Inertial Updating with General Information

TL;DR

This paper explores belief revision with general information represented by sets of probability distributions, introducing inertial updating and a new Bayesian updating concept for such information, highlighting behavioral and divergence characterizations.

Contribution

It introduces inertial updating for general information, extends Bayesian updating to this setting, and characterizes f-divergences consistent with Bayesian principles.

Findings

Inertial updating minimizes subjective distance from prior.

Bayesian updating for general info may lead to disagreements.

f-divergences are characterized as distances compatible with Bayesian updating.

Abstract

We study belief revision when information is represented by a set of probability distributions, or general information. General information extends the standard event notion while including qualitative information (A is more likely than B), interval information (A has a ten-to-twenty percent chance), and more. We behaviorally characterize Inertial Updating: the decision maker's posterior is of minimal subjective distance from her prior, given the information constraint. Further, we introduce and characterize a notion of Bayesian updating for general information and show that Bayesian agents may disagree. We also behaviorally characterize f-divergences, the class of distances consistent with Bayesian updating.