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


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.


Social Choice Econ Theory Aggregation Rule Preference Ranking Judgment Aggregation 
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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

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