Decision making in phantom spaces

This paper introduces a new model of decision making under uncertainty. Aiming to provide a more realistic depiction of decision making, it generalizes the von Neumann–Morgenstern theory by including additional tiers of uncertainty. In this model, beliefs about the probabilities of events are ambiguous and their consequential utilities are vague; both are naturally formulated in the phantom space using phantom numbers. The degree of uncertainty, determined by the decision maker’s beliefs, is distinguished from the attitude toward uncertainty, which is drawn from her preferences. Decision making under ambiguity is a particular case of our model in which probabilities are ambiguous, but resulting utilities of events are knowable.