Abstract
We recast subjective probabilities by rejecting behaviourist accounts of belief by explicitly distinguishing between judgements of uncertainty and expressions of those judgements. We argue that this entails rejecting that orderings of uncertainty be complete. This in turn leads naturally to several generalizations of the probability calculus. We define probability-like functions over incomplete algebras that reflect a subject’s incomplete judgements of uncertainty. These functions can be further generalized to (partial) inner and outer measures that reflect approximate elicitations.
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Acknowledgements
The authors wish to thank Colin Howson, Peter Milne, Samuel Fletcher, Jeff Paris and two anonymous reviewers for helpful comments. Work on this paper was supported by grant no. GA16-15621S of the Czech Science Foundation.
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Childers, T., Majer, O. Eliciting Uncertainties: A Two Structure Approach. Stud Logica 106, 615–636 (2018). https://doi.org/10.1007/s11225-017-9757-5
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DOI: https://doi.org/10.1007/s11225-017-9757-5