Related papers: Projective Expected Utility
Classical decision theory models behaviour in terms of utility maximisation where utilities represent rational preference relations over outcomes. However, empirical evidence and theoretical considerations suggest that we need to go beyond…
The Ellsberg and Machina paradoxes reveal that expected utility theory is problematical when real subjects take decisions under uncertainty. Suitable generalizations of expected utility exist which attempt to solve the Ellsberg paradox, but…
Influence diagrams provide a compact graphical representation of decision problems. Several algorithms for the quick computation of their associated expected utilities are available in the literature. However, often they rely on a full…
We investigate how the choice of decision makers can be varied under the presence of risk and uncertainty. Our analysis is based on the approach we have previously applied to individual decision makers, which we now generalize to the case…
The predictions that quantum theory makes about the outcomes of measurements are generally probabilistic. This has raised the question whether quantum theory can be considered complete, or whether there could exist alternative theories that…
The study of complex systems through the lens of category theory consistently proves to be a powerful approach. We propose that cognition deserves the same category-theoretic treatment. We show that by considering a highly-compact cognitive…
We derive an analogue of the quantum total probability rule by constructing a probability theory based on paraconsistent logic. Bayesian probability theory is constructed upon classical logic and a desiderata, that is, a set of desired…
Cooperative game theory studies how to allocate the joint value generated by a set of players. These games are typically analyzed using the characteristic function form with transferable utility, which represents the value attainable by…
Generalized conditional expectations, optional projections and predictable projections of stochastic processes play important roles in the general theory of stochastic processes, semimartingale theory and stochastic calculus. They share…
It is standard in computational social choice to analyse welfare considerations under the assumptions of normalized utilities. In this note, we summarize some common reasons for this approach. We then mention another justification which is…
Quantum mechanics emerged as the result of a successful resolution of stringent empirical and profound conceptual conflicts within the development of atomic physics at the beginning of the last century. At first glance, it seems to be…
We study preferences estimated from finite choice experiments and provide sufficient conditions for convergence to a unique underlying "true" preference. Our conditions are weak, and therefore valid in a wide range of economic environments.…
Quantum theory shares with classical probability theory many important properties. I show that this common core regards at least the following six areas, and I provide details on each of these: the logic of propositions, symmetry,…
We give a strict mathematical description for a refinement of the Marinatto-Weber quantum game scheme. The model allows the players to choose projector operators that determine the state on which they perform their local operators. The game…
Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the…
The concept of probability was prominent in the original foundations of quantum mechanics, and continues to be so today. Indeed, the controversies regarding objective and subjective interpretations of probability have again become active. I…
We study group decision making with changing preferences as a Markov Decision Process. We are motivated by the increasing prevalence of automated decision-making systems when making choices for groups of people over time. Our main…
We develop a new interpretation of quantum theory by combining insights from extended Wigner's friend scenarios and quantum causal modelling. In this interpretation, which synthesizes ideas from relational quantum mechanics and consistent…
The application of the methods of quantum mechanics to game theory provides us with the ability to achieve results not otherwise possible. Both linear superpositions of actions and entanglement between the players' moves can be exploited.…
Since its discovery, quantum theory has proven to be one of the most precise theories ever made. Measurement processes, however, do not seem to be governed by the unitary law of quantum mechanics, and one can ask if the theory is complete.…