On the Qualitative Comparison of Decisions Having Positive and Negative
  Features
  Making a decision is often a matter of listing and comparing positive and
negative arguments. In such cases, the evaluation scale for decisions should be
considered bipolar, that is, negative and positive values should be explicitly
distinguished. That is what is done, for example, in Cumulative Prospect
Theory. However, contraryto the latter framework that presupposes genuine
numerical assessments, human agents often decide on the basis of an ordinal
ranking of the pros and the cons, and by focusing on the most salient
arguments. In other terms, the decision process is qualitative as well as
bipolar. In this article, based on a bipolar extension of possibility theory,
we define and axiomatically characterize several decision rules tailored for
the joint handling of positive and negative arguments in an ordinal setting.
The simplest rules can be viewed as extensions of the maximin and maximax
criteria to the bipolar case, and consequently suffer from poor decisive power.
More decisive rules that refine the former are also proposed. These refinements
agree both with principles of efficiency and with the spirit of
order-of-magnitude reasoning, that prevails in qualitative decision theory. The
most refined decision rule uses leximin rankings of the pros and the cons, and
the ideas of counting arguments of equal strength and cancelling pros by cons.
It is shown to come down to a special case of Cumulative Prospect Theory, and
to subsume the Take the Best heuristic studied by cognitive psychologists.
