applications to game theory and resource allocation. Social Choice and Welfare, 18, 327–386.

    Article  Google Scholar 

  • Wilson, R. (1975). On the theory of aggregation. Journal of Economic Theory, 10, 89–99.

    Article  Google Scholar 

  • Xu, Y. (2010). Axiomatizations of approval voting. In J. F. Laslier & M. R. Sanver (Eds.), Handbook on approval voting. Heildelberg: Springer-Verlag

    Google Scholar 

  • Yeh, C.-H. (2006). Reduction-consistency in collective choice problems. Journal of Mathematical Economics, 42, 637–652.

    Article  Google Scholar 

  • Young, H. P. (1975). Social choice scoring functions. SIAM Journal of Applied Mathematics, 28, 824–838.

    Article  Google Scholar 

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Acknowledgments

I am grateful to William Thomson for helpful comments. I also thank Seong-Jae Oh and Seongkyu Park for their careful reading, discussion and comments.

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Authors and Affiliations

  1. Department of Economics, Korea University, Anam-dong 5-1, Seong-buk-gu, Seoul, 136-701, Korea

    Biung-Ghi Ju

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  1. Biung-Ghi Ju
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Correspondence to Biung-Ghi Ju .

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Editors and Affiliations

  1. Labo. d'Econometrie, École Polytechnique, Palaiseau CX, 91128, France

    Jean-François Laslier

  2. Dept. Economics, Istanbul Bilgi University, Kurtulus Deresi Cad. 47, Istanbul, 34440, Turkey

    M. Remzi Sanver

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Ju, BG. (2010). Collective Choice for Simple Preferences. In: Laslier, JF., Sanver, M. (eds) Handbook on Approval Voting. Studies in Choice and Welfare. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02839-7_4

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  • DOI: https://doi.org/10.1007/978-3-642-02839-7_4

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