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Aggregation theory and the relevance of some issues to others

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  • Dietrich, Franz

Abstract

I propose a new axiom on the aggregation of individual yes/no judgments on propositions into collective judgments: each collective judgment depends only on people's judgments on 'relevant' propositions. This contrasts with classical independence: each collective judgment depends only on people's judgments on the 'current' proposition. I generalize the premise-based and sequential-priority rules to an arbitrary priority structure over propositions, instead of a dichotomous premise/conclusion structure or a linear order of priority. I prove four impossibility theorems on relevance-based aggregation. One theorem simultaneously generalizes Arrow's Theorem (in its general and indifference-free versions) and the Arrow-type theorem in judgment aggregation.

Suggested Citation

  • Dietrich, Franz, 2006. "Aggregation theory and the relevance of some issues to others," MPRA Paper 58870, University Library of Munich, Germany, revised Sep 2014.
  • Handle: RePEc:pra:mprapa:58870
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    References listed on IDEAS

    as
    1. Conal Duddy & Ashley Piggins & William Zwicker, 2016. "Aggregation of binary evaluations: a Borda-like approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(2), pages 301-333, February.
    2. Franz Dietrich, 2007. "A generalised model of judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 529-565, June.
    3. Mongin, Philippe, 2008. "Factoring out the impossibility of logical aggregation," Journal of Economic Theory, Elsevier, vol. 141(1), pages 100-113, July.
    4. Nehring, Klaus & Pivato, Marcus & Puppe, Clemens, 2014. "The Condorcet set: Majority voting over interconnected propositions," Journal of Economic Theory, Elsevier, vol. 151(C), pages 268-303.
    5. Carl Claussen & Øistein Røisland, 2010. "A quantitative discursive dilemma," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(1), pages 49-64, June.
    6. List, Christian & Pettit, Philip, 2002. "Aggregating Sets of Judgments: An Impossibility Result," Economics and Philosophy, Cambridge University Press, vol. 18(1), pages 89-110, April.
    7. Franz Dietrich & Christian List, 2007. "Arrow’s theorem in judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(1), pages 19-33, July.
    8. Pivato, Marcus, 2008. "The geometry of consistent majoritarian judgement aggregation," MPRA Paper 9608, University Library of Munich, Germany.
    9. Franz Dietrich & Christian List, 2008. "Judgment aggregation without full rationality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(1), pages 15-39, June.
    10. Franz Dietrich, 2014. "Scoring rules for judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 873-911, April.
    11. Franz Dietrich & Christian List, 2013. "Propositionwise judgment aggregation: the general case," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(4), pages 1067-1095, April.
    12. Dietrich, Franz & Mongin, Philippe, 2010. "The premiss-based approach to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 562-582, March.
    13. Franz Dietrich & Christian List, 2007. "Judgment Aggregation By Quota Rules," Journal of Theoretical Politics, , vol. 19(4), pages 391-424, October.
    14. repec:dau:papers:123456789/6413 is not listed on IDEAS
    15. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, vol. 145(2), pages 544-561, March.
    16. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
    17. Klaus Nehring, 2005. "The (Im)Possibility of a Paretian Rational," Economics Working Papers 0068, Institute for Advanced Study, School of Social Science.
    18. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
    19. 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.
    20. Nehring, Klaus, 2003. "Arrow's theorem as a corollary," Economics Letters, Elsevier, vol. 80(3), pages 379-382, September.
    21. 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.
    22. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations," Journal of Economic Theory, Elsevier, vol. 145(2), pages 495-511, March.
    23. Dietrich, Franz, 2006. "Judgment aggregation: (im)possibility theorems," Journal of Economic Theory, Elsevier, vol. 126(1), pages 286-298, January.
    24. Klaus Nehring & Clemens Puppe, 2008. "Consistent judgement aggregation: the truth-functional case," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(1), pages 41-57, June.
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    Citations

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    Cited by:

    1. Franz Dietrich & Christian List, 2008. "A liberal paradox for judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(1), pages 59-78, June.
    2. List, Christian & Polak, Ben, 2010. "Introduction to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 441-466, March.
    3. Dietrich, Franz, 2016. "Judgment aggregation and agenda manipulation," Games and Economic Behavior, Elsevier, vol. 95(C), pages 113-136.
    4. Schoch, Daniel, 2015. "Game Form Representation for Judgement and Arrovian Aggregation," MPRA Paper 64311, University Library of Munich, Germany.
    5. List, Christian, 2010. "The theory of judgment aggregation: an introductory review," LSE Research Online Documents on Economics 27596, London School of Economics and Political Science, LSE Library.
    6. Peleg, Bezalel & Zamir, Shmuel, 2018. "Judgments aggregation by a sequential majority procedure," Mathematical Social Sciences, Elsevier, vol. 95(C), pages 37-46.
    7. Dietrich Franz & List Christian, 2008. "The aggregation of propositional attitudes: towards a general theory," Research Memorandum 047, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

    More about this item

    Keywords

    judgment aggregation; relevance connections vs. logical connections between issues; generalized Arrow theorem; premise-based rule; sequential priority rule; general priority rule; priority graph; aggregation of non-binary evaluations;

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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