Weighted regret-based likelihood: a new approach to describing uncertainty
Abstract
Recently, Halpern and Leung 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.
Keywords
Cite
@article{arxiv.1309.1228,
title = {Weighted regret-based likelihood: a new approach to describing uncertainty},
author = {Joseph Y. Halpern},
journal= {arXiv preprint arXiv:1309.1228},
year = {2013}
}
Comments
Appeared in 12th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU)}, 2013, pp. 266--277