Arrow’s theorem in judgment aggregation
- 340 Downloads
In response to recent work on the aggregation of individual judgments on logically connected propositions into collective judgments, it is often asked whether judgment aggregation is a special case of Arrowian preference aggregation. We argue for the converse claim. After proving two impossibility theorems on judgment aggregation (using “systematicity” and “independence” conditions, respectively), we construct an embedding of preference aggregation into judgment aggregation and prove Arrow’s theorem (stated for strict preferences) as a corollary of our second result. Although we thereby provide a new proof of Arrow’s theorem, our main aim is to identify the analogue of Arrow’s theorem in judgment aggregation, to clarify the relation between judgment and preference aggregation, and to illustrate the generality of the judgment aggregation model.
Unable to display preview. Download preview PDF.
- Dietrich F (forthcoming) A generalized model of judgment aggregation. Soc Choice and WelfareGoogle Scholar
- Dietrich F, List C (2005) Judgment aggregation by quota rules. Working paper, LSEGoogle Scholar
- Dokow E, Holzman R (2005) Aggregation of binary evaluations. Working paper, Technion Israel Institute of TechnologyGoogle Scholar
- Gärdenfors P (forthcoming) An Arrow-like theorem for voting with logical consequences. Econ PhilosGoogle Scholar
- Guilbaud GT (1966) Theories of the general interest, and the logical problem of aggregation. In: Lazarsfeld PF, Henry NW (eds) Readings in mathematical social science. MIT Press, Cambridge, pp 262–307Google Scholar
- van Hees M (forthcoming) The limits of epistemic democracy. Soc Choice WelfareGoogle Scholar
- List C, Pettit P (2001/2004) Aggregating sets of judgments: two impossibility results compared. Social and Political Theory Paper W20 (technical report ID 931), Australian National published in Synthese 140(1–2):207–235Google Scholar
- List C, Pettit P (2002) Aggregating sets of judgments: an impossibility result. Econ Philos 18:89–110Google Scholar
- Nehring K, Puppe C (2002) Strategy proof social choice on single-peaked domains: possibility, impossibility and the space between. Working paper, University of California, DavisGoogle Scholar
- Nehring K, Puppe C (2005) Consistent judgment aggregation: a characterization. Working paper, University of KarlsruheGoogle Scholar
- Pigozzi G (forthcoming) Belief merging and the discursive dilemma: an argument-based account to paradoxes of judgment aggregation. SyntheseGoogle Scholar