Decision-making Under Ordinal Preferences and Comparative Uncertainty

TL;DR

This paper explores a non-numeric, purely symbolic approach to decision-making under uncertainty, revealing fundamental limitations and inconsistencies with probabilistic models, and connecting to non-monotonic reasoning theories.

Contribution

It introduces a novel symbolic framework for decision-making without utility or probability scales, highlighting its limitations and relation to possibility theory.

Findings

The approach is inconsistent with probabilistic uncertainty representation.

It often leads to indecisive or overly risky decisions.

The method aligns with non-monotonic reasoning and possibility theory.

Abstract

This paper investigates the problem of finding a preference relation on a set of acts from the knowledge of an ordering on events (subsets of states of the world) describing the decision-maker (DM)s uncertainty and an ordering of consequences of acts, describing the DMs preferences. However, contrary to classical approaches to decision theory, we try to do it without resorting to any numerical representation of utility nor uncertainty, and without even using any qualitative scale on which both uncertainty and preference could be mapped. It is shown that although many axioms of Savage theory can be preserved and despite the intuitive appeal of the method for constructing a preference over acts, the approach is inconsistent with a probabilistic representation of uncertainty, but leads to the kind of uncertainty theory encountered in non-monotonic reasoning (especially preferential and rational inference), closely related to possibility theory. Moreover the method turns out to be either very little decisive or to lead to very risky decisions, although its basic principles look sound. This paper raises the question of the very possibility of purely symbolic approaches to Savage-like decision-making under uncertainty and obtains preliminary negative results.