Choice axioms for a positive value of information

Debates around the assumption of rationality in economic theory abound and are too numerous to be listed here. Traditionally, rationality of a decision maker is captured by a set of (testable) axioms, whose meaning and strength can be discussed. These rationality axioms however do not all have the same status in the sense that they bear on different things. One could actually distinguish three categories of axioms or rationality principles. The first one bears on preferences: a decision maker’s preferences are rational if they satisfy a set of axioms (transitivity and so forth). The set of axioms that is imposed might depend on the context. For instance, in the case of decision making under uncertainty, rationality axioms often include the sure thing principle (Savage (1954)). The second category of axioms is the one that bears on choices. In this view the decision maker’s choices or behavior is judged to be rational or not whether it satisfies axioms such as the weak axiom of revealed preferences. The methodology of revealed preferences, which assesses that choice behavior reveals the underlying preferences ties in these two notions of rationality (Sen (1971)), making it possible to relate axioms on choice behavior to axioms on preferences. The third category is the one that assesses the rationality of the consequences of the decision maker’s choices. We will name it “economic” rationality. It is based on a few principles such as, for instance, the fact that the decision maker should not be susceptible to be exploited through a money pump (that is, a dynamic process through which the decision maker loses money for sure, after a series of desirable exchanges). Another principle along this line, which will be analyzed in this paper is the fact that a decision maker should never refuse information before making a choice. Indeed, it can be shown that if this were the case, a decision maker would be willing to pay a positive amount to avoid getting informed. This behavior could then be exploited, implying that the decision maker could be made worse off in in similar fashion as in the case of a money pump. In this paper, we look at the relationship between these three notions of rationality (namely, rationality of preferences, rationality of choices, and economic rationality) in ∗CNRS–EUREQua, [email protected] †CNRS–EUREQua, [email protected]