Decision Making in Phantom Spaces

Yehuda Izhakian and Zur Izhakian

Abstract

This paper introduces a new model of decision-making under uncertainty that generalizes the von Neumann-Morgenstern theory by adding additional tiers of uncertainty. In this model, beliefs are subjective variations of objective probabilities, capturing risk as well as ambiguity. The degree of uncertainty, determined by the beliefs of a decision maker, is distinguished from the attitude toward uncertainty that is drawn from her preferences. In our model, ambiguous probabilities of events and their vague consequences are naturally formulated in the phantom space using its unique probability measure. Decision making under ambiguity is a special case of this model in which probabilities are ambiguous, but outcomes of events are knowable.