Research Interests: Mathematics, Computer Science, Economic Theory, Inference, Probabilistic Logic, and 10 moreConditional probability, Expected Utility, Conditional Expectation, EXPECTED UTILITY HYPOTHESIS, Graphical Model, Graphical Representation, Probabilistic Inference, Representation Politics, Conditional Independence, and arXiv
We introduce the first non-parametric approach to the problem of inferring a model of a consumer’s preferences on the basis of available evidence. The evidence can take a variety of different forms, including survey and transaction data.... more
We introduce the first non-parametric approach to the problem of inferring a model of a consumer’s preferences on the basis of available evidence. The evidence can take a variety of different forms, including survey and transaction data. We use an axiomatic approach to infer a unique utility model that complies with the given data and is maximally non-committal with regard to missing information. Moreover, our method does not rely on a priori assumptions about the functional form of the utilities. We develop a consumer model, and demonstrate the applicability of our method to a variety of preference estimation problems using synthetic data. In our examples we infer different consumer utilities over bundles of goods or product characteristics. We compare our method with Conjoint Analysis, and show that it can compete favorably even in areas which are ideally suitable for the latter. Furthermore, we show that our approach can be useful in important marketing domains where Conjoint Ana...
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Et si la science physique la plus récente sortait de son domaine d’application traditionnel ? Si la physique quantique, développée par Planck, Bohr et Einstein, se confrontaient aux sciences dites humaines ? Tel est le projet de Michel... more
Et si la science physique la plus récente sortait de son domaine d’application traditionnel ? Si la physique quantique, développée par Planck, Bohr et Einstein, se confrontaient aux sciences dites humaines ? Tel est le projet de Michel Bitbol et de son équipe dans cet ouvrage hors norme, faisant fi des frontières traditionnelles. Quelles affinités peuvent partager ces deux types de science ? Quels rôles y jouent l’homme ? Parmi les thèmes choisis pour cette confrontation citons : la prise de décision, la théorie du comportement, la recherche de l’utilité
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We consider a set of empirical assumptions formulated by Gamson (1961), namely, Gamson’s Laws, which remain at the heart of government formation forecast in parliamentary systems. While the critical resource postulated in Gamson’s... more
We consider a set of empirical assumptions formulated by Gamson (1961), namely, Gamson’s Laws, which remain at the heart of government formation forecast in parliamentary systems. While the critical resource postulated in Gamson’s approach is the proportion of votes received by each party, other versions of Gamson’s Laws can be defined by a different choice of critical resource. We model coalition formation as a cooperative game, and provide axiomatic foundations for a version of Gamson’s Laws in which the critical resource is identified with strategic influence, as measured by the Shapley value. We compare the empirical accuracy of the resulting Gamson–Shapley theory against the original Gamson’s Laws in a panel of 33 parliamentary elections, and find that it leads to significantly more accurate predictions of both coalition structure and power distribution. Finally, we propose an extension of the Gamson–Shapley approach which also incorporates information about policy distance amo...
We extend the setup of Arrow's General Possibility Theorem by introducing as additional policy alternatives the possibility to delegate certain decisions to an external institution or random device. We show that in this extended... more
We extend the setup of Arrow's General Possibility Theorem by introducing as additional policy alternatives the possibility to delegate certain decisions to an external institution or random device. We show that in this extended setting there exists a Social Welfare Functional with universal domain which satisfies the Pareto principle and is independent of irrelevant alternatives, while also being non-dictatorial.
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We discuss the possible nature and role of non‐physical entanglement, and the classical vs. non‐classical interface, in models of human decision‐making. We also introduce an experimental setting designed after the double‐slit experiment... more
We discuss the possible nature and role of non‐physical entanglement, and the classical vs. non‐classical interface, in models of human decision‐making. We also introduce an experimental setting designed after the double‐slit experiment in physics, and discuss how it could be used to discriminate between classical and non‐classical interference effects in human decisions.
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The framework of algorithmic knowledge assumes that agents use deterministic knowledge algorithms to compute the facts they explicitly know. We extend the framework to allow for randomized knowledge algorithms. We then characterize the... more
The framework of algorithmic knowledge assumes that agents use deterministic knowledge algorithms to compute the facts they explicitly know. We extend the framework to allow for randomized knowledge algorithms. We then characterize the information provided by a randomized knowledge algorithm when its answers have some probability of being incorrect. We formalize this information in terms of evidence; a randomized knowledge algorithm returning ``Yes'' to a query about a fact \phi provides evidence for \phi being true. Finally, we discuss the extent to which this evidence can be used as a basis for decisions.
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Research Interests: Mathematics, Computer Science, Economic Theory, Inference, Probabilistic Logic, and 10 moreConditional probability, Expected Utility, Conditional Expectation, EXPECTED UTILITY HYPOTHESIS, Graphical Model, Graphical Representation, Probabilistic Inference, Representation Politics, Conditional Independence, and arXiv
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The states of the qubit, the basic unit of quantum information, are 2 × 2 positive semi-definite Hermitian matrices with trace 1. We contribute to the program to axiomatize quantum mechanics by characterizing these states in terms of an... more
The states of the qubit, the basic unit of quantum information, are 2 × 2 positive semi-definite Hermitian matrices with trace 1. We contribute to the program to axiomatize quantum mechanics by characterizing these states in terms of an entropic uncertainty principle formulated on an eight-point phase space. We do this by employing Rényi entropy (a generalization of Shannon entropy) suitably defined for the signed phase-space probability distributions that arise in representing quantum states.
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© Copyright: 2005 Jede Form der Weitergabe und Vervielfältigung bedarf der Genehmigung des HerausgebersDecision theory in the presence of risk and uncertainty
Motivated by several classic decision-theoretic paradoxes, and by analogies with the paradoxes which in physics motivated the development of quantum mechanics, we introduce a projective generalization of expected utility along the lines... more
Motivated by several classic decision-theoretic paradoxes, and by analogies with the paradoxes which in physics motivated the development of quantum mechanics, we introduce a projective generalization of expected utility along the lines of the quantum-mechanical generalization of probability theory. The resulting decision theory accommodates the dominant paradoxes, while retaining significant simplicity and tractability. In particular, every finite game within this larger class of preferences still has an equilibrium.
Is the world quantum? An active research line in quantum foundations is devoted to exploring what constraints can rule out the post-quantum theories that are consistent with experimentally observed results. We explore this question in the... more
Is the world quantum? An active research line in quantum foundations is devoted to exploring what constraints can rule out the post-quantum theories that are consistent with experimentally observed results. We explore this question in the context of epistemics, and ask whether agreement between observers can serve as a physical principle that must hold for any theory of the world. Aumann’s seminal Agreement Theorem states that two (classical) agents cannot agree to disagree. We propose an extension of this theorem to no-signaling settings. In particular, we establish an Agreement Theorem for quantum agents, while we construct examples of (post-quantum) no-signaling boxes where agents can agree to disagree. The PR box is an extremal instance of this phenomenon. These results make it plausible that agreement between observers might be a physical principle, while they also establish links between the fields of epistemics and quantum information that seem worthy of further exploration.
Is the world quantum? An active research line in quantum foundations is devoted to exploring what constraints can rule out the post-quantum theories that are consistent with experimentally observed results. We explore this question in the... more
Is the world quantum? An active research line in quantum foundations is devoted to exploring what constraints can rule out the post-quantum theories that are consistent with experimentally observed results. We explore this question in the context of epistemics, and ask whether agreement between observers can serve as a physical principle that must hold for any theory of the world. Aumann’s seminal Agreement Theorem states that two (classical) agents cannot agree to disagree. We propose an extension of this theorem to no-signaling settings. In particular, we establish an Agreement Theorem for quantum agents, while we construct examples of (post-quantum) no-signaling boxes where agents can agree to disagree. The PR box is an extremal instance of this phenomenon. These results make it plausible that agreement between observers might be a physical principle, while they also establish links between the fields of epistemics and quantum information that seem worthy of further exploration.
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Is the world quantum? An active research line in quantum foundations is devoted to exploring what constraints can rule out the postquantum theories that are consistent with experimentally observed results. We explore this question in the... more
Is the world quantum? An active research line in quantum foundations is devoted to exploring what constraints can rule out the postquantum theories that are consistent with experimentally observed results. We explore this question in the context of epistemics, and ask whether agreement between observers can serve as a physical principle that must hold for any theory of the world. Aumann’s seminal Agreement Theorem states that two observers (of classical systems) cannot agree to disagree. We propose an extension of this theorem to no-signaling settings. In particular, we establish an Agreement Theorem for observers of quantum systems, while we construct examples of (postquantum) no-signaling boxes where observers can agree to disagree. The PR box is an extremal instance of this phenomenon. These results make it plausible that agreement between observers might be a physical principle, while they also establish links between the fields of epistemics and quantum information that seem wo...
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We introduce Game networks (G nets), a novel representation for multi-agent decision problems. Compared to other game-theoretic representations, such as strategic or extensive forms, G nets are more structured and more compact; more... more
We introduce Game networks (G nets), a novel representation for multi-agent decision problems. Compared to other game-theoretic representations, such as strategic or extensive forms, G nets are more structured and more compact; more fundamentally, G nets constitute a computationally advantageous framework for strategic inference, as both probability and utility independencies are captured in the structure of the network and can be exploited in order to simplify the inference process. An important aspect of multiagent reasoning is the identification of some or all of the strategic equilibria in a game; we present original convergence methods for strategic equilibrium which can take advantage of strategic separabilities in the G net structure in order to simplify the computations. Specifically, we describe a method which identifies a unique equilibrium as a function of the game payoffs, and one which identifies all equilibria.
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The context in which a mechanism is defined and meant to operate plays an important role, and in more than one way. We advocate a contextual approach to mechanism design, that extends to both non-classical aspects of decision and of the... more
The context in which a mechanism is defined and meant to operate plays an important role, and in more than one way. We advocate a contextual approach to mechanism design, that extends to both non-classical aspects of decision and of the physical and information-theoretic environment in which the mechanism operates. We demonstrate the approach in two applications: one to auctions with ambiguity, and one to decentralized decision-making.
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Purpose This paper aims to provide a theoretical explanation of why credit rating agencies typically disclose credit risk of issuers in classes rather than publishing the qualitative ranking those classes are based upon. Thus, its goal is... more
Purpose This paper aims to provide a theoretical explanation of why credit rating agencies typically disclose credit risk of issuers in classes rather than publishing the qualitative ranking those classes are based upon. Thus, its goal is to develop a better understanding of what determines the number and size of rating classes. Design/methodology/approach Investors expect ratings to be sufficiently accurate in estimating credit risk. In a theoretical model framework, it is therefore assumed that credit rating agencies, which observe credit risk with limited accuracy, are careful in not misclassifying an issuer with a lower credit quality to a higher rating class. This situation is analyzed as a Bayesian inference setting for the credit rating agencies. Findings A disclosure in intervals, typically used by credit rating agencies results from their objective of keeping misclassification errors sufficiently low in conjunction with the limited accuracy with which they observe credit ri...
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We study team decision problems where communication is not possible, but coordination among team members can be realized via signals in a shared environment. We consider a variety of decision problems that differ in what team members know... more
We study team decision problems where communication is not possible, but coordination among team members can be realized via signals in a shared environment. We consider a variety of decision problems that differ in what team members know about one another's actions and knowledge. For each type of decision problem, we investigate how different assumptions on the available signals affect team performance. Specifically, we consider the cases of perfectly correlated, i.i.d., and exchangeable classical signals, as well as the case of quantum signals. We find that, whereas in perfect-recall trees (Kuhn 1950 Proc. Natl Acad. Sci. USA 36, 570–576; Kuhn 1953 In Contributions to the theory of games , vol. II (eds H Kuhn, A Tucker), pp. 193–216) no type of signal improves performance, in imperfect-recall trees quantum signals may bring an improvement. Isbell (Isbell 1957 In Contributions to the theory of games , vol. III (eds M Drescher, A Tucker, P Wolfe), pp. 79–96) proved that, in non-...
Research Interests: Mathematics, Computer Science, Physics, Medicine, Multidisciplinary, and 3 moreQuantum, Recall, and Imperfect
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We extend the setup of Arrow's General Possibility Theorem by introducing as additional policy alternatives the delegation of certain decisions to an external institution or random device. We show that in this extended setting there... more
We extend the setup of Arrow's General Possibility Theorem by introducing as additional policy alternatives the delegation of certain decisions to an external institution or random device. We show that in this extended setting there exists a social welfare function with universal domain which satisfies appropriate extensions of the Weak Pareto Principle and Independence of Irrelevant Alternatives, while also being non-dictatorial.
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The subject of multi-agent systems is relevant to both economic,theory and artificial intelligence. Yet, very little work so far has tried to bridge the gap be-
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Correlated equilibria are sometimes more efficient than the Nash equilibria of a game without signals. We investigate whether the availability of quantum signals in the context of a classical strategic game may allow the players to... more
Correlated equilibria are sometimes more efficient than the Nash equilibria of a game without signals. We investigate whether the availability of quantum signals in the context of a classical strategic game may allow the players to achieve even greater efficiency than in any correlated equilibrium with classical signals, and find the answer to be positive.
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Research Interests: Psychology, Cognitive Science, Mathematics, Applied Mathematics, Probability Theory, and 15 moreComputer Science, Physics, Quantum Physics, Mathematical Economics, Mathematical Psychology, Quantum Mechanics, Decision Theory, Generalization, Quantum, Expected Utility, Simplicity, EXPECTED UTILITY HYPOTHESIS, Projective test, arXiv, and projective
This short note aims to show that Rabin's anomaly can be avoided while re- maining within the bounds of the final-wealth, expected utility approach, if the hypothesis of risk aversion over monetary amounts is replaced by the... more
This short note aims to show that Rabin's anomaly can be avoided while re- maining within the bounds of the final-wealth, expected utility approach, if the hypothesis of risk aversion over monetary amounts is replaced by the assumption of risk aversion over subjective consequences. We argue that the assumption of monetary risk aversion may return unrealistic predictions in specific decision con- texts, or in the presence of large stakes. Rabin's anomaly (Rabin 2000, Rabin and Thaler 2001) pointed out a possible de- ficiency of the approach based on the expected utility of final wealth. Safra and Segal (2008a, 2008b) showed that the problem is not directly related to expected utility, as most other non-expected utility theories are prone to the same anomaly. The alterna- tive route of abandoning final wealth as a basis for the theory (Cox and Sadiraj 2006, Rubinstein 2006) is generally regarded as unappealing, as it seems to imply that only relative theories of preferences ...
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This paper introduces a new class of mechanisms based on negotiation between market participants. This model allows us to circumvent Myerson and Satterthwaite's impossibility result and present a bilateral market mechanism that is... more
This paper introduces a new class of mechanisms based on negotiation between market participants. This model allows us to circumvent Myerson and Satterthwaite's impossibility result and present a bilateral market mechanism that is efficient, individually rational, incentive compatible, and budget balanced in the single-unit heterogeneous setting. The underlying scheme makes this combination of desirable qualities possible by reporting a price