Weighted regret-based likelihood: a new approach to describing
  uncertainty
  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.
