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Truth-tracking judgment aggregation over interconnected issues

  • Irem BozbayEmail author
Original Paper
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Abstract

This paper analyzes the problem of aggregating individual judgments over two interconnected issues. Voters share a common preference which is state-dependent, but they hold private information about what the state might be. I assume strategic voting in a Bayesian voting game setting and I want to determine voting rules which induce an efficient Bayesian Nash equilibrium in truthful strategies, hence lead to collective judgments that efficiently incorporate all private information. Interconnectedness may lead to private information that is inconsistent with the state, which leads to the impossibility of efficient information aggregation. Once I introduce the possibility of abstention, the negative conclusion no longer prevails and there is always a voting rule which aggregates information efficiently. I obtain a similar positive result when I rule out the possibility of inconsistent private information. I analyze the situations in which such rules exist whenever necessary, as well as the nature of these rules.

Notes

Acknowledgements

I am grateful to Franz Dietrich and Hans Peters for their valuable comments. I would also like to thank audiences at various occasions where this work was presented.

References

  1. Ahn D, Oliveros S (2014) Condorcet jur(ies) theorem. J Econ Theory 150:841–851CrossRefGoogle Scholar
  2. Ahn D, Oliveros S (2012) Combinatorial voting. Econometrica 80(1):89–141CrossRefGoogle Scholar
  3. Austen-Smith D, Banks J (1996) Information aggregation, rationality, and the Condorcet jury theorem. Am Polit Sci Rev 90(1):34–45CrossRefGoogle Scholar
  4. Austen-Smith D, Feddersen T (2006) Deliberation, preference uncertainty and voting rules. Am Polit Sci Rev 100(2):209–217CrossRefGoogle Scholar
  5. Barelli P, Bhattacharya S, Siga L (2018) Full information equivalence in large elections. SSRN 3183959Google Scholar
  6. Blumrosen L, Feldman M (2013) Mechanism design with a restricted action space. Games Econ Behav 82:424–443CrossRefGoogle Scholar
  7. Bovens L, Rabinowicz W (2006) Democratic answers to complex questions: an epistemic perspective. Synthese 150(1):131–153CrossRefGoogle Scholar
  8. Bozbay I, Dietrich F, Peters H (2014) Judgment aggregation in search for the truth. Games Econ Behav 87:571–590CrossRefGoogle Scholar
  9. Bozbay I, Peters H (2017) Information aggregation with a continuum of types. Maastricht University GSBE Research Memoranda, No. 032Google Scholar
  10. De Clippel G, Eliaz K (2015) Premise versus outcome-based information aggregation. Games Econ Behav 89:34–42CrossRefGoogle Scholar
  11. Dietrich F (2016) Judgment aggregation and agenda manipulation. Games Econ Behav 95:113–136CrossRefGoogle Scholar
  12. Dietrich F, List C (2007a) Strategy-proof judgment aggregation. Econ Philos 23:269–300CrossRefGoogle Scholar
  13. Dietrich F, List C (2007b) Judgment aggregation by quota rules: majority voting generalized. J Theor Polit 19(4):391–424CrossRefGoogle Scholar
  14. Dokow E, Falik D (2012) Models of manipulation on aggregation of binary evaluations. In: Proceedings of the 4th international workshop on computational social choice, pp 191–202Google Scholar
  15. Feddersen T, Pesendorfer W (1996) The Swing voter’s curse. Am Econ Rev 86(3):408–424Google Scholar
  16. Feddersen T, Pesendorfer W (1997) Voting behavior and information aggregation in elections with private information. Econometrica 65(5):1029–1058CrossRefGoogle Scholar
  17. List C (2005) The probability of inconsistencies in complex collective decisions. Soc Choice Welf 24(1):3–32CrossRefGoogle Scholar
  18. List C, Pettit P (2011) Group agency: the possibility, design and status of corporate agents. Oxford University Press, OxfordCrossRefGoogle Scholar
  19. List C, Polak B (eds) (2010) Symposium on judgment aggregation. J Econ Theory 145(2):441–466Google Scholar
  20. McLennan A (1998) Consequences of the Condorcet jury theorem for beneficial information aggregation by rational agents. Am Polit Sci Rev 92(2):413–418CrossRefGoogle Scholar
  21. Nehring K, Puppe C (2002) Strategy-proof social choice on single-peaked domains: possibility, impossibility and the space between. Department of Economics, University of California at Davis (Unpublished manuscript)Google Scholar
  22. Nehring K, Puppe C (2007) The structure of strategy-proof social choice. Part I: General characterization and possibility results on median spaces. J Econ Theory 135:269–305CrossRefGoogle Scholar
  23. Pivato M (2013) Voting rules as statistical estimators. Soc Choice Welf 40(2):581–630CrossRefGoogle Scholar
  24. Schmitz PW, Tröger T (2012) The (sub-) optimality of the majority rule. Games Econ Behav 74(2):651–665CrossRefGoogle Scholar
  25. Van Zandt T (2007) Communication complexity and mechanism design. J Eur Econ Assoc 5:543–553CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.University of SurreyGuildfordUK

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