Are beliefs a matter of taste? A case for Objective Imprecise Information

We argue, in the spirit of some of Jean-Yves Jaffray's work, that explicitly incorporating the information, however imprecise, available to the decision maker is relevant, feasible, and fruitful. In particular, we show that it can lead us to know whether the decision maker has wrong beliefs and whether it matters or not, that it makes it possible to better model and analyze how the decision maker takes into account new information, even when this information is not an event and finally that it is crucial when attempting to identify and measure the decision maker's attitude toward imprecise information.Decision under uncertainy;Objective Information;Belief Formation;Methodology of Decision Theory

Are Beliefs a Matter of Taste ? A case for Objective Imprecise Information

We argue, in the spirit of some of Jean-Yves Jaffray's work, that explicitly incorporating the information, however imprecise, available to the decision marker is relevant, feasible and fruitful. In particular, we show that it can lead us to know whether the decision maker has wrong beliefs and whether it matters or not, that it makes it possible to better model and analyze how the decision maker takes into account new information, even when this information is not an event and finally that it is crucial when attempting to identify and measure the decision maker's attitude toward imprecise information.Beliefs, imprecision, information.

Are Beliefs a Matter of Taste ? A case for Objective Imprecise Information

URL des Documents de travail : http://ces.univ-paris1.fr/cesdp/CESFramDP2009.htmDocuments de travail du Centre d'Economie de la Sorbonne 2009.86 - ISSN : 1955-611XWe argue, in the spirit of some of Jean-Yves Jaffray's work, that explicitly incorporating the information, however imprecise, available to the decision marker is relevant, feasible and fruitful. In particular, we show that it can lead us to know whether the decision maker has wrong beliefs and whether it matters or not, that it makes it possible to better model and analyze how the decision maker takes into account new information, even when this information is not an event and finally that it is crucial when attempting to identify and measure the decision maker's attitude toward imprecise information.Nous défendons l'idée qu'incorporer l'information disponible dans une approche axiomatique en théorie de la décision est pertinent, faisable et fructueux. Nous montrons que cela peut identifier les situations dans lesquelles le décideur a des croyances erronées, permet d'enrichir l'analyse d'arrivée de nouvelles informations et finalement est essentiel pour estimer l'attitude des décideurs face à l'imprécision

Intertemporal Equilibria with Knightian Uncertainty

We study a dynamic and infinite-dimensional model with Knightian uncertainty modeled by incomplete multiple prior preferences. In interior efficient allocations, agents share a common risk-adjusted prior and use the same subjective interest rate. Interior efficient allocations and equilibria coincide with those of economies with subjective expected utility and priors from the agents' multiple prior sets. We show that the set of equilibria with inertia contains the equilibria of the economy with variational preferences anchored at the initial endowments. A case study in an economy without aggregate uncertainty shows that risk is fully insured, while uncertainty can remain fully uninsured. Pessimistic agents with Gilboa-Schmeidler's max-min preferences would fully insure risk and uncertainty.Knightian Uncertainty, Ambiguity, Incomplete Preferences, General Equilibrium Theory, No Trade

Objective Rationality Foundations for (Dynamic) α-MEU

We show how incorporating Gilboa, Maccheroni, Marinacci, and Schmeidler’s (2010) notion of objective rationality into the alpha-MEU model of choice under ambiguity (Hurwicz, 1951) can overcome several challenges faced by the baseline model without objective rationality. The decision-maker (DM) has a subjectively rational preference $\succsim^\wedge$, which captures the complete ranking over acts the DM expresses when forced to make a choice; in addition, we endow the DM with a (possibly incomplete) objectively rational preference $\succsim^*$, which captures the rankings the DM deems uncontroversial. Under the objectively founded alpha-MEU model, $\succsim^\wedge$ has an alpha-MEU representation and $\succsim^*$ has a unanimity representation à la Bewley (2002), where both representations feature the same utility index and set of beliefs. While the axiomatic foundations of the baseline alpha-MEU model are still not fully understood, we provide a simple characterization of its objectively founded counterpart. Moreover, in contrast with the baseline model, the model parameters are uniquely identified. Finally, we provide axiomatic foundations for prior-by-prior Bayesian updating of the objectively founded alpha-MEU model, while we show that, for the baseline model, standard updating rules can be ill-defined

Objective rationality foundations for (dynamic) α-MEU

We show how incorporating Gilboa, Maccheroni, Marinacci, and Schmeidler’s (2010) notion of objective rationality into the alpha-MEU model of choice under ambiguity (Hurwicz, 1951) can overcome several challenges faced by the baseline model without objective rationality. The decision-maker (DM) has a subjectively rational preference $\succsim^\wedge$, which captures the complete ranking over acts the DM expresses when forced to make a choice; in addition, we endow the DM with a (possibly incomplete) objectively rational preference $\succsim^*$, which captures the rankings the DM deems uncontroversial. Under the objectively founded alpha-MEU model, $\succsim^\wedge$ has an alpha-MEU representation and $\succsim^*$ has a unanimity representation à la Bewley (2002), where both representations feature the same utility index and set of beliefs. While the axiomatic foundations of the baseline alpha-MEU model are still not fully understood, we provide a simple characterization of its objectively founded counterpart. Moreover, in contrast with the baseline model, the model parameters are uniquely identified. Finally, we provide axiomatic foundations for prior-by-prior Bayesian updating of the objectively founded alpha-MEU model, while we show that, for the baseline model, standard updating rules can be ill-defined

Objective rationality foundations for (dynamic) Alpha-MEU

We show how incorporating Gilboa, Maccheroni, Marinacci, and Schmeidler’s (2010) notion of objective rationality into the α-MEU model of choice under ambiguity can overcome several challenges faced by the baseline model without objective rationality. The decision-maker (DM) has a subjectively rational preference ≿^, which captures the complete ranking overacts the DM expresses when forced to make a choice; in addition, we endow the DM with a (possibly incomplete) objectively rational preference ≿*, which captures the rankings the DM deems uncontroversial. Under the objectively founded α-MEU model, ≿^ has an α-MEU representation and ≿*has a unanimity representation à la Bewley (2002), where both representations feature the same utility index and set of beliefs. While the axiomatic foundations of the baseline α-MEU model are still not fully understood, we provide a simple characterization of its objectively founded counterpart. Moreover, in contrast with the baseline model, the model parameters are uniquely identified. Finally, we provide axiomatic foundations for prior-by-prior Bayesian updating of the objectively founded α-MEU model, while we show that, for the baseline model, standard updating rules can be ill-defined

SECOND-ORDER IMPRECISE STOCHASTIC DOMINANCE

Master'sMASTER OF ENGINEERIN

EXTREME POINTS OF THE CREDAL SETS GENERATED BY COMPARATIVE PROBABILITIES

ABSTRACT. When using convex probability sets (or, equivalently, lower previsions) as uncertainty models, identifying extreme points can help simplifying various computations or the use of some algorithms. In general, sets induced by specific models such as possibility distributions, linear vacuous mixtures or 2-monotone measures may have extreme points easier to compute than generic convex sets. In this paper, we study extreme points of another specific model: comparative probability orderings between the singletons of a finite space. We characterise these extreme points by mean of a graphical representation of the comparative model, and use them to study the properties of the lower probability induced by this set. By doing so, we show that 2-monotone capacities are not informative enough to handle this type of comparisons without a loss of information. In addition, we connect comparative probabilities with other uncertainty models, such as imprecise probability masses