Scoring rules for judgment aggregation

• Published in: Social choice and welfare Vol. 42; no. 4; pp. 873 - 911
• Main Author: Dietrich, Franz
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer 01.04.2014; Springer Berlin Heidelberg; Springer Nature B.V; Springer Verlag
• Subjects: Aggregation; Algebra; Analysis; Choices; Collective behaviour; Decision Making; Economic Models; Economic theory; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Economics and Finance; Entailment; Game Theory; Humanities and Social Sciences; Individuals; International Political Economy; Judgement; Judgment; Majority voting; Mathematical functions; Mathematical vectors; Original Paper; Paradoxes; Preferences; Präferenztheorie; Public choice; Public Finance; Social and Behav. Sciences; Social Class; Social conditions & trends; Social Policy; Social research; Social welfare; Studies; Truth; Voting paradox; social choice; Kemeny rule; judgment aggregation; Borda rule; scoring rules; distance-based aggregation
• ISSN: 0176-1714; 1432-217X
• DOI: 10.1007/s00355-013-0757-8

This paper introduces a new class of judgment aggregation rules, to be called 'scoring rules' after their famous counterparts in preference aggregation theory. A scoring rule generates the collective judgment set which reaches the highest total 'score' across the individuals, subject to the judgment set having to be rational. Depending on how we define 'scores', we obtain several (old and new) solutions to the judgment aggregation problem, such as distance-based aggregation, premise- and conclusion-based aggregation, truth-tracking rules, and a generalization of the Borda rule to judgment aggregation theory. Scoring rules are shown to generalize the classical scoring rules of preference aggregation theory.