An overview of bipolar qualitative decision rules

Abstract

Making a good decision is often a matter of listing and comparing positive and negative arguments, as studies in cognitive psychology have shown. In such cases, the evaluation scale should be considered bipolar, that is, negative and positive values are explicitly distinguished. Generally, positive and negative features are evaluated separately, as done in Cumulative Prospect Theory. However, contrary to the latter framework that presupposes genuine numerical assessments, decisions are often made on the basis of an ordinal ranking of the pros and the cons, and focusing on the most salient features, i.e., the decision process is qualitative. In this paper, we report on a project aiming at characterizing several decision rules, based on possibilistic order of magnitude reasoning, and tailored for the joint handling of positive and negative affects, and at testing their empirical validity. The simplest rules can be viewed as extensions of the maximin and maximax criteria to the bipolar case and, like them, suffer from a lack of discrimination power. More decisive rules that refine them are also proposed. They account for both the principle of Pareto-efficiency and the notion of order of magnitude reasoning. The most decisive one uses a lexicographic ranking of the pros and cons. It comes down to a special case of Cumulative Prospect Theory, and subsumes the “Take the best” heuristic.