Skip to main content
SpringerLink
Log in

Some Complexity Results for Distance-Based Judgment Aggregation

  • Conference paper
AI 2013: Advances in Artificial Intelligence (AI 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8272))

Included in the following conference series:

  • 2600 Accesses

Abstract

Judgment aggregation is a social choice method for aggregating information on logically related issues. In distance-based judgment aggregation, the collective opinion is sought as a compromise between information sources that satisfies several structural properties. It would seem that the standard conditions on distance and aggregation functions are strong enough to guarantee existence of feasible procedures. In this paper, we show that it is not the case, though the problem becomes easier under some additional assumptions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bartholdi, J., Tovey, C.A., Trick, M.A.: Voting schemes for which it can be difficult to tell who won the election. Social Choice and Welfare 6, 157–165 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  2. Baumeister, D., Erdélyi, G., Erdélyi, O.J., Rothe, J.: Control in judgment aggregation. In: Proceedings of the 6th European Starting AI Researcher Symposium, pp. 23–34 (2012)

    Google Scholar 

  3. Baumeister, D., Erdélyi, G., Erdélyi, O.J., Rothe, J.: Computational aspects of manipulation and control in judgment aggregation. In: Proceedings of the 3rd International Conference on Algorithmic Decision Theory, ADT 2013 (forthcomming, 2013)

    Google Scholar 

  4. Baumeister, D., Erdélyi, G., Rothe, J.: How hard is it to bribe the judges? A study of the complexity of bribery in judgment aggregation. In: Brafman, R., Roberts, F.S., Tsoukiàs, A. (eds.) ADT 2011. LNCS, vol. 6992, pp. 1–15. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  5. Bulling, N., Farwer, B.: On the (un-)decidability of model checking resource-bounded agents. In: Proceedings of ECAI. Frontiers in Artificial Intelligence and Applications, vol. 215, pp. 567–572. IOS Press (2010)

    Google Scholar 

  6. Chevaleyre, Y., Endriss, U., Lang, J., Maudet, N.: A short introduction to computational social choice. In: van Leeuwen, J., Italiano, G.F., van der Hoek, W., Meinel, C., Sack, H., Plášil, F. (eds.) SOFSEM 2007. LNCS, vol. 4362, pp. 51–69. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  7. Conitzer, V., Sandholm, T.: Complexity of manipulating elections with few candidates. In: Proceedings of AAAI 2002, pp. 314–319. American Association of Artificial Intelligence (2002)

    Google Scholar 

  8. Conitzer, V., Sandholm, T.: Communication complexity of common voting rules. In: Proceedings of the ACM Conference on Electronic Commerce, pp. 78–87 (2005)

    Google Scholar 

  9. Dempster, A.P.: Upper and lower probabilities induced by a multivalued mapping. The Annals of Mathematical Statistics 38(2) (1967)

    Google Scholar 

  10. Deza, M.M., Deza, E.: Encyclopedia of Distances. Springer (2009)

    Google Scholar 

  11. Dietrich, F.: A generalised model of judgment aggregation. Social Choice and Welfare 28(4), 529–565 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  12. Dietrich, F.: Judgment aggregation by quota rules majority voting generalized. Journal of Theoretical Politics 19(4), 391–424 (2007)

    Article  MathSciNet  Google Scholar 

  13. Dietrich, F.: Scoring rules for judgment aggregation. Social Choice and Welfare (to appear, 2013)

    Google Scholar 

  14. Dietrich, F., Mongin, P.: The premiss-based approach to judgment aggregation. Journal of Economic Theory 145(2), 562–582 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  15. Dima, C., Tiplea, F.L.: Model-checking atl under imperfect information and perfect recall semantics is undecidable. CoRR, abs/1102.4225 (2011)

    Google Scholar 

  16. Dokow, E., Holzman, R.: Aggregation of binary evaluations with abstentions. Journal of Economic Theory 145(2), 544–561 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  17. Duddy, C., Piggins, A.: Many-valued judgment aggregation: Characterizing the possibility/impossibility boundary. Journal of Economic Theory 148(2), 793–805 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  18. Eckert, D., Klamler, C., Mitlöhner, J., Schlötterer, C.: A distance-based comparison of basic voting rules. Central European Journal of Operations Research 14(4), 377–386 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  19. Eckert, D., Mitlöhner, J.: Logical representation and merging of preference information. In: Proceedings of the IJCAI 2005 Multidisciplinary Workshop on Preference Handling (2005)

    Google Scholar 

  20. Endriss, U., Grandi, U., Porello, D.: Complexity of judgment aggregation: Safety of the agenda. In: Proceedings of AAMAS 2010, pp. 359–366 (2010)

    Google Scholar 

  21. Endriss, U., Grandi, U., Porello, D.: Complexity of winner determination and strategic manipulation in judgment aggregation. In: Proceedings of COMSOC 2010 (2010)

    Google Scholar 

  22. Endriss, U., Grandi, U., Porello, D.: Complexity of judgment aggregation. Journal of Artificial Intelligence Research 45, 481–514 (2012)

    MathSciNet  MATH  Google Scholar 

  23. Escoffier, B., Lang, J., Öztürk, M.: Single-peaked consistency and its complexity. In: Proceedings of ECAI 2008, pp. 366–370. IOS Press (2008)

    Google Scholar 

  24. Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about Knowledge. MIT Press (1995)

    Google Scholar 

  25. Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press (2009)

    Google Scholar 

  26. Grossi, D.: Correspondences in the theory of aggregation. In: Bonanno, G., Löwe, B., van der Hoek, W. (eds.) LOFT 2008. LNCS, vol. 6006, pp. 34–60. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  27. Hemaspaandra, E., Spakowski, H., Vogel, J.: The complexity of kemeny elections. Theoretical Computer Science 349(3), 382–391 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  28. Konieczny, S., Lang, J., Marquis, P.: Distance-based merging: A general framework and some complexity results. In: Proceedings of KR 2002, pp. 97–108 (2002)

    Google Scholar 

  29. Lang, J., Pigozzi, G., Slavkovik, M., van der Torre, L.: Judgment aggregation rules based on minimization. In: Proceedings of TARK, pp. 238–246 (2011)

    Google Scholar 

  30. Lang, J., Slavkovik, M.: Judgment aggregation rules and voting rules. In: Perny, P., Pirlot, M., Tsoukiás, A. (eds.) ADT 2013. LNCS, vol. 8176, pp. 230–243. Springer, Heidelberg (2013)

    Google Scholar 

  31. Li, N.: Decision paths in sequential non-binary judgment aggregation. Technical report, Universitat Autònoma de Barcelona (2010)

    Google Scholar 

  32. List, C., Pettit, P.: Aggregating sets of judgments: An impossibility result. Economics and Philosophy 18(01), 89–110 (2002)

    Google Scholar 

  33. List, C., Polak, B.: Introduction to judgment aggregation. Journal of Economic Theory 145(2), 441–466 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  34. Miller, M.K., Osherson, D.: Methods for distance-based judgment aggregation. Social Choice and Welfare 32(4), 575–601 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  35. Nehring, K., Pivato, M.: Incoherent majorities: The McGarvey problem in judgement aggregation. Discrete Applied Mathematics 159(15), 1488–1507 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  36. Pauly, M., van Hees, M.: Logical constraints on judgement aggregation. Journal of Philosophical Logic 35(6), 569–585 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  37. Peterson, G., Reif, J., Azhar, S.: Lower bounds for multiplayer noncooperative games of incomplete information. Computers and Mathematics with Applications 41(7), 957–992

    Google Scholar 

  38. Pigozzi, G.: Belief merging and the discursive dilemma: an argument-based account to paradoxes of judgment aggregation. Synthese 152(2), 285–298 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  39. Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press (1976)

    Google Scholar 

  40. Slavkovik, M., Jamroga, W.: Distance-based judgment aggregation of three-valued judgments with weights. In: Proceedings of the IJCAI Workshop on Social Choice and Artificial Intelligence

    Google Scholar 

  41. van der Hoek, W., Verbrugge, R.: Epistemic logic: A survey. Game Theory and Applications 8, 53–94 (2002)

    Google Scholar 

  42. Wilson, R.: On the theory of aggregation. Journal of Economic Theory 10(1), 89–99 (1975)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Luxembourg, Luxembourg

    Wojciech Jamroga

  2. University of Bergen, Norway

    Marija Slavkovik

Authors
  1. Wojciech Jamroga
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marija Slavkovik
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Information Science, University of Otago, 9054, Dunedin, New Zealand

    Stephen Cranefield

  2. Macquarie University, 2109, Sydney, NSW, Australia

    Abhaya Nayak

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer International Publishing Switzerland

About this paper

Cite this paper

Jamroga, W., Slavkovik, M. (2013). Some Complexity Results for Distance-Based Judgment Aggregation. In: Cranefield, S., Nayak, A. (eds) AI 2013: Advances in Artificial Intelligence. AI 2013. Lecture Notes in Computer Science(), vol 8272. Springer, Cham. https://doi.org/10.1007/978-3-319-03680-9_33

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-03680-9_33

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03679-3

  • Online ISBN: 978-3-319-03680-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation