  Instance ranking problems intend to recover the true ordering of the
instances in a data set with a variety of applications in for example
scientific, social and financial contexts. Robust statistics studies the
behaviour of estimators in the presence of perturbations of the data resp. the
underlying distribution and provides different concepts to characterize local
and global robustness. In this work, we concentrate on the global robustness of
parametric ranking problems in terms of the breakdown point which measures the
fraction of samples that need to be perturbed in order to let the estimator
take unreasonable values. However, existing breakdown point notions do not
cover ranking problems so far. We propose to define a breakdown of the
estimator as a sign-reversal of all components which causes the predicted
ranking to be inverted, therefore we call our concept the order-inversal
breakdown point (OIBDP). We will study the OIBDP, based on a linear model, for
several different ranking problems that we carefully distinguish and provide
least favorable outlier configurations, characterizations of the order-inversal
breakdown point as well as sharp asymptotic upper bounds. We also outline the
case of SVM-type ranking estimators.
