Chapter 9 - Coherent Uncertainties and Consensus

Abstract

This chapter characterizes increments of information which leave a decision maker's preferences unchanged. It categorizes increments of information which leave a decision maker's preferences unchanged. Under this, it discusses a theorem and two corollaries, which specify the conditions under which a decision maker's preferences (based on the robustness function) are preserved when presented with an increment of information. The chapter also demonstrates that if two info-gap models are sufficiently coherent then the robustness-based preferences will be the same, for any choice of the reward function. Conversely, behaviorally significant information—which causes a modification of preference—must break the coherence between old and new uncertainty models. A decision maker's preference ranking of the available options depends upon a reward function and also upon knowledge as expressed by info-gap models of uncertainty. The chapter then evaluates the coherency of several pairs of info-gap models. It also presents an example of the evaluation and interpretation of coherence functions.