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Aggregation of binary evaluations with abstentions

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  • Dokow, Elad
  • Holzman, Ron
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    Abstract

    A general model of aggregation of binary evaluations over interrelated issues, introduced by Wilson and further studied by Rubinstein and Fishburn and by the authors, is extended here to allow for abstentions on some of the issues. It is shown that the same structural conditions on the set of feasible evaluations that lead to dictatorship in the model without abstentions, lead to oligarchy in the presence of abstentions. Arrow's impossibility theorem for social welfare functions, Gibbard's oligarchy theorem for quasi-transitive social decision functions, as well as some apparently new theorems on preference aggregation, are obtained as corollaries.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Economic Theory.

    Volume (Year): 145 (2010)
    Issue (Month): 2 (March)
    Pages: 544-561

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    Handle: RePEc:eee:jetheo:v:145:y:2010:i:2:p:544-561

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    Web page: http://www.elsevier.com/locate/inca/622869

    Related research

    Keywords: Aggregation Abstention Arrow's impossibility Judgment Social choice;

    References

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    1. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
    2. List, Christian & Pettit, Philip, 2002. "Aggregating Sets of Judgments: An Impossibility Result," Economics and Philosophy, Cambridge University Press, vol. 18(01), pages 89-110, April.
    3. Franz Dietrich & Christian List, 2008. "Judgment aggregation without full rationality," Social Choice and Welfare, Springer, vol. 31(1), pages 15-39, June.
    4. Peter Fishburn & Ariel Rubinstein, 1986. "Aggregation of equivalence relations," Journal of Classification, Springer, vol. 3(1), pages 61-65, March.
    5. Mongin, Philippe, 2008. "Factoring out the impossibility of logical aggregation," Journal of Economic Theory, Elsevier, vol. 141(1), pages 100-113, July.
    6. Franz Dietrich & Christian List, 2005. "Judgment aggregation by quota rules," Public Economics 0501005, EconWPA.
    7. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations," Journal of Economic Theory, Elsevier, vol. 145(2), pages 495-511, March.
    8. Nehring, Klaus, 2003. "Arrow's theorem as a corollary," Economics Letters, Elsevier, vol. 80(3), pages 379-382, September.
    9. Blair, Douglas H. & Pollak, Robert A., 1979. "Collective rationality and dictatorship: The scope of the arrow theorem," Journal of Economic Theory, Elsevier, vol. 21(1), pages 186-194, August.
    10. G Rdenfors, Peter, 2006. "A Representation Theorem For Voting With Logical Consequences," Economics and Philosophy, Cambridge University Press, vol. 22(02), pages 181-190, July.
    11. Klaus Nehring & Clemens Puppe, 2008. "Consistent judgement aggregation: the truth-functional case," Social Choice and Welfare, Springer, vol. 31(1), pages 41-57, June.
    12. Franz Dietrich, 2007. "A generalised model of judgment aggregation," Social Choice and Welfare, Springer, vol. 28(4), pages 529-565, June.
    13. Dietrich, Franz, 2006. "Judgment aggregation: (im)possibility theorems," Journal of Economic Theory, Elsevier, vol. 126(1), pages 286-298, January.
    14. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
    15. Blau, Julian H., 1979. "Semiorders and collective choice," Journal of Economic Theory, Elsevier, vol. 21(1), pages 195-206, August.
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    Cited by:
    1. Duddy, Conal & Piggins, Ashley, 2013. "Many-valued judgment aggregation: Characterizing the possibility/impossibility boundary," Journal of Economic Theory, Elsevier, vol. 148(2), pages 793-805.
    2. Dietrich, Franz & List, Christian, 2014. "Probabilistic Opinion Pooling," MPRA Paper 54806, University Library of Munich, Germany.
    3. Dietrich, Franz & List, Christian, 2013. "Probabilistic opinion pooling generalized Part one: General agendas," MPRA Paper 57253, University Library of Munich, Germany, revised Jul 2014.
    4. Dietrich, Franz & List, Christian, 2010. "Majority voting on restricted domains," Journal of Economic Theory, Elsevier, vol. 145(2), pages 512-543, March.
    5. Franz Dietrich, 2014. "Scoring rules for judgment aggregation," Social Choice and Welfare, Springer, vol. 42(4), pages 873-911, April.
    6. Mongin, Philippe, 2012. "The doctrinal paradox, the discursive dilemma, and logical aggregation theory," MPRA Paper 37752, University Library of Munich, Germany.
    7. Bozbay Irem & Dietrich Franz & Peters Hans, 2011. "Judgment aggregation in search for the truth," Research Memorandum 040, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    8. Franz Dietrich & Philippe Mongin, 2010. "The premiss-based approach to judgment aggregation," LSE Research Online Documents on Economics 27896, London School of Economics and Political Science, LSE Library.
    9. Dietrich, Franz, 2013. "Judgment aggregation and agenda manipulation," MPRA Paper 51775, University Library of Munich, Germany.
    10. Eckert, Daniel & Klamler, Christian, 2010. "An equity-efficiency trade-off in a geometric approach to committee selection," European Journal of Political Economy, Elsevier, vol. 26(3), pages 386-391, September.
    11. Bozbay, Irem, 2012. "Truth-Seeking Judgment Aggregation over Interconnected Issues," Working Papers 2012:31, Lund University, Department of Economics.
    12. Christian List & Ben Polak, 2010. "Introduction to judgment aggregation," LSE Research Online Documents on Economics 27900, London School of Economics and Political Science, LSE Library.
    13. Christian List & Ben Polak, 2010. "Introduction to Judgment Aggregation," Levine's Working Paper Archive 661465000000000006, David K. Levine.
    14. Nehring, Klaus & Pivato, Marcus & Puppe, Clemens, 2011. "Condorcet admissibility: Indeterminacy and path-dependence under majority voting on interconnected decisions," MPRA Paper 32434, University Library of Munich, Germany.
    15. Nehring, Klaus & Puppe, Clemens, 2010. "Justifiable group choice," Journal of Economic Theory, Elsevier, vol. 145(2), pages 583-602, March.
    16. Nehring, Klaus & Puppe, Clemens, 2010. "Abstract Arrowian aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 467-494, March.
    17. Conal Duddy & Ashley Piggins, 2012. "A measure of distance between judgment sets," Social Choice and Welfare, Springer, vol. 39(4), pages 855-867, October.
    18. Mongin, Philippe, 2011. "Une source méconnue de la théorie de l'agrégation des jugements," Les Cahiers de Recherche 953, HEC Paris.

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