Quantum-like model of subjective expected utility

We present a very general quantum-like model of lottery selection based on representation of beliefs of an agent by pure quantum states. Subjective probabilities are mathematically realized in the framework of quantum probability (QP). Utility functions are borrowed from the classical decision theory. But in the model they are represented not only by their values. Heuristically one can say that each value ui=u(xi) is surrounded by a cloud of information related to the event (A,xi). An agent processes this information by using the rules of quantum information and QP. This process is very complex; it combines counterfactual reasoning for comparison between preferences for different outcomes of lotteries which are in general complementary. These comparisons induce interference type effects (constructive or destructive). The decision process is mathematically represented by the comparison operator and the outcome of this process is determined by the sign of the value of corresponding quadratic form on the belief state. This operational process can be decomposed into a few subprocesses. Each of them can be formally treated as a comparison of subjective expected utilities and interference factors (the latter express, in particular, risks related to lottery selection). The main aim of this paper is to analyze the mathematical structure of these processes in the most general situation: representation of lotteries by noncommuting operators

Piecewise smooth systems near a co-dimension 2 discontinuity manifold: can one say what should happen?

We consider a piecewise smooth system in the neighborhood of a co-dimension 2 discontinuity manifold $\Sigma$. Within the class of Filippov solutions, if $\Sigma$ is attractive, one should expect solution trajectories to slide on $\Sigma$. It is well known, however, that the classical Filippov convexification methodology is ambiguous on $\Sigma$. The situation is further complicated by the possibility that, regardless of how sliding on $\Sigma$ is taking place, during sliding motion a trajectory encounters so-called generic first order exit points, where $\Sigma$ ceases to be attractive. In this work, we attempt to understand what behavior one should expect of a solution trajectory near $\Sigma$ when $\Sigma$ is attractive, what to expect when $\Sigma$ ceases to be attractive (at least, at generic exit points), and finally we also contrast and compare the behavior of some regularizations proposed in the literature. Through analysis and experiments we will confirm some known facts, and provide some important insight: (i) when $\Sigma$ is attractive, a solution trajectory indeed does remain near $\Sigma$, viz. sliding on $\Sigma$ is an appropriate idealization (of course, in general, one cannot predict which sliding vector field should be selected); (ii) when $\Sigma$ loses attractivity (at first order exit conditions), a typical solution trajectory leaves a neighborhood of $\Sigma$; (iii) there is no obvious way to regularize the system so that the regularized trajectory will remain near $\Sigma$ as long as $\Sigma$ is attractive, and so that it will be leaving (a neighborhood of) $\Sigma$ when $\Sigma$ looses attractivity. We reach the above conclusions by considering exclusively the given piecewise smooth system, without superimposing any assumption on what kind of dynamics near $\Sigma$ (or sliding motion on $\Sigma$) should have been taking place.Comment: 19 figure

Probabilistic sophistication and reverse Bayesianism

This paper extends our earlier work on reverse Bayesianism by relaxing the assumption that decision makers abide by expected utility theory, assuming instead weaker axioms that merely imply that they are probabilistically sophisticated. We show that our main results, namely, (modified) representation theorems and corresponding rules for updating beliefs over expanding state spaces and null events that constitute “reverse Bayesianism,” remain valid

Quantum decision making by social agents

The influence of additional information on the decision making of agents, who are interacting members of a society, is analyzed within the mathematical framework based on the use of quantum probabilities. The introduction of social interactions, which influence the decisions of individual agents, leads to a generalization of the quantum decision theory developed earlier by the authors for separate individuals. The generalized approach is free of the standard paradoxes of classical decision theory. This approach also explains the error-attenuation effects observed for the paradoxes occurring when decision makers, who are members of a society, consult with each other, increasing in this way the available mutual information. A precise correspondence between quantum decision theory and classical utility theory is formulated via the introduction of an intermediate probabilistic version of utility theory of a novel form, which obeys the requirement that zero-utility prospects should have zero probability weights.Comment: This paper has been withdrawn by the authors because a much extended and improved version has been submitted as arXiv:1510.02686 under the new title "Role of information in decision making of social agents

How brains make decisions

This chapter, dedicated to the memory of Mino Freund, summarizes the Quantum Decision Theory (QDT) that we have developed in a series of publications since 2008. We formulate a general mathematical scheme of how decisions are taken, using the point of view of psychological and cognitive sciences, without touching physiological aspects. The basic principles of how intelligence acts are discussed. The human brain processes involved in decisions are argued to be principally different from straightforward computer operations. The difference lies in the conscious-subconscious duality of the decision making process and the role of emotions that compete with utility optimization. The most general approach for characterizing the process of decision making, taking into account the conscious-subconscious duality, uses the framework of functional analysis in Hilbert spaces, similarly to that used in the quantum theory of measurements. This does not imply that the brain is a quantum system, but just allows for the simplest and most general extension of classical decision theory. The resulting theory of quantum decision making, based on the rules of quantum measurements, solves all paradoxes of classical decision making, allowing for quantitative predictions that are in excellent agreement with experiments. Finally, we provide a novel application by comparing the predictions of QDT with experiments on the prisoner dilemma game. The developed theory can serve as a guide for creating artificial intelligence acting by quantum rules.Comment: Latex file, 20 pages, 3 figure

Paradoxes and Mechanisms for Choice under Risk

Experiments on choice under risk typically involve multiple decisions by individual subjects. The choice of mechanism for selecting decision(s) for payoff is an essential design feature unless subjects isolate each one of the multiple decisions. We report treatments with different payoff mechanisms but the same decision tasks. The data show large differences across mechanisms in subjects’ revealed risk preferences, a clear violation of isolation. We illustrate the importance of these mechanism effects by identifying their implications for classical tests of theories of decision under risk. We discuss theoretical properties of commonly used mechanisms, and new mechanisms introduced herein, in order to clarify which mechanisms are theoretically incentive compatible for which theories. We identify behavioral properties of some mechanisms that can introduce bias in elicited risk preferences – from cross-task contamination – even when the mechanism used is theoretically incentive compatible. We explain that selection of a payoff mechanism is an important component of experimental design in many topic areas including social preferences, public goods, bargaining, and choice under uncertainty and ambiguity as well as experiments on decisions under risk

Investigation of livestock for presence of Trypanosoma brucei gambiense in Tafa Local Government Area of Niger State, Nigeria

The study investigated the presence of Trypanosoma brucei gambiense in livestock to ascertain their reservoir role and also screened for other pathogenic trypanosomes of animals in Tafa Local Government Area of Niger state, Nigeria. A total of 460 livestock comprising (cattle, sheep, goats, and dogs) selected at random were bled, examined using the buffy coat and Giemsa stained thin film and packed cell volume estimated. Questionnaire was filled for each animal on demography, awareness and management practices. An overall prevalence of 2.17% with Trypanosoma brucei, T. congolense, T. vivax and a mixed infection of T. brucei and T. congolense observed microscopically awaiting characterization. Interviews revealed high awareness (82.8%) of tsetse and trypanosomiasis described as bush disease and abortion in four cows. The PCV values were within the normal range, however, a significant decrease (P<0.05) was observed in sheep aged 7months to 4years in two communities. Therefore, the study indicated the presence of T. brucei and other trypanosomes suggesting that animal trypanosomiasis is still a problem to animal health and wellbeing in the study area. The study recommends effective integrated chemotherapy and vector control including livestock rearing under intensive management system to boost livestock production and productivity