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...

This paper extends decision making under risk and uncertainty to group theory via representations of invariant behavioural space for prospect theory. First, we predict that canonical specifications for value functions, probability weighting functions, and stochastic choice maps are homomorphic....

The goal programming (GP) is a well-known approach applied to multi-criteria decision making (M-DM). It has been used in many domains and the literature offers diverse extensions of this procedure. On the other hand, so far, some evident analogies between M-DM under certainty and scenario-based...

Quantum decision theory (QDT) is a recently developed theory of decision making based on the mathematics of Hilbert spaces, a framework known in physics for its application to quantum mechanics. This framework formalizes the concept of uncertainty and other effects that are particularly manifest...

In this paper, we propose an interpretation of the Hilbert space method used in quantum theory in the context of decision making under uncertainty. For a clear comparison we will stay as close as possible to the framework of SEU suggested by Savage (1954). We will use the Ellsberg (1961) paradox...

This paper contributes to the literature on decision making under risk and uncertainty by attaching a weighted probability space to outcome space. Thereby inducing a commutative map of behavior on prospect theory's function space. We endow that space with a psychological metric space, and a time...

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...