Coarse Descriptions and Cautious Preferences

TL;DR

This paper models decision making with imprecise, linguistically described alternatives, using a lattice structure and maximin principles to derive preferences over possible states based on worst-case outcomes.

Contribution

It introduces a formal framework for decision making with coarse descriptions, characterizing preferences through axioms and a maximin decision rule within a distributive lattice.

Findings

Preferences can be derived from worst-case outcomes over a state space.

The model applies to alternatives described by logical combinations of basic descriptions.

Axioms characterize maximin decision making in a lattice-structured setting.

Abstract

We consider a model where an agent is must choose between alternatives that each provide only an imprecise description of the world (e.g. linguistic expressions). The set of alternatives is closed under logical conjunction and disjunction, but not necessarily negation. (Formally: it is a distributive lattice, but not necessarily a Boolean algebra). In our main result, each alternative is identified with a subset of an (endogenously defined) state space, and two axioms characterize maximin decision making. This means: from the agent's preferences over alternatives, we derive a preference order on the endogenous state space, such that alternatives are ranked in terms of their worst outcomes.