Rationality and Dynamic Consistency Under Risk and Uncertainty

Abstract

For choice with deterministic consequences, the standard rationality hypothesis is ordinality -i.e., maximization of a weak preference ordering. For choice under risk (resp. uncertainty), preferences are assumed to be represented by the objectively (resp. subjectively) expected value of a von NeumannMorgenstern utility function. For choice under risk, this implies a key independence axiom; under uncertainty, it implies some version of Savage's sure thing principle. This chapter investigates the extent to which ordinality, independence, and the sure thing principle can be derived from more fundamental axioms concerning behaviour in decision trees. Following Cubitt (1996), these principles include dynamic consistency, separability, and reduction of sequential choice, which can be derived in turn from one consequentialist hypothesis applied to continuation subtrees as well as entire decision trees. Examples of behavior violating these principles are also reviewed, as are possible explanations of why such violations are often observed in experiments.

Choosing the Future: Markets, Ethics, and Rapprochement in Social Discounting

“…We refer the reader to e.g. Hammond & Zank (2014); Ghirardato (2002) for detailed treatments. We note however that two of the standard constraints on rational dynamic choice do not imply expected discounted utilitarian preferences.…”

Dynamic decision making under ambiguity: An experimental investigation

“…A sophisticated DM applies backward induction in order to figure out the optimal strategy for every given problem. As Hammond and Zank (2014) describe, sophistication is like the sub-game perfect Nash equilibrium of an extensive form game, between the future and present self of the DM, as in Selten (1975). Starting from the final decision nodes of a decision tree (the last period), a DM anticipates an event E to occur and therefore, the future course of action is determined by the conditional preferences of the ex-post self.…”

Conditional non-expected utility preferences induced by mixture of lotteries: a note on the normative invalidity of expected utility theory

“…The significance of the model largely rests on the independence axiom of EU theory, which ensures dynamically consistent choices in multiple-stage decision making under risk. Dynamic consistency of risky choice, in turn, is a basic criterion of economic rationality in the sense that it requires an individual´s choices at later stages of a decision process to conform with this individual´s preferred course of action planned at earlier stages (Karni and Schmeidler 1991; for a related concept of dynamically consistent behaviour, see Hammond 1998;Hammond and Zank 2014). In recent decision research, dynamic choice theory has indeed been extended beyond EU maximisation from various perspectives, especially those of risk, uncertainty and ambiguity (Machina 1989;Sarin and Wakker 1998;Siniscalchi 2011;Nebout 2014).…”