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Bayesian Group Agents and Two Modes of Aggregation

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Abstract

Suppose we have a group of Bayesian agents, and suppose that theywould like for their group as a whole to be a Bayesian agent as well. Moreover, suppose that thoseagents want the probabilities and utilities attached to this group agent to be aggregated from theindividual probabilities and utilities in reasonable ways. Two ways of aggregating their individual data areavailable to them, viz., ex ante aggregation and ex post aggregation. The former aggregatesexpected utilities directly, whereas the latter aggregates probabilities and utilities separately.A number of recent formal results show that both approaches have problematic implications. This studydiscusses the philosophical issues arising from those results. In this process, I hope to convincethe reader that these results about Bayesian aggregation are highly significant to decision theorists, butalso of immense interest to theorists working in areas such as ethics and political philosophy.

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REFERENCES

  • Anscombe, F. and R. Aumann: 1963, 'A Definition of Subjective Probability', Annals of Mathematical Statistics 35, 199–203.

    Google Scholar 

  • Arrow, K.: 1951, Social Choice and Individual Values, Wiley, New York.

    Google Scholar 

  • Arrow, K.: 1964, 'The Role of Securities in the Optimal Allocation of Risk-Bearing', Review of Economic Studies 31.

  • Bolker, E.: 1966, 'Functions Resembling Quotients of Measure', Transactions of the American Mathematical Society 124, 292–312.

    Google Scholar 

  • Bolker, E.: 1967, 'A Simultaneous Axiomatization of Utility and Subjective Probability', Philosophy of Science 34, 333–340.

    Google Scholar 

  • Broome, J.: 1990, 'Bolker-Jeffrey Expected Utility Theory and Axiomatic Utilitarianism', Review of Economic Studies 57, 477–502.

    Google Scholar 

  • Fishburn, P.: 1964, Decision and Value Theory, Wiley, New York.

    Google Scholar 

  • Fishburn, P.: 1970, Utility Theory for Decision Making, Wiley, New York.

    Google Scholar 

  • Goodman, J. H.: 1988, 'Existence of Compromises in Simple Group Decisions', PhD Thesis, Department of Statistics, Carnegie Mellon University.

  • Hammond, P.: 1982, 'Ex-ante and Ex-post Welfare Optimality under Uncertainty', Economica 48, 231–250.

    Google Scholar 

  • Hammond, P.: 1983, 'Ex-post Optimality as a Dynamically Consistent Objective for Collective Choice under Uncertainty', in P. Pattanaik and M. Salles (eds.), Social Choice and Welfare, North Holland, Amsterdam.

    Google Scholar 

  • Harsanyi, J.: 1955, Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility', Journal of Political Economy 63, 309–321.

    Google Scholar 

  • Hild, M.: 1998, 'The Instability of Ex Post Aggregation', Typescript.

  • Hild, M., R. Jeffrey, and M. Risse: 1998, ‘Preference Aggregation after Harsanyi’, in M. Salles and J.Weymark (eds.), Justice, Political Liberalism, and Utilitarianism: Proceedings of the Caen Conference in Honor of John Harsanyi and John Rawls, Cambridge University Press, Cambridge, forthcoming.

    Google Scholar 

  • Hylland, A. and R. Zeckhauser: 1979, 'The Impossibility of Bayesian Group Decision Making with Separate Aggregation of Beliefs and Values', Econometrica 47, 1321–1336.

    Google Scholar 

  • Jeffrey, R.: 1983 (first published 1965), The Logic of Decision, University of Chicago Press, Chicago.

    Google Scholar 

  • Joyce, R.: 1999, The Foundations of Causal Decision Theory, Cambridge University Press, Cambridge.

    Google Scholar 

  • Kemp, M. and Y. Ng: 1976, 'On the Existence of Social Welfare Functions, Social Ordering, and Social Decision Functions', Economica 43, 59–66.

    Google Scholar 

  • Kreps, D.: 1988, Theory of Choice, Westview, London.

    Google Scholar 

  • Leeds, S.: 1990, 'Levi's Decision Theory', Philosophy of Science 57, 158–168.

    Google Scholar 

  • Levi, I.: 1982, 'Conflict and Social Agency', Journal of Philosophy 79, 231–247.

    Google Scholar 

  • Levi, I.: 1986, Hard Choices, Cambridge University Press, Cambridge.

    Google Scholar 

  • Levi, I.: 1990, 'Pareto Unanimity and Consensus', Journal of Philosophy 87.

  • Levi, I.: 1999, 'Value Commitments, Value Conflicts, and the Separability of Belief and Value', Philosophy of Science 66, 509–533.

    Google Scholar 

  • Mongin, P.: 1995, 'Consistent Bayesian Aggregation', Journal of Economic Theory 66, 313–351.

    Google Scholar 

  • Mongin, P.: 1998, 'The Paradox of the Bayesian Experts and State-Dependent Utility Theory', Journal of Mathematical Economics 29, 331–361.

    Google Scholar 

  • Parks, R.: 1976, 'An Impossibility Theorem for Fixed Preferences: A Dictatorial Bergson-Samuelson Welfare Function', Review of Economic Studies 43, 447–450.

    Google Scholar 

  • Risse, M.: 2001, 'Instability of Ex Post Aggregation in the Bolker-Jeffrey Framework and Related Instability Phenomena', Erkenntnis 55, 239–269.

    Google Scholar 

  • Savage, L.: 1954, The Foundations of Statistics, Wiley, New York.

    Google Scholar 

  • Schervish, M. J., T. Seidenfeld, and M. J. Kadane: 1991, 'Shared Preferences and State-Dependent Utilities', Management Science 37, 1575–1589.

    Google Scholar 

  • Seidenfeld, T.: 1993, 'Outline of a Theory of Partially Ordered Preferences', Philosophical Topics 21, 173–189.

    Google Scholar 

  • Seidenfeld, T., J. Kadane, and M. Schervish: 1989, 'On the Shared Preferences of Two Bayesian Decision Makers', Journal of Philosophy 86, 220–244.

    Google Scholar 

  • Seidenfeld, T., M. Schervish, and J. Kadane: 1990. 'Decisions Without Ordering', in W. Sieg (ed.), Acting and Reflecting, Kluwer Academic Publishers, Dordrecht.

    Google Scholar 

  • Spohn, W.: 1978, Grundlagen der Entscheidungstheorie, Scriptor, Kronberg.

    Google Scholar 

  • von Neumann, J. and O. Morgenstern: 1944, 1947, Theory of Games and Economic Behavior, Princeton University Press, Princeton.

    Google Scholar 

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Risse, M. Bayesian Group Agents and Two Modes of Aggregation. Synthese 135, 347–377 (2003). https://doi.org/10.1023/A:1023531909371

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