A measure of distance between judgment sets

Conal Duddy and Ashley Piggins ()

Social Choice and Welfare, 2012, vol. 39, issue 4, 855-867

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 A−B share the same truth value, then the disagreement between A and B over those propositions in A−B 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. Copyright Springer-Verlag 2012

Date: 2012
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DOI: 10.1007/s00355-011-0565-y

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