A seminal theorem due to Blackwell (1951) shows that every Bayesian decision-maker prefers an informative signal Y to another signal X if and only if Y is statistically sufficient for X. Sufficiency is an unduly strong requirement in most economic problems because it does not incorporate any...

It is well-known that various criteria for comparing aversion to real-outcome risks are equivalent. Some of this theory has been extended to Euclidean-outcome risks. We extend it further by:(a) filling the conceptual gaps, most notably by providing a criterion using our generalized Arrow-Pratt...

We can overcome uncertainty with uncertainty. Using randomness in our choices and in what we control, and hence in the decision making process, could potentially offset the uncertainty inherent in the environment and yield better outcomes. The example we develop in greater detail is the...

We can overcome uncertainty with uncertainty. Using randomness in our choices and in what we control and hence in the decision making process, could potentially offset the uncertainty inherent in the environment and yield better outcomes. This methodology is suitable for the social sciences...

Ordering alternatives by their degree of ambiguity is a crucial element in decision-making processes in general and in asset pricing in particular. Thus far the literature has not provided an applicable measure of ambiguity allowing for such ordering. The current paper addresses this need by...

Assuming that probabilities (capacities) of events are random, this paper introduces a novel model of decision making under ambiguity, called Shadow probability theory, a generalization of the Choquet expected utility. In this model, probabilities of observable events in a subordinated...

This paper analyzes the root cause of Ellsberg-type choices. This class of problems shares the feature that at the time of the decision, t=m, the decision maker (DM) possesses partial information about the events/propositions of interest: DM knows the objective probabilities of some sub-class...

Probabilistic preference models predict that a subject makes different choices with different probabilities in repeatedly experiments with the same stimuli. This paper explains why. First, we prove that a gamble is a statistical ensemble or sample function of a random field with canonical...

We present a general classification of the conditions under which cognitive science, concerned e.g. with decision making, requires the use of quantum theoretical notions. The analysis is done in the frame of the mathematical approach based on the theory of quantum measurements. We stress that...

Many decision problems in various fields of application can be characterized as diagnostic problems trying to assess the true state (of the world) of given cases. The investigation of assessment criteria improves the initial information according to observed signal outcomes, which are related to...