Expected utility within a generalized concept of probability — a comprehensive framework for decision making under ambiguity

It has often been complained that the standard framework of decision theory is insufficient. In most applications, neither the maximin paradigm (relving on complete ignorance on the states of natures) nor the classical Bayesian paradigm (assuming perfect probabilistic information on the states of nature) reflect the situation under consideration adequately. Typically one possesses some, but incomplete, knowledge on the stochastic behaviour of the states of nature. In this paper first steps towards a comprehensive framework for decision making under such complex uncertainty will be provided. Common expected utility theory will be extended to interval probability, a generalized probabilistic setting which has the power to express incomplete stochastic knowledge and to take the extent of ambiguity (non-stochastic uncertainty) into account. Since two-monotone and totally monotone capacities are special cases of general interval probatility, wher Choquet integral and interval-valued expectation correspond to one another, the results also show, as a welcome by-product, how to deal efficiently with Choquet Expected Utility and how to perform a neat decision analysis in the case of belief functions. Received: March 2000; revised version: July 2001