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  • Seamus Bradley and Katie Steele

There has been much recent interest in imprecise probabilities, models of belief that allow unsharp or fuzzy credence. There have also been some influential criticisms of this position. Here we argue, chiefly against Elga (2010), that subjective probabilities need not be sharp. The key question is whether the imprecise probabilist can make reasonable sequences of decisions. We argue that she can. We outline Elga's argument and clarify the assumptions he makes and the principles of rationality he is implicitly committed to. We argue that these assumptions are too strong and that rational imprecise choice is possible in the absence of these overly strong conditions.

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Bradley, S. 2012. ‘Dutch book Arguments and Imprecise Probabilities.’ In Dieks, D., González, W. J., Hartmann, S., Stöltzner, M. and Weber, M. (eds), Probabilities, Laws and Structures, pp. 317. New York, NY: Springer.
Chandler, J. In press. ‘Subjective Probabilities need not be Sharp.’ Erkenntnis.
Elga, A. 2010. ‘Subjective Probabilities should be Sharp.’ Philosophers' Imprint 10.
Gustafsson, J. E. 2010. ‘A Money-pump for Acyclic Intransitive Preferences.’ Dialectica, 64: 251–7.
Paris, J. 2005 [2001]. ‘A Note on the Dutch book Method.’ In Proceedings of the Second International Symposium on Imprecise Probabilities and their Applications, pp. 301–306.
Rabinowicz, W. 1995. ‘To Have One's Cake and Eat it too: Sequential Choice and Expected-utility Violations.’ Journal of Philosophy, 92: 586620.
Sahlin, N.-E. and Weirich, P. 2014. ‘Unsharp Sharpness.’ Theoria, 80: 100–3.
Schick, F. 1986. ‘Dutch Bookies and Money Pumps.’ Journal of Philosophy, 83: 112–19.
Seidenfeld, T. 1994. ‘When Normal and Extensive Form Decisions Differ.’ Logic, Methodology and Philosophy of Science, IX: 451–63.
Seidenfeld, T. 2004. ‘A Contrast between two Decision Rules for use with (Convex) Sets of Probabilities: Γ-maximin versus E-admissibility.’ Synthese, 140: 6988.
Steele, K. 2010. ‘What are the Minimal Requirements of Rational Choice? Arguments from the Sequential Setting.’ Theory and Decision, 68: 463–87.
van Fraassen, B. 1990. ‘Figures in a Probability Landscape.’ In Dunn, M. and Segerberg, K. (eds), Truth or Consequences, pp. 345–56. Amsterdam: Kluwer.
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  • ISSN: 1742-3600
  • EISSN: 1750-0117
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