In search of characterization of the preference for safety under the Choquet model

Victor prefers safety more than Ursula if whenever Ursula prefers some constant to some uncertain act, so does Victor. This paradigm, whose Expected Utility version takes the form of Arrow & Pratt's more risk averse concept, will be studied in the Choquet Uncertainty model, letting u and μ (v and ν) be Ursula's (Victor's) utility and capacity. A necessary and sufficient condition (A) on the pairs (u, μ) and (v, ν) will be presented for dichotomous weak increased uncertainty aversion, the preference by Victor of a constant over a dichotomous act whenever such is the preference of Ursula. This condition, pointwise inequality between a function defined in terms of v (u-1(⋅)) and another defined purely in terms of the capacities, preserves the flavor of the "more pessimism than greediness" characterization of monotone risk aversion by Chateauneuf, Cohen & Meilijson in the Rank-dependent Utility Model and its extension by Grant & Quiggin to the Choquet Utility Model. A sufficient condition (B) in terms of the capacities only, satisfied in particular if ν (⋅) = f (μ (⋅)) for some convex f, will be presented for more simplicity seeking, the preference by Victor over any act for some dichotomous act, that leaves Ursula indifferent. Condition A is thus a characterization of weak increased uncertainty aversion for convex f. An example will be exhibited disproving the more far reaching conjecture under which the dichotomous case implies the general case.Choquet Utility, greediness, pessimism, Rank-dependent Utility, Risk aversion, uncertainty.

Four notions of mean preserving increase in risk, risk attitudes and applications to the Rank-Dependent Expected Utility model

This article presents various notions of risk generated by the intuitively appealing single-crossing operations between distribution functions. These stochastic orders, Bickel & Lehmann dispersion or (its equal-mean version) Quiggin's monotone mean-preserving increase in risk and Jewitt's location-independent risk, have proved to be useful in the study of Pareto allocations, ordering of insurance premia and other applications in the Expected Utility setup. These notions of risk are also relevant tothe Quiggin-Yaari Rank-dependent Expected Utility (RDEU) model of choice among lotteries. Risk aversion is modeled in the vNM Expected Utility model by Rothschild & Stiglitz's Mean Preserving Increase in Risk (MPIR). Realizing that in the broader rank-dependent set-up this order is too weak to classify choice, Quiggin developed the stronger monotone MPIR for this purpose. This paper reviews four notions of mean-preserving increase in risk - MPIR, monotoneMPIR and two versions of location-independent risk (renamed here left and right monotone MPIR) - and shows which choice questions are consistently modeled by each of these four orders.Location-independent risk, monotone increase in risk, rank-dependent expected utility.

More pessimism than greediness: a characterization of monotone risk aversion in the Rank-Dependent Expected Utility model

This paper studies monotone risk aversion, the aversion to monotone, meanpreserving increase in risk (Quiggin [21]), in the Rank Dependent Expected Utility (RDEU) model. This model replaces expected utility by another functional, characterized by twofunctions, a utility function u in conjunction with a probability-perception function f.Monotone mean-preserving increases in risk are closely related to the notion of comparative dispersion introduced by Bickel & Lehmann [3, 4] in Non-parametric Statistics. We present a characterization of the pairs (u; f) of monotone risk averse decision makers, based on an index of greediness Gu of the utility function u and an index of pessimism Pf of the probability perception function f: the decision maker is monotone risk averse if and onlyif Pf exceeds Gu. A novel element is that concavity of u is not necessary. In fact, u must be concave only if Pf = 1.Risk aversion, pessimism, greediness, Rank-dependent Expected Utility

The notion of the will in the old testament: a contribution to the understanding of Talmudic thought

On examining the psychological usages of the Old Testament, and taking into consideration the style of Hebrew thought and expression, it is found that all the elements of man which are generally thought of as associated with, or originating in the Will, such as the principle of life, consciousness, mind, feeling, volition, and character are considered as activities of the Soul. These psychical activities are described by various Hebrew terms which are so often interchangeable that the activities of the Soul appear to be shared by both Spirit and Body, and the place of the Soul may be traced almost to any part of the entity of man* The functioning of the Soul, the exercise of Reason and the Senses and the initiation and prosecution of movement are all considered as the activities of man as a whole, as a single dynamic personality.The unique creativeness and independence of human personality is one of the great conceptions of Jewish religious thought and is in no way diminished, but rather enhanced, by the worship of God and by obedience to God's law.The principle of the freedom of the Will is universally assumed in the Old Testament, Jewish Apocryphal literature and Rabbinic literature as the basis of Jewish ethics and theology. It is possible for man to perfect his own personality by training his character through the proper exercise of thought, emotion and habit. The religious system of the Torah is effective in engendering the best attitudes of thought and feeling, in deterring man from evil, and in inspiring him to do good.In mediaeval Jewish philosophy where Free Will is unequivocally expounded the freedom of the Will is generally associated with the power of acting in accordance with Reason. Philosophical and exegetical problems raised by this notion of the Will in ethics and theology are discussed and explained by, among others, Saadia and Maimonides.In Rabbinic usage, as in the Old Testament, Mind, Soul and Will almost coincide with each other except that in the concept of Daath it is seen that the Will transcends both Mind and Soul and is the basic agent of Personality.Whatever faculties man possesses, both physical and psychical, are faculties of the Will. The attributes of the Will coincide, in Hebrew thought, with the powers of the central force of human personality. The Will may therefore be stated to correspond with the entire Self, Ego or Personality of man.That which is generally identified with the Will is spoken of in the Old Testament and in Rabbinic literature as the choice, mood or energy of the man. The totality of the power of the Will is far more than just a capacity of the individual; it is rather the power of the individual as a whole.The power of the Will is nothing more nor less than the entire power of the man

Population scale data reveals the antidepressant effects of ketamine and other therapeutics approved for non-psychiatric indications.

Current therapeutic approaches to depression fail for millions of patients due to lag in clinical response and non-adherence. Here we provide new support for the antidepressant effect of an anesthetic drug, ketamine, by Inverse-Frequency Analysis of eight million reports from the FDA Adverse Effect Reporting System. The results of the examination of population scale data revealed that patients who received ketamine had significantly lower frequency of reports of depression than patients who took any other combination of drugs for pain. The analysis also revealed that patients who took ketamine had significantly lower frequency of reports of pain and opioid induced side effects, implying ketamine's potential to act as a beneficial adjunct agent in pain management pharmacotherapy. Further, the Inverse-Frequency Analysis methodology provides robust statistical support for the antidepressant action of other currently approved therapeutics including diclofenac and minocycline

Large distance expansion of Mutual Information for disjoint disks in a free scalar theory

We compute the next-to-leading order term in the long-distance expansion of the mutual information for free scalars in three space-time dimensions. The geometry considered is two disjoint disks separated by a distance $r$ between their centers. No evidence for non-analyticity in the R\'enyi parameter $n$ for the continuation $n \rightarrow 1$ in the next-to-leading order term is found.Comment: 15 pages, This version contains few extra references, some technical material has been move to appendices, and other minor modifications to match with the version accepted for publicatio

In search of characterization of the preference for safety under the Choquet model

URL des Documents de travail : http://centredeconomiesorbonne.univ-paris1.fr/bandeau-haut/documents-de-travail/Documents de travail du Centre d'Economie de la Sorbonne 2011.31 - ISSN : 1955-611XVictor prefers safety more than Ursula if whenever Ursula prefers some constant to some uncertain act, so does Victor. This paradigm, whose Expected Utility version takes the form of Arrow & Pratt's more risk averse concept, will be studied in the Choquet Uncertainty model, letting u and μ (v and ν) be Ursula's (Victor's) utility and capacity. A necessary and sufficient condition (A) on the pairs (u, μ) and (v, ν) will be presented for dichotomous weak increased uncertainty aversion, the preference by Victor of a constant over a dichotomous act whenever such is the preference of Ursula. This condition, pointwise inequality between a function defined in terms of v (u-1(⋅)) and another defined purely in terms of the capacities, preserves the flavor of the "more pessimism than greediness" characterization of monotone risk aversion by Chateauneuf, Cohen & Meilijson in the Rank-dependent Utility Model and its extension by Grant & Quiggin to the Choquet Utility Model. A sufficient condition (B) in terms of the capacities only, satisfied in particular if ν (⋅) = f (μ (⋅)) for some convex f, will be presented for more simplicity seeking, the preference by Victor over any act for some dichotomous act, that leaves Ursula indifferent. Condition A is thus a characterization of weak increased uncertainty aversion for convex f. An example will be exhibited disproving the more far reaching conjecture under which the dichotomous case implies the general case.Victor aime plus la sécurité que Ursula si, dès que Ursula préfère une constante à un acte incertain, il en est de même pour Victor. Ce paradigme, qui, dans le modèle EU, n'est autre que le concept d'Arrow-Pratt : "plus d'aversion pour le risque que", sera étudié dans le modèle CEU, modèle de Choquet de décision dans l'incertain, où on appelle u et μ (v et ν) l'utilité et la capacité d'Ursula (de Victor). Nous présentons une condition nécessaire et suffisante (A) sur les paires (u, μ) et (v, ν) pour l'accroissement faible d'aversion pour l'incertain dichotomique, la préférence de Victor pour une constante à un acte dichotomique dès que Ursula a cette préférence. Cette condition, inégalité ponctuelle entre une fonction en termes de v (u-1(⋅)) et une autre uniquement en termes de capacités, garde la forme de la caractérisation de l'aversion pour le risque monotone de Chateauneuf, Cohen et Meilijson et de son extension à l'incertain monotone de Grant et Quiggin dans le modèle de Choquet. Nous présentons une condition suffisante (B) de "plus de goût pour la simplicité" (préférence de Victor pour un acte dichotomique sur tout autre acte, qui laisse Ursula indifférente), uniquement en termes de capacités, satisfaite en particulier si ν (⋅) = f (μ (⋅)) pour une f convexe. Nous exposons un contre-exemple à la conjecture suivant laquelle le cas dichotomique impliquerait le cas général