Robust ordinal regression for decision under risk and uncertainty

We apply the Robust Ordinal Regression (ROR) approach to decision under risk and uncertainty. ROR is a methodology proposed within multiple criteria decision aiding (MCDA) with the aim of taking into account the whole set of instances of a given preference model, for example instances of a value function, which are compatible with preference information supplied by the Decision Maker (DM) in terms of some holistic preference comparisons of alternatives. ROR results in two preference relations, necessary and possible; the necessary weak preference relation holds if an alternative is at least as good as another one for all instances compatible with the DM’s preference information, while the possible weak preference relation holds if an alternative is at least as good as another one for at least one compatible instance. To apply ROR to decision under risk and uncertainty we have to reformulate such a problem in terms of MCDA. This is obtained by considering as criteria a set of quantiles of the outcome distribution, which are meaningful for the DM. We illustrate our approach in a didactic example based on the celebrated newsvendor problem.