Dietrich, Franz and List, Christian (2014): From degrees of belief to binary beliefs: Lessons from judgmentaggregation theory.
This is the latest version of this item.

PDF
MPRA_paper_80844.pdf Download (730kB)  Preview 
Abstract
What is the relationship between degrees of belief and binary beliefs? Can the latter be expressed as a function of the former – a socalled “beliefbinarization rule” – without running into difficulties such as the lottery paradox? We show that this problem can be usefully analyzed from the perspective of judgmentaggregation theory. Although some formal similarities between belief binarization and judgment aggregation have been noted before, the connection between the two problems has not yet been studied in full generality. We seek to fill this gap. This paper is organized around a baseline impossibility theorem, which we use to map out the space of possible solutions to the beliefbinarization problem. Our theorem shows that, except in limiting cases, there exists no beliefbinarization rule satisfying four initially plausible desiderata. Surprisingly, this result is a direct corollary of the judgmentaggregation variant of Arrow’s classic impossibility theorem in social choice theory.
Item Type:  MPRA Paper 

Original Title:  From degrees of belief to binary beliefs: Lessons from judgmentaggregation theory 
Language:  English 
Keywords:  subjective probability, yes/no belif, impossibility theorem on binarization, analytic philosophy, judgment aggregation 
Subjects:  C  Mathematical and Quantitative Methods > C0  General C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods D  Microeconomics > D0  General D  Microeconomics > D0  General > D01  Microeconomic Behavior: Underlying Principles D  Microeconomics > D7  Analysis of Collective DecisionMaking D  Microeconomics > D7  Analysis of Collective DecisionMaking > D70  General D  Microeconomics > D8  Information, Knowledge, and Uncertainty D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D80  General D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D81  Criteria for DecisionMaking under Risk and Uncertainty D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D89  Other 
Item ID:  80844 
Depositing User:  Franz Dietrich 
Date Deposited:  19 Aug 2017 14:07 
Last Modified:  27 Sep 2019 00:03 
References:  Arrow, K. (1951/1963) Social Choice and Individual Values. New York: Wiley. Bovens, L., and W. Rabinowicz (2006) “Democratic answers to complex questions — an epistemic perspective.” Synthese 150(1): 131–153. Briggs, R., F. Cariani, K. Easwaran, and B. Fitelson (2014) “Individual Coherence and Group Coherence.” In J. Lackey (ed.), Essays in Collective Epistemology. Oxford: Oxford University Press. Cariani, F. (2014) “Local Supermajorities.” Working paper, Northwestern University. Chandler, J. (2013) “Acceptance, Aggregation and Scoring Rules.” Erkenntnis 78(1): 201217. Chapman, B. (2002) “Rational Aggregation.” Politics, Philosophy and Economics 1: 337–354. Dietrich, F. (2006) “Judgment Aggregation: (Im)Possibility Theorems.” Journal of Economic Theory 126: 286–298. Dietrich, F. (2007) “A generalised model of judgment aggregation.” Social Choice and Welfare 28: 529–565. Dietrich, F. (2015) “Aggregation theory and the relevance of some issues to others.” Journal of Economic Theory 160: 463493. Dietrich, F., and C. List (2007a) “Judgment aggregation by quota rules: majority voting generalized.” Journal of Theoretical Politics 19: 391–424. Dietrich, F., and C. List (2007b) “Arrow’s theorem in judgment aggregation.” Social Choice and Welfare 29: 19–33. Dietrich, F., and C. List (2007c) “Strategyproof judgment aggregation.” Economics and Philosophy 23(3): 269–300. Dietrich, F., and C. List (2013) “Propositionwise judgment aggregation: the general case.” Social Choice and Welfare 40(4): 1067–1095. Dietrich, F. and P. Mongin (2010) “The premisebased approach to judgment aggregation.” Journal of Economic Theory 145: 562–582. Dokow, E., and R. Holzman (2010a) “Aggregation of binary evaluations.” Journal of Economic Theory 145: 495–511. Dokow, E., and R. Holzman (2010b) “Aggregation of binary evaluations with abstentions.” Journal of Economic Theory 145: 544–561. Douven, I., and J.W. Romeijn (2007) “The Discursive Dilemma as a Lottery Paradox.” Economics and Philosophy 23(3): 301–319. Douven, I., and T. Williamson (2006) “Generalizing the Lottery Paradox.” British Journal for the Philosophy of Science 57(4): 755–779. Easwaran, K., and B. Fitelson (2015) “Accuracy, Coherence and Evidence.” In T. Szab´o Gendler and J. Hawthorne (eds.), Oxford Studies in Epistemology 5. Hawthorne, J., and L. Bovens (1999) “The preface, the lottery, and the logic of belief.” Mind 108(430): 241–264. Kelly, K. T., and H. Lin (2011) “Judgment aggregation: A geometrical impossibility proof.” Presentation at the 2011 Episteme Conference, Carnegie Mellon University, June 2011. Konieczny, S., and R. Pino P´erez (2002) “Merging Information Under Constraints: A Logical Framework.” Journal of Logic and Computation 12: 773–808. Kornhauser, L. A. (1992) “Modeling collegial courts. II. Legal doctrine.” Journal of Law, Economics and Organization 8: 441–470. Kornhauser, L. A., and L. G. Sager (1986) “Unpacking the Court.” Yale Law Journal 96: 82–117. Kyburg, H. E. (1961) Probability and the Logic of Rational Belief. Middletown: Wesleyan University Press (1961) Leitgeb, H. (2014) “The Stability Theory of Belief.” Philosophical Review 123(2): 131–171. Levi, I. (2004) “List and Pettit.” Synthese 140(1/2): 237–242. Lin, H., and K. T. Kelly (2012a) “Propositional Reasoning that Tracks Probabilistic Reasoning.” Journal of Philosophical Logic 41(6): 957–981. Lin, H., and K. T. Kelly (2012b) “A Geological Solution to the Lottery Paradox.” Synthese 186: 531–575. List, C. (2004) “A Model of PathDependence in Decisions over Multiple Propositions.” American Political Science Review 98: 495–513. List, C. (2006) “The Discursive Dilemma and Public Reason.” Ethics 116: 362–402. List, C. (2012) “The Theory of Judgment Aggregation: An Introductory Review.” Synthese 187: 179–207. List, C. (2014) “When to defer to supermajority testimony – and when not.” In J. Lackey (ed.), Essays in Collective Epistemology. Oxford: Oxford University Press. List, C., and P. Pettit (2002) “Aggregating Sets of Judgments: An Impossibility Result.” Economics and Philosophy 18(1): 89–110. List, C., and P. Pettit (2004) “Aggregating Sets of Judgments: Two Impossibility Results Compared.” Synthese 140(1/2): 207–235. Nehring, K., and C. Puppe (2010) “Abstract Arrovian Aggregation.” Journal of Economic Theory 145: 467–494. Pauly, M., and M. van Hees (2006) “Logical Constraints on Judgment Aggregation.” Journal of Philosophical Logic 35: 569–585. Pettit, P. (2001) “Deliberative Democracy and the Discursive Dilemma.” Philosophical Issues 11: 268–299. Pigozzi, G. (2006) “Belief merging and the discursive dilemma: an argumentbased account to paradoxes of judgment aggregation.” Synthese 152: 285–298. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/80844 
Available Versions of this Item

From degrees of belief to beliefs: Lessons from judgmentaggregation theory. (deposited 05 Sep 2014 07:32)
 From degrees of belief to binary beliefs: Lessons from judgmentaggregation theory. (deposited 19 Aug 2017 14:07) [Currently Displayed]