Weighted Regret-Based Likelihood: A New Approach to Describing Uncertainty
Abstract
Recently, Halpern and Leung suggested representing uncertainty by a set of weighted 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 set of weighted 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.
Cite
Text
Halpern. "Weighted Regret-Based Likelihood: A New Approach to Describing Uncertainty." Journal of Artificial Intelligence Research, 2015. doi:10.1613/JAIR.4859Markdown
[Halpern. "Weighted Regret-Based Likelihood: A New Approach to Describing Uncertainty." Journal of Artificial Intelligence Research, 2015.](https://mlanthology.org/jair/2015/halpern2015jair-weighted/) doi:10.1613/JAIR.4859BibTeX
@article{halpern2015jair-weighted,
title = {{Weighted Regret-Based Likelihood: A New Approach to Describing Uncertainty}},
author = {Halpern, Joseph Y.},
journal = {Journal of Artificial Intelligence Research},
year = {2015},
pages = {471-492},
doi = {10.1613/JAIR.4859},
volume = {54},
url = {https://mlanthology.org/jair/2015/halpern2015jair-weighted/}
}