David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Synthese 186 (2):577-600 (2012)
This paper analyzes concepts of independence and assumptions of convexity in the theory of sets of probability distributions. The starting point is Kyburg and Pittarelli’s discussion of “convex Bayesianism” (in particular their proposals concerning E-admissibility, independence, and convexity). The paper offers an organized review of the literature on independence for sets of probability distributions; new results on graphoid properties and on the justification of “strong independence” (using exchangeability) are presented. Finally, the connection between Kyburg and Pittarelli’s results and recent developments on the axiomatization of non-binary preferences, and its impact on “complete” independence, are described
|Keywords||Sets of probability distributions Independence Decision-making Preferences Convexity|
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References found in this work BETA
Bruno de Finetti (1970). Theory of Probability. New York: John Wiley.
P. Diaconis & D. Freedman (1980). Finite Exchangeable Sequences. The Annals of Probability 8:745--64.
Persi Diaconis & Sandy L. Zabell (1982). Updating Subjective Probability. Journal of the American Statistical Association 77 (380):822-830.
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Alan Hájek (2003). What Conditional Probability Could Not Be. Synthese 137 (3):273--323.
Citations of this work BETA
Arthur Paul Pedersen & Gregory Wheeler (2013). Demystifying Dilation. Erkenntnis (6):1-38.
Seamus Bradley & Katie Steele (2014). Uncertainty, Learning, and the “Problem” of Dilation. Erkenntnis 79 (6):1287-1303.
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