Bayesian Decision Theory and Stochastic Independence

Stochastic independence has a complex status in probability theory. It is not part of the definition of a probability measure, but it is nonetheless an essential property for the mathematical development of this theory. Bayesian decision theorists such as Savage can be criticized for being silent about stochastic independence. From their current preference axioms, they can derive no more than the definitional properties of a probability measure. In a new framework of twofold uncertainty, we introduce preference axioms that entail not only these definitional properties, but also the stochastic independence of the two sources of uncertainty. This goes some way towards filling a curious lacuna in Bayesian decision theory

Bayesian Decision Theory and Stochastic Independence

As stochastic independence is essential to the mathematical development of probability theory, it seems that any foundational work on probability should be able to account for this property. Bayesian decision theory appears to be wanting in this respect. Savage’s postulates on preferences under uncertainty entail a subjective expected utility representation, and this asserts only the existence and uniqueness of a subjective probability measure, regardless of its properties. What is missing is a preference condition corresponding to stochastic independence. To fill this significant gap, the article axiomatizes Bayesian decision theory afresh and proves several representation theorems in this novel framework

Analytic Narratives: What they are and how they contribute to historical explanation

The expression "analytic narratives" is used to refer to a range of quite recent studies that lie on the boundaries between history, political science, and economics. These studies purport to explain specific historical events by combining the usual narrative approach of historians with the analytic tools that economists and political scientists draw from formal rational choice theories. Game theory, especially of the extensive form version, is currently prominent among these tools, but there is nothing inevitable about such a technical choice. The chapter explains what analytic narratives are by reviewing the studies of the major book Analytic Narratives (1998), which are concerned with the workings of political institutions broadly speaking, as well as several cases drawn from military and security studies, which form an independent source of the analytic narratives literature. At the same time as it gradually develops a definition of analytic narratives, the chapter investigates how they fulfil one of their main purposes, which is to provide explanations of a better standing than those of traditional history. An important principle that will emerge in the course of the discussion is that narration is called upon not only to provide facts and problems, but also to contribute to the explanation itself. The chapter distinguishes between several expository schemes of analytic narratives according to the way they implement this principle. From all the arguments developed here, it seems clear that the current applications of analytic narratives do not exhaust their potential, and in particular that they deserve the attention of economic historians, if only because they are concerned with microeconomic interactions that are not currently their focus of attention

A concept of progress for normative economics

On se demande en quel sens il serait permis de décrire comme progressives les transformations qu'a connues l'économie normative du 20ème siècle. On propose alors un critère simple de progrès qui convienne aux séquences de théories normatives, et on le fait jouer sur la transition historique de la nouvelle économie du bien-être à la théorie du choix social. Après avoir rétabli les articulations conceptuelles des deux théories, l'article conclut que celle-ci a représenté un progrès par rapport à celle-là. Il commente aussi, mais plus brièvement, les développements récents de l'économie normative et leur relation avec les deux étapes précédentes.Economie du bien-être;Théorie du choix social;Progrès;Economie normative;Fonction de bien-être social;Théorème d'Arrow;Welfarisme

The Present and Future of Judgement Aggregation Theory. A Law and Economics Perspective

This chapter briefly reviews the present state of judgment aggregation theory and tentatively suggests a future direction for that theory. In the review, we start by emphasizing the difference between the doctrinal paradox and the discursive dilemma, two idealized examples which classically serve to motivate the theory, and then proceed to reconstruct it as a brand of logical theory, unlike in some other interpretations, using a single impossibility theorem as a key to its technical development. In the prospective part, having mentioned existing applications to social choice theory and computer science, which we do not discuss here, we consider a potential application to law and economics. This would be based on a deeper exploration of the doctrinal paradox and its relevance to the functioning of collegiate courts. On this topic, legal theorists have provided empirical observations and theoretical hints that judgment aggregation theorists would be in a position to clarify and further elaborate. As a general message, the chapter means to suggest that the future of judgment aggregation theory lies with its applications rather than its internal theoretical development

The Impartial Observer Theorem of Social Ethics

Following a long-standing philosophical tradition, impartiality is a distinctive and determining feature of moral judgments, especially in matters of distributive justice. This broad ethical tradition was revived in welfare economics by Vickrey, and above all, Harsanyi, under the form of the so-called Impartial Observer Theorem. The paper offers an analytical reconstruction of this argument, using a simple mathematical formalism, as well as a conceptual critique of each its premisses.Utilitarianism, Impartiality, Sympathy, Von Neumann- Morgenstern Utility Theory, Subjective Probability.

Social Preference Under Twofold Uncertainty

We investigate the conflict between the ex ante and ex post criteria of social welfare in a new framework of individual and social decisions, which distinguishes between two sources of uncertainty, here interpreted as an objective and a subjective source respectively. This framework makes it possible to endow the individuals and society not only with ex ante and ex post preferences, as is usually done, but also with interim preferences of two kinds, and correspondingly, to introduce interim forms of the Pareto principle. After characterizing the ex ante and ex post criteria, we present a first solution to their conflict that extends the former as much possible in the direction of the latter. Then, we present a second solution, which goes in the opposite direction, and is also maximally assertive. Both solutions translate the assumed Pareto conditions into weighted additive utility representations, and both attribute to the individuals common probability values on the objective source of uncertainty, and different probability values on the subjective source. We discuss these solutions in terms of two conceptual arguments, i.e., the by now classic spurious unanimity argument and a novel informational argument labelled complementary ignorance. The paper complies with the standard economic methodology of basing probability and utility representations on preference axioms, but for the sake of completeness, also considers a construal of objective uncertainty based on the assumption of an exogeneously given probability measure. JEL classification: D70; D81

Rethinking Nudge: Not One But Three Concepts

Nudge is a concept of policy intervention that originates in Thaler and Sunstein's (2008) popular eponymous book. Following their own hints, we distinguish three properties of nudge interventions: they redirect individual choices by only slightly altering choice conditions (here nudge 1), they use rationality failures instrumentally (here nudge 2), and they alleviate the unfavourable effects of these failures (here nudge 3). We explore each property in semantic detail and show that no entailment relation holds between them. This calls into question the theoretical unity of nudge, as intended by Thaler and Sunstein and most followers. We eventually recommend pursuing each property separately, both in policy research and at the foundational level. We particularly emphasize the need of reconsidering the respective roles of decision theory and behavioural economics to delineate nudge 2 correctly. The paper differs from most of the literature in focusing on the definitional rather than the normative problems of nudge

Expected utility theory, Jeffrey’s decision theory, and the paradoxes

In Richard Bradley’s book, Decision Theory with a Human Face, we have selected two themes for discussion. The first is the Bolker-Jeffrey theory of decision, which the book uses throughout as a tool to reorganize the whole field of decision theory, and in particular to evaluate the extent to which expected utility theories may be normatively too demanding. The second theme is the redefinition strategy that can be used to defend EU theories against the Allais and Ellsberg paradoxes, a strategy that the book by and large endorses, and even develops in an original way concerning the Ellsberg paradox. We argue that the BJ theory is too specific to fulfil Bradley’s foundational project and that the redefinition strategy fails in both the Allais and Ellsberg cases. Although we share Bradley’s conclusion that EU theories do not state universal rationality requirements, we reach it not by a comparison with BJ theory, but by a comparison with the non-EU theories that the paradoxes have heuristically suggested

L'apriori et l'a posteriori en économie

The paper relates the microeconomic law of demand to the theories of empirical confirmation that are developed by Hempel and Popper, respectively. After restating the Hicksian basis of consumer theory and stressing that this theory has never subjected the law to a rigorous test, the paper analyzes Hildenbrand's novel contribution. In Market Demand (1994), Hildenbrand offers an original derivation of the law of demand to the market, with a view of making it eventually possible to test the law. The article shows that Hildenbrand's approach makes sense within a neo-Hempelian, as opposed to a Popperian, outlook on empirical confirmation, and it uses the case itself to argue for the former against the latter.L'article rapporte la loi microéconomique de la demande aux thèses sur la confirmation empirique développées, respectivement, par Hempel et par Popper. Après avoir rappelé les bases hicksiennes de la théorie du consommateur et souligné que la loi n'y avait jamais fait l'objet d'un test rigoureux, il analyse la contribution novatrice d'Hildenbrand. Dans Market Demand (1994), celui-ci propose une dérivation logico-mathématique originale de la loi de la demande au marché, qui vise à rendre enfin possible un test de cette loi. L'article montre que la démarche d'Hildenbrand s'inscrit dans une perspective qui est néo-hempélienne, et non pas poppérienne, et il tire argument de cette étude même en faveur de la première contre la seconde