Decisions can be evaluated by sets of positive and negative arguments - the problem is then to compare these sets. Studies in psychology have shown that in this case the scale of evaluation of decisions is generally bipolar. Moreover decisions are often made on the basis of an ordinal ranking of the arguments rather than on a genuine numerical evaluation of their degrees of attractiveness or rejection, hence the qualitative nature of the decision process in practice. In this paper, assuming bipolarity of evaluations and qualitative ratings, we present and axiomatically characterise two decision rules based on possibilistic order of magnitude reasoning that are capable of handling positive and negative affects. They are extensions of the maximin and maximax criteria to the bipolar case. A bipolar extension of possibility theory is thus obtained. In order to overcome the lack of discrimination power of the decision rules, refinements are also proposed, capturing both the efficiency principle and the idea of order of magnitude reasoning.
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