An Interpretive Account of Logical Aggregation Theory

P. MONGIN, F. Dietrich

Revue d'Economie Politique

novembre-décembre 2010, vol. 120, n°6, pp.929-972

Départements : Economie et Sciences de la décision, GREGHEC (CNRS)

Abstract: Judgment aggregation theory, or rather, as we conceive of it here, logical aggregation theory generalizes social choice theory by having the aggregation rule bear on judgments of all kinds whatever, and not barely judgments of preference. It derives from Kornhauser and Sager's doctrinal paradox and Pettit's discursive dilemma, two problems that we restate by emphasizing their conceptual differences. Henceforth, we follow the main technical advances of the theory, from the first impossibility theorem proved by List and Pettit to the completely general results of Dietrich and Mongin. We stress the collective achievement of the canonical theorem - by Dietrich and List, Dokow and Holzman, Nehring and Puppe - which provided the theory with a specific method of analysis: it consists in mathematically characterizing the impossibility agendas of a given aggregator - i.e., the sets of propositions such that no collective judgment function exists with a certain list of axiomatic properties. The presentation is unified here by the use of formal logic, for which we claim relevance at every step, and by the above-mentioned distinction between the doctrinal paradox and the discursive dilemma, which we reelaborate upon technically.Author Keywords: Judgment Aggregation; Logical Aggregattion; Doctrinal Paradox; Discursive Dilemma; General Logic; Premiss-Based vs Conclusion; Based Approach; Social Choice TheoryKeyWords Plus: JUDGMENT AGGREGATION; ARROWS THEOREM; COLLEGIAL COURTS; IMPOSSIBILITY; PROPOSITIONS; CONSTRAINTS; LANGUAGE; AGENDAS; CHOICE; BELIEF