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Inferring probability comparisons

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  • Harrison-Trainor, Matthew
  • Holliday, Wesley H.
  • Icard, Thomas F.

Abstract

The problem of inferring probability comparisons between events from an initial set of comparisons arises in several contexts, ranging from decision theory to artificial intelligence to formal semantics. In this paper, we treat the problem as follows: beginning with a binary relation ≿ on events that does not preclude a probabilistic interpretation, in the sense that ≿ has extensions that are probabilistically representable, we characterize the extension ≿+ of ≿ that is exactly the intersection of all probabilistically representable extensions of ≿. This extension ≿+ gives us all the additional comparisons that we are entitled to infer from ≿, based on the assumption that there is some probability measure of which ≿ gives us partial qualitative information. We pay special attention to the problem of extending an order on states to an order on events. In addition to the probabilistic interpretation, this problem has a more general interpretation involving measurement of any additive quantity: e.g., given comparisons between the weights of individual objects, what comparisons between the weights of groups of objects can we infer?

Suggested Citation

  • Harrison-Trainor, Matthew & Holliday, Wesley H. & Icard, Thomas F., 2018. "Inferring probability comparisons," Mathematical Social Sciences, Elsevier, vol. 91(C), pages 62-70.
    • Handle: RePEc:eee:matsoc:v:91:y:2018:i:c:p:62-70
    DOI: 10.1016/j.mathsocsci.2017.08.003
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    References listed on IDEAS

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    1. Matthew Harrison-Trainor & Wesley Holliday & Thomas Icard, 2016. "A note on cancellation axioms for comparative probability," Theory and Decision, Springer, vol. 80(1), pages 159-166, January.
    2. Lehrer, Ehud & Teper, Roee, 2011. "Justifiable preferences," Journal of Economic Theory, Elsevier, vol. 146(2), pages 762-774, March.
    3. Itzhak Gilboa & Fabio Maccheroni & Massimo Marinacci & David Schmeidler, 2010. "Objective and Subjective Rationality in a Multiple Prior Model," Econometrica, Econometric Society, vol. 78(2), pages 755-770, March.
    4. Alon, Shiri & Lehrer, Ehud, 2014. "Subjective multi-prior probability: A representation of a partial likelihood relation," Journal of Economic Theory, Elsevier, vol. 151(C), pages 476-492.
    5. Matthew Harrison-Trainor & Wesley H. Holliday & Thomas F. Icard, 2016. "A note on cancellation axioms for comparative probability," Theory and Decision, Springer, vol. 80(1), pages 159-166, January.
    6. Kannai, Yakar & Peleg, Bezalel, 1984. "A note on the extension of an order on a set to the power set," Journal of Economic Theory, Elsevier, vol. 32(1), pages 172-175, February.
    7. Bruno Girotto & Silvano Holzer, 2003. "Representing complete and incomplete subjective linear preferences on random numbers," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 26(2), pages 129-144, November.
    8. Rumbos, Beatriz, 2001. "Representing subjective orderings of random variables: an extension," Journal of Mathematical Economics, Elsevier, vol. 36(1), pages 31-43, September.
    9. Nehring, Klaus, 2009. "Imprecise probabilistic beliefs as a context for decision-making under ambiguity," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1054-1091, May.
    10. Kelsey, David, 1993. "Choice under Partial Uncertainty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(2), pages 297-308, May.
    11. Barbera, Salvador & Pattanaik, Prasanta K., 1984. "Extending an order on a Set to the power set: Some remarks on Kannai and Peleg's approach," Journal of Economic Theory, Elsevier, vol. 32(1), pages 185-191, February.
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