Schedule - Parallel Session 7 - Updating and Ambiguity 2IDL Auditorium - 09:00 - 10:30
Ambiguity Aversion under Maximum Likelihood Updating
Daniel Heyen; Timo Goeschl; Boris Wiesenfarth
Maximum likelihood updating (MLU) is a well-known approach for extending static ambiguity sensitive preferences to dynamic set-ups. This paper develops an example in which MLU induces an ambiguity averse maxmin expected utility (MEU) decision-maker to (i) prefer a bet on an ambiguous over a risky urn and (ii) be more willing to bet on the ambiguous urn compared to an (ambiguity neutral) subjective expected utility (SEU) decision-maker. These preferences are challenging for two reasons. The first reason is that prior to observing any draws from the urns, the MEU decision-maker – in line with the usual notion of ambiguity aversion – actually preferred the risky over the ambiguous bet and was less willing to bet on the ambiguous urn than the SEU decision-maker. The second reason is that the information that caused this switch in betting preferences was symmetric across urns and agents: both decision-makers observed from both urns a draw of the same color. Relating this finding to other well-known results in the context of dynamic extensions of ambiguity averse preferences, the paper clarifies that the identified switch in betting preferences is not due to a violation of dynamic consistency or consequentialism. Rather, the deeper reason lies in MLU’s selection of extreme priors, causing a violation of the stability of set-inclusion over the course of the updating process.
Belief Updating under Ambiguity
Belief updating is at the heart of decision theory and statistical theory, and has been applied to economic theory and artificial intelligence. This paper examines belief updating under ambiguity from three approaches. One is the traditional Bayesian updating, where only ambiguity neutral behavior is accommodated. The other two approaches are non-Bayesian, introduced by Gilboa and Schmeidler (1993) (GS) as well as Dempster (1967) and Shafer (1976) (DS) respectively, where both ambiguity averse and ambiguity seeking behavior are accommodated. Under the framework of decision theory, this paper compares Bayesian and non-Bayesian updating in its model specification and numerical implications. Ambiguity attitudes affect not only static decisions, but also the way in which new information is incorporated. For an ambiguity averse (seeking) decision maker, GS updating leads to more pessimistic (optimistic) behavior than DS updating, and favorable or unfavorable information has bigger (smaller) impact on GS updating than on DS updating.
Are Intertemporal Preferences Transitive? A Bayesian Analysis of Repeated Choices
Transitivity of preferences is a central axiom of rational decision making. Previous research on intertemporal choice has suggested that intertemporal preferences might be intransitive, for which nonadditivity in delay discounting is one of the reasons. Most studies in this line of research have either analyzed aggregate data or ignored the probabilistic nature of intertemporal choice when addressing individual data. In this article, I present a refined experiment for studying transitivity of intertemporal preferences with repeatedly presented choice questions tailored to each individual participant. A state-of-the-art Bayesian model comparison was applied to the individual choice data to test four stochastic models of transitivity”weak, moderate, and strong stochastic transitivity, as well as a mixture model of transitive preference”against the most general model allowing for all types of preference orders, and intermediate models accommodating nonadditivity in delay discounting. The results showed that individual data from a majority of participants were consistent with a transitive view of intertemporal preferences. In addition, nonadditivity in delay discounting “defined as special cases of violating weak, moderate, or strong stochastic transitivity” rarely occurred at an individual level. On the other hand, the individual data of a small portion of participants provided strong evidence for intransitive intertemporal preferences, suggesting either subadditivity or superadditivity in delay discounting. The heterogeneous individual responses bring about a theoretical issue, that is, whether different participants adopt distinct decision strategies for intertemporal choice, and thus are best described by distinct choice models. The relevant findings also provide critical information for developing and testing competing cognitive models of intertemporal choice. One critical question to answer in this endeavor is whether models consistent with both transitive and intransitive preferences, such as the tradeoff model, should be preferred to models that provide better description of individual data from a majority of participants with transitive intertemporal preferences but perform poorly for intransitive participants.
Dynamic Collective Choice under Ambiguity: an Experimental Investigation
Konstantinos Georgalos; Enrica Carbone; John Hey
Recently, inspired by the advances in the theory of decision making under ambiguity1, there have been several empirical studies aiming to test either for the ambiguity attitudes of the subjects or to fit different non-Expected Utility models to identify which theory best describes the data (see among others Halevy (2007), Ahn et al. (2014), Hey and Pace (2014) and Stahl (2014)). Most of these studies have shown extensive heterogeneity in behaviour and attitudes towards ambiguity, and violations of the Expected Utility axioms. Furthermore, this framework has been recently extended so as to capture the effects of group choice to ambiguity attitudes (Charness et al. (2013), Keck et al. (2014)). These studies compare decisions of individuals and groups and aim to understand whether social interactions lead to more ambiguity neutral decisions or not. All the aforementioned studies focus on decision making in an atemporal environment. Nevertheless, a crucial question in the theory of decision making under ambiguity how beliefs are updated upon the arrival of new information. In the standard economic theory, when a decision maker has to cope with a dynamic problem where the various probabilities of the possible states of the world are not given, it is assumed that prior beliefs are updated in a Bayesian way and decisions are made by maximising Expected Utility preferences (Savage (1954)). This requires that the agents’ preferences satisfy both the axioms of Dynamic Consistency and Consequentialism. When the agents have not ambiguity neutral attitudes (violate EU), one of the two rationality axioms is not satisfied leading to potential inconsistencies in choices. We extend the collective choice framework to its dynamic dimension where we compare individual and group choice in a dynamic decision problem under ambiguity. We use a transparent and non-manipulable device (a Bingo blower) to represent ambiguity in the lab and we ask the subjects a set of allocation questions in a sequential choice task. Based on the information that is provided by the Bingo blower the participants are able to form priors regarding the probability distribution of the future states of the world. Based on these priors, the subjects are asked to make an initial choice. In the next period, partial information is revealed which provides the decision makers the opportunity to update their prior beliefs and adapt, if necessary, their initial decision. Our data from this experimental design allows the fitting of preference functionals for both individuals and groups. Based on this analysis we are able to investigate the following questions: (1) which axioms do individuals and groups violate, (2) what are the effects of group decision making to the risk and ambiguity attitudes of the subjects, (3) how does decision making in groups influences the updating process and (4) when individuals are dynamically inconsistent, does group decision making help to eliminate these inconsistencies?