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Acting on belief functions

Author

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  • Nicholas J. J. Smith

    (The University of Sydney)

Abstract

The degrees of belief of rational agents should be guided by the evidence available to them. This paper takes as a starting point the view—argued elsewhere—that the formal model best able to capture this idea is one that represents degrees of belief using Dempster–Shafer belief functions. However, degrees of belief should not only respect evidence; they also guide decision and action. Whatever formal model of degrees of belief we adopt, we need a decision theory that works with it: that takes as input degrees of belief so represented. The task of this paper is to develop such a decision theory for the belief function model of degrees of belief. This is not the first paper to attempt that task, but compared to the existing literature it takes a more abstract route to its destination, via a consideration of the very idea of rational decision making in light of one’s beliefs and desires. After presenting the new decision theory and comparing it to existing views, the paper goes on to consider diachronic decision situations.

Suggested Citation

  • Nicholas J. J. Smith, 2023. "Acting on belief functions," Theory and Decision, Springer, vol. 95(4), pages 575-621, November.
    • Handle: RePEc:kap:theord:v:95:y:2023:i:4:d:10.1007_s11238-023-09937-9
    DOI: 10.1007/s11238-023-09937-9
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    References listed on IDEAS

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    5. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
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