Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-22T17:05:17.369Z Has data issue: false hasContentIssue false
  • English
  • Français

IMAGING ALL THE PEOPLE

Published online by Cambridge University Press:  10 June 2016

Hannes Leitgeb
Get access Rights & Permissions [Opens in a new window]

Abstract

It is well known that aggregating the degree-of-belief functions of different subjects by linear pooling or averaging is subject to a commutativity dilemma: other than in trivial cases, conditionalizing the individual degree-of-belief functions on a piece of evidence E followed by linearly aggregating them does not yield the same result as first aggregating them linearly and then conditionalizing the resulting social degree-of-belief function on E. In the present paper we suggest a novel way out of this dilemma: adapting the method of update or learning such that linear pooling commutes with it. As it turns out, the resulting update scheme – (general) imaging on the evidence – is well-known from areas such as the study of conditionals and causal decision theory, and a formal result from which the required commutativity property is derivable was supplied already by Gärdenfors (1982) in a different context. We end up determining under which conditions imaging would seem to be right method of update, and under which conditions, therefore, group update would not be affected by the commutativity dilemma.

Type
Articles
Information
Episteme , Volume 14 , Issue 4 , December 2017 , pp. 463 - 479
Check for updates
Copyright
Copyright © Cambridge University Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Alchourron, C. E., Gärdenfors, P. and Makinson, D. 1985. ‘On the Logic of Theory Change. Partial Meet Contraction and Revision Functions.’ Journal of Symbolic Logic, 50: 510–30.CrossRefGoogle Scholar
Baratgin, J. and Politzer, G. 2011. ‘Updating: A Psychologically Basic Situation of Probability Revision.’ Thinking and Reasoning, 16: 253–87.CrossRefGoogle Scholar
Dalkey, N. C. 1975. ‘Toward a Theory of Group Estimation.’ In Linstone, H. and Turoff, M. (eds), The Delphi Method: Techniques and Applications, pp. 231–56. Reading, MA: Addison-Wesley.Google Scholar
Dietrich, F. 2010. ‘Bayesian Group Belief.’ Social Choice and Welfare, 35: 595–626.CrossRefGoogle Scholar
Dietrich, F. and List, C. Forthcoming. ‘Probabilistic Opinion Pooling.’ In Hitchcock, C. and Hajek, A. (eds), Oxford Handbook of Probability and Philosophy. Oxford: Oxford University Press.Google Scholar
Gärdenfors, P. 1982. ‘Imaging and Conditionalization.’ Journal of Philosophy, 79: 747–60.CrossRefGoogle Scholar
Genest, C. and Zidek, J. V. 1986. ‘Combining Probability Distributions: A Critique and an Annotated Bibliography.’ Statistical Science, 1: 114–48.Google Scholar
Genest, C., McConway, K. J. and Schervish, M. J. 1986. ‘Characterization of Externally Bayesian Pooling Operators.’ Annals of Statistics, 14: 487–501.CrossRefGoogle Scholar
Joyce, J. M. 1999. The Foundation of Causal Decision Theory. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Joyce, J. M. 2010. ‘Causal Reasoning and Backtracking.’ Philosophical Studies, 147: 139–54.CrossRefGoogle Scholar
Katzuno, H. and Mendelzon, A. O. 1992. ‘On the Difference Between Updating a Knowledge Base and Revising It.’ In Gärdenfors, P. (ed.), Belief Revision, pp. 183–203. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Lewis, D. K. 1976. ‘Probabilities of Conditionals and Conditional Probabilities.’ Philosophical Review, 85: 297–315.CrossRefGoogle Scholar
Lewis, D. K. 1981. ‘Causal Decision Theory.’ Australasian Journal of Philosophy, 59: 5–30.CrossRefGoogle Scholar
Madansky, A. 1964. ‘Externally Bayesian Groups.’ Technical Report RM-4141-PR. RAND Corporation.Google Scholar
Pearl, J. 1994. ‘From Imaging and Stochastic Control to a Calculus of Actions.’ AAAI Technical Report, SS-94-06: 204–9.Google Scholar
Skyrms, B. 1980a. ‘The Prior Propensity Account of Subjunctive Conditionals.’ In Harper, W., Stalnaker, R. and Pearce, G. (eds), pp. 259–65. Ifs. Conditionals, Belief, Decision, Chance, and Time. Dordrecht: Reidel.Google Scholar
Skyrms, B. 1980b. Causal Necessity. New Haven, CT: Yale University Press.Google Scholar
Skyrms, B. 1984. Pragmatics and Empiricism. New Haven, CT: Yale University Press.Google Scholar
Skyrms, B., Bell, G. D. and Woodruff, P. 1999. ‘Theories of Counter-Factual and Subjunctive Conditionals in Contexts of Strategic Interaction.’ Research in Economics, 53: 275–91.CrossRefGoogle Scholar
Steele, K. 2012. ‘Testimony as Evidence: More Problems for Linear Pooling.’ Journal of Philosophical Logic, 41: 983–99.CrossRefGoogle Scholar
Wagner, C. 1985. ‘On the Formal Properties of Averaging as a Method of Aggregation.’ Synthese, 62: 97–108.CrossRefGoogle Scholar