In this paper, I investigate the relationship between preference and judgment aggregation, using the notion of ranking judgment introduced in List and Pettit (Synthese 140(1–2):207–235, 2004). Ranking judgments were introduced in order to state the logical connections between the impossibility theorem of aggregating sets of judgments proved in List and Pettit (Economics and Philosophy 18:89–110, 2002) and Arrow’s theorem (Arrow, Social choice and individual values, 1963). I present a proof of the theorem concerning ranking judgments as a corollary of Arrow’s theorem, extending the translation between preferences and judgments defined in List and Pettit (Synthese 140(1–2):207–235, 2004) to the conditions on the aggregation procedure.
KeywordsArrow’s theorem Conodorcet’s paradox Discursive dilemma Aggregation of ranking judgments First order logic
I wish to thank Valeria Ottonelli for the invaluable discussions. I also thank an anonymous referee for the very helpful comments on notation.
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- Arrow K. (1963) Social choice and individual values. Wiley, New YorkGoogle Scholar
- Kornhauser L.A. (1992) Modelling collegial courts. II. Legal doctrine. Journal of Law, Economics and Organization 8: 441–470Google Scholar
- List C., Elsholtz C. (2005) A simple proof of Sen’s possibility theorem on majority decisions. Elemente der Mathematik 60: 45–56Google Scholar
- List C., Pettit P. (2002) Aggregating sets of judgments: An impossibility result. Economics and Philosophy 18: 89–110Google Scholar
- Ottonelli V. (2005) Errore deliberativo e legittimità democratica. Networks 5: 32–51Google Scholar
- Ottonelli, V. (2009). What does the discursive paradox really mean for democracy? Political Studies (forthcoming).Google Scholar
- Pettit, P. (2001). Deliberative democracy and the discursive dilemma. Philosophical Issues (supplement to Nous 39), 11, 268–299.Google Scholar