Machina Paradoxes Research Articles

Expected Utility with Relative Loss Reduction: A Unifying Decision Model for Resolving Four Well-Known Paradoxes

Some well-known paradoxes in decision making (e.g., the Allais paradox, the St. Peterburg paradox, the Ellsberg paradox, and the Machina paradox) reveal that choices conventional expected utility theory predicts could be inconsistent with empirical observations. So, solutions to these paradoxes can help us better understand humans decision making accurately. This is also highly related to the prediction power of a decision-making model in real-world applications. Thus, various models have been proposed to address these paradoxes. However, most of them can only solve parts of the paradoxes, and for doing so some of them have to rely on the parameter tuning without proper justifications for such bounds of parameters. To this end, this paper proposes a new descriptive decision-making model, expected utility with relative loss reduction, which can exhibit the same qualitative behaviours as those observed in experiments of these paradoxes without any additional parameter setting. In particular, we introduce the concept of relative loss reduction to reflect people's tendency to prefer ensuring a sufficient minimum loss to just a maximum expected utility in decision-making under risk or ambiguity.

A proposal to extend expected utility in a quantum probabilistic framework

Expected utility theory (EUT) is widely used in economic theory. However, its subjective probability formulation, first elaborated by Savage, is linked to Ellsberg-like paradoxes and ambiguity aversion. This has led various scholars to work out non-Bayesian extensions of EUT which cope with its paradoxes and incorporate attitudes toward ambiguity. A variant of the Ellsberg paradox, recently proposed by Mark Machina and confirmed experimentally, challenges existing non-Bayesian models of decision-making under uncertainty. Relying on a decade of research which has successfully applied the formalism of quantum theory to model cognitive entities and fallacies of human reasoning, we put forward a non-Bayesian extension of EUT in which subjective probabilities are represented by quantum probabilities, while the preference relation between acts depends on the state of the situation that is the object of the decision. We show that the benefits of using the quantum theoretical framework enables the modeling of the Ellsberg and Machina paradoxes, as the representation of ambiguity and behavioral attitudes toward it. The theoretical framework presented here is a first step toward the development of a `state-dependent non-Bayesian extension of EUT' and it has potential applications in economic modeling.

An Ambiguity Aversion Model for Decision Making under Ambiguity

In real life, decisions are often made under ambiguity, where it is difficult to estimate accurately the probability of each single possible consequence of a choice. However, this problem has not been solved well in existing work for the following two reasons. (i) Some of them cannot cover the Ellsberg paradox and the Machina Paradox. Thus, the choices that they predict could be inconsistent with empirical observations. (ii) Some of them rely on parameter tuning without offering explanations for the reasonability of setting such bounds of parameters. Thus, the prediction of such a model in new decision making problems is doubtful. To the end, this paper proposes a new decision making model based on D-S theory and the emotion of ambiguity aversion. Some insightful properties of our model and the validating on two famous paradoxes show that our model indeed is a better alternative for decision making under ambiguity.

A quantum-like model of selection behavior

In this paper, we introduce a new model of selection behavior under risk that describes an essential cognitive process for comparing values of objects and making a selection decision. This model is constructed by the quantum-like approach that employs the state representation specific to quantum theory, which has the mathematical framework beyond the classical probability theory. We show that our quantum approach can clearly explain the famous examples of anomalies for the expected utility theory, the Ellsberg paradox, the Machina paradox and the disparity between WTA and WTP. Further, we point out that our model mathematically specifies the characteristics of the probability weighting function and the value function, which are basic concepts in the prospect theory.

Editorial: Quantum Structures in Cognitive and Social Science.

Editorial: Quantum Structures in Cognitive and Social Science.

From ambiguity aversion to a generalized expected utility. Modeling preferences in a quantum probabilistic framework

Ambiguity and ambiguity aversion have been widely studied in decision theory and economics both at a theoretical and an experimental level. After Ellsberg’s seminal studies challenging subjective expected utility theory (SEUT), several (mainly normative) approaches have been put forward to reproduce ambiguity aversion and Ellsberg-type preferences. However, Machina and other authors have pointed out some fundamental difficulties of these generalizations of SEUT to cope with some variants of Ellsberg’s thought experiments, which has recently been experimentally confirmed. Starting from our quantum modeling approach to human cognition, we develop here a general probabilistic framework to model human decisions under uncertainty. We show that our quantum theoretical model faithfully represents different sets of data collected on both the Ellsberg and the Machina paradox situations, and is flexible enough to describe different subjective attitudes with respect to ambiguity. Our approach opens the way toward a quantum-based generalization of expected utility theory (QEUT), where subjective probabilities depend on the state of the conceptual entity at play and its interaction with the decision-maker, while preferences between acts are determined by the maximization of this ‘state-dependent expected utility’.

Identifying Quantum Structures in the Ellsberg Paradox

Empirical evidence has confirmed that quantum effects occur frequently also outside the microscopic domain, while quantum structures satisfactorily model various situations in several areas of science, including biological, cognitive and social processes. In this paper, we elaborate a quantum mechanical model which faithfully describes the Ellsberg paradox in economics, showing that the mathematical formalism of quantum mechanics is capable to represent the ambiguity present in this kind of situations, because of the presence of contextuality. Then, we analyze the data collected in a concrete experiment we performed on the Ellsberg paradox and work out a complete representation of them in complex Hilbert space. We prove that the presence of quantum structure is genuine, that is, interference and superposition in a complex Hilbert space are really necessary to describe the conceptual situation presented by Ellsberg. Moreover, our approach sheds light on ‘ambiguity laden’ decision processes in economics and decision theory, and allows to deal with different Ellsberg-type generalizations, e.g., the Machina paradox.

Ambiguity Models and the Machina Paradoxes

Machina (2009) introduced two examples that falsify Choquet expected utility, presently one of the most popular models of ambiguity. This article shows that Machina's examples falsify not only the model mentioned, but also four other popular models for ambiguity of the literature, namely maxmin expected utility, variational preferences, α-maxmin, and the smooth model of ambiguity aversion. Thus, Machina's examples pose a challenge to most of the present field of ambiguity. Finally, the paper discusses how an alternative representation of ambiguity-averse preferences works to accommodate the Machina paradoxes and what drives the results. (JEL D81)