Advertisement

Social Choice and Welfare

, Volume 39, Issue 4, pp 855–867 | Cite as

A measure of distance between judgment sets

  • Conal Duddy
  • Ashley Piggins
Open Access
Original Paper

Abstract

In the literature on judgment aggregation, an important open question is how to measure the distance between any two judgment sets. This is relevant for issues of social choice: if two individuals hold different beliefs then we might want to find a compromise that lies somewhere between them. We propose a set of axioms that determine a measure of distance uniquely. This measure differs from the widely used Hamming metric. The difference between Hamming’s metric and ours boils down to one axiom. Given judgment sets A and B, this axiom says that if the propositions in \({A \cap B}\) jointly imply that the propositions in AB share the same truth value, then the disagreement between A and B over those propositions in AB should be counted as a single disagreement. We consider the application of our metric to judgment aggregation, and also use the metric to measure the distance between preference rankings.

Keywords

Social Choice Econ Theory Aggregation Rule Preference Ranking Judgment Aggregation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Arrow KJ (1963) Social choice and individual values. Wiley, New YorkGoogle Scholar
  2. Dietrich F (2006) Judgment aggregation: (im)possibility theorems. J Econ Theory 126: 286–298CrossRefGoogle Scholar
  3. Dietrich F (2007) A generalised model of judgment aggregation. Soc Choice Welf 28: 529–565CrossRefGoogle Scholar
  4. Dietrich F, List C (2007) Arrow’s theorem in judgment aggregation. Soc Choice Welf 29: 19–33CrossRefGoogle Scholar
  5. Dietrich F, List C (2009) Propositionwise judgment aggregation: the general case. Working paper, London School of EconomicsGoogle Scholar
  6. Dietrich F, List C (2010) The aggregation of propositional attitudes: towards a general theory. In: Gendler TS, Hawthorne J (eds) Oxford studies in epistemology, vol 3. Oxford University Press, OxfordGoogle Scholar
  7. Dietrich F, Mongin P (2010) The premiss-based approach to judgment aggregation. J Econ Theory 145: 562–582CrossRefGoogle Scholar
  8. Dokow E, Holzman R (2010) Aggregation of binary evaluations. J Econ Theory 145: 495–511CrossRefGoogle Scholar
  9. Duddy C, Piggins A (2009) Many-valued judgment aggregation: characterizing the possibility/impossibility boundary for an important class of agendas. Working paper, NUI GalwayGoogle Scholar
  10. Duddy C, Piggins A (2010) Aggregating partitions. Working paper, NUI GalwayGoogle Scholar
  11. Kemeny JG (1959) Mathematics without numbers. Daedalus 88: 577–591Google Scholar
  12. Kemeny JG, Snell JL (1962) Mathematical models in the social sciences. Ginn, New YorkGoogle Scholar
  13. Konieczny S, Pino Pérez R (2002) Merging information under constraints: a logical framework. J Log Comput 12: 773–808CrossRefGoogle Scholar
  14. Kornhauser LA (1992) Modelling collegial courts II: legal doctrine. J Law Econom Organ 8: 441–470Google Scholar
  15. Kornhauser LA, Sager LG (1993) The one and the many: adjudication in collegial courts. Calif Law Rev 81: 1–59CrossRefGoogle Scholar
  16. List C (2008) Which worlds are possible? A judgment aggregation problem. J Philos Log 37: 57–65CrossRefGoogle Scholar
  17. List C, Pettit P (2002) Aggregating sets of judgments: an impossibility result. Econ Philos 18: 89–110Google Scholar
  18. List C, Polak B (2010) Introduction to judgment aggregation. J Econ Theory 145: 441–446CrossRefGoogle Scholar
  19. List C, Puppe C (2009) Judgment aggregation: a survey. In: Anand P, Pattanaik P, Puppe C (eds) The handbook of rational and social choice. Oxford University Press, OxfordGoogle Scholar
  20. Miller MK, Osherson D (2009) Methods for distance-based judgment aggregation. Soc Choice Welf 32: 575–601CrossRefGoogle Scholar
  21. Nehring K, Puppe C (2002) Strategy-proof social choice on single-peaked domains: possibility, impossibility and the space between. Working paper, University of California at DavisGoogle Scholar
  22. Nehring K, Puppe C (2010) Abstract arrowian aggregation. J Econ Theory 145: 467–494CrossRefGoogle Scholar
  23. Pigozzi G (2006) Belief merging and the discursive dilemma: an argument-based account to paradoxes of judgment aggregation. Synthese 152: 285–298CrossRefGoogle Scholar
  24. Young HP, Levenglick A (1978) A consistent extension of Condorcet’s election principle. SIAM J Appl Math 35: 285–300CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Government of Ireland Scholar, J.E. Cairnes School of Business and EconomicsNational University of Ireland GalwayGalwayIreland
  2. 2.J.E. Cairnes School of Business and EconomicsNational University of Ireland GalwayGalwayIreland

Personalised recommendations