Imprecise probabilities and scenarios

This paper argues that imprecise probability can be used to describe uncertainty about scenarios. Scenarios are conceptualized as written descriptions of potential future worlds that are based on assessments of economic, political, social, technological, and environmental trends [This description of scenarios follows that provided by Peter Schwartz. P. Schwartz [9], The Art of the Long View, Doubleday, New York, 1991 [9]. Because written, qualitative scenarios are beginning to find application in important policy contexts, such as with respect to global climate change [N. Nakicenovic, R. Swart [5], Emission Scenarios: Special Report of the Intergovernmental Panel on Climate Change, Cambridge University Press, Cambridge, England, 2000 [5], where uncertainty estimates are of some importance to policy makers, there is a growing need to address the question of whether uncertainty estimates can be assessed over qualitative scenarios. Section 1 of this short paper contrasts imprecise probability with standard classical (or precise) probability. Section 2 provides a technique for assessing the amount of information (referred to as 'determinateness') expressed by imprecise (i.e. lower and upper) probabilities over a set of scenarios. Section 3 discusses how to assess to what degree the scenarios may represent the whole space of potential futures. Section 4 brings all the pieces together to show how scenario developers can use measures of determinateness and the coverage of a set of scenarios over all potential possible futures to improve the development and use of scenarios.