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European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty

ECSQARU 2013: Symbolic and Quantitative Approaches to Reasoning with Uncertainty pp 266–277Cite as

Weighted Regret-Based Likelihood: A New Approach to Describing Uncertainty

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7958))

Abstract

Recently, Halpern and Leung [8] suggested representing uncertainty by a weighted set of probability measures, and suggested a way of making decisions based on this representation of uncertainty: maximizing weighted regret. Their paper does not answer an apparently simpler question: what it means, according to this representation of uncertainty, for an event E to be more likely than an event E′. In this paper, a notion of comparative likelihood when uncertainty is represented by a weighted set of probability measures is defined. It generalizes the ordering defined by probability (and by lower probability) in a natural way; a generalization of upper probability can also be defined. A complete axiomatic characterization of this notion of regret-based likelihood is given.

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Author information

Authors and Affiliations

  1. Cornell University, Ithaca, NY, 14853, USA

    Joseph Y. Halpern

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  1. Joseph Y. Halpern
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Editor information

Editors and Affiliations

  1. Department of Information and Computing Sciences, Utrecht University, Princetonplein 5, 3584 CC, Utrecht, The Netherlands

    Linda C. van der Gaag

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Halpern, J.Y. (2013). Weighted Regret-Based Likelihood: A New Approach to Describing Uncertainty. In: van der Gaag, L.C. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2013. Lecture Notes in Computer Science(), vol 7958. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39091-3_23

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  • DOI: https://doi.org/10.1007/978-3-642-39091-3_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39090-6

  • Online ISBN: 978-3-642-39091-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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