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As the issue of robustness in AI systems becomes vital, statistical learningtechniques that are reliable even in presence of partly contaminated data haveto be developed. Preference data, in the form of (complete) rankings in thesimplest situations, are no exception and the demand for appropriate conceptsand tools is all the more pressing given that technologies fed by or producingthis type of data (e.g. search engines, recommending systems) are now massivelydeployed. However, the lack of vector space structure for the set of rankings(i.e. the symmetric group $\mathfrak{S}_n$) and the complex nature ofstatistics considered in ranking data analysis make the formulation ofrobustness objectives in this domain challenging. In this paper, we introducenotions of robustness, together with dedicated statistical methods, forConsensus Ranking the flagship problem in ranking data analysis, aiming atsummarizing a probability distribution on $\mathfrak{S}_n$ by a median ranking.Precisely, we propose specific extensions of the popular concept of breakdownpoint, tailored to consensus ranking, and address the related computationalissues. Beyond the theoretical contributions, the relevance of the approachproposed is supported by an experimental study.

Robust Consensus in Ranking Data Analysis: Definitions, Properties and Computational Issues