Random Choice and Private Information

Abstract

We consider an agent who chooses an option after receiving some private information. This information, however, is unobserved by an analyst, so from the latter's perspective, choice is probabilistic or random. We provide a theory in which information can be fully identified from random choice. In addition, the analyst can perform the following inferences even when information is unobservable: (1) directly compute ex ante valuations of menus from random choice and vice versa, (2) assess which agent has better information by using choice dispersion as a measure of informativeness, (3) determine if the agent's beliefs about information are dynamically consistent, and (4) test to see if these beliefs are well‐calibrated or rational.

Inertial Behavior and Generalized Partition

“…In our formal environment, we interpret cognitive inertia to mean that the only information the DM reacts to is which states have conclusively been ruled out, and that this information is taken into account following Bayes'law. Our result then establishes that, for a forward looking DM (for whom the expectation over 10 https://en.wikipedia.org/wiki/Cognitive_inertia posteriors coincides with the prior), cognitive inertia can explain behavior only if the true information structure is such that the biased one -which is derived from the true one by ignoring all information about relative weights -is a generalized partition. In this case it is unnecessary to model the DM as biased, even if he is subject to cognitive inertia; learning by generalized partition provides a rational as if model of his behavior.…”

“…10 For instance, one explanation for the di¢ culties of implementing organizational change is that managers fail to update and revise their understanding of a situation even when the environment changes, say when new technologies emerge (Tripsas and Gavett 2000). This impedes their ability to adjust their actions in response to relevant information, and may lead to inertial behavior.…”

“…They further derived a partitional learning representation, in which signals correspond to events that partition the state space. Partitional learning is also studied in De Oliveira et al (2016), who adopt the same menu choice approach but, unlike us, allow the DM to choose his information structure, and in Lu (2015), who uses the random choice approach to elicit information. A dynamic version of partitional learning appears in Dillenberger, Krishna, and Sadowski (2016).…”

A Mechanism for Eliciting Second-Order Beliefs and the Inclination to Choose

“…Karni (2016) provides a detailed discussion of the differences. The mechanism proposed by Chambers and Lambert is designed to elicit the information structure in the choicebased models of Dillenberger et al (2014) and Lu (2016). Since these models are anchored in the revealed preference methodology, it is not surprising that the information can be elicited using revealed preference methods.…”

A theory of stochastic choice under uncertainty

“…Both invoke preference relation on the nonempty subsets of Anscombe-Aumann (1963) acts but take di erent approaches. Lu (2014) extends the random choice model of Gul and Pesendorfer (2006) to include decision problems that consist of Anscombe-Aumann acts. In the individual interpretation of Lu's model, a decision maker receives a signal that a ects his choice behavior.…”