Ranking and top-k ranking robustness index to measure dependence to parameters

Abstract : A ranking depends on the data available on the alternatives for one hand, and for a second hand on a aggregation function in order to obtain a global score for each alternative. The choice of the aggregation function (e.g. a weighted sum) and the choice of the parameters of the function (e.g. the weights) may have a great influence on the obtained ranking. We introduce in this communication a ratio index that can quantify the respective part of the ranking due to the parameters and due to the data. KEYWORDS Ranking, index, robustness, top-k list 1. Ranking issues Ranking items using composite indices is a very common issue that can be faced in several application fields. Ranking universities through the famous Shanghai index [2] or others [14]; ranking countries regarding their development levels [7]; ranking anything in newspapers (like " best place to live, to study,... "); but also page-rank when asking a query to any web search engine, and so on. The methodology to obtain such rankings is often the same: in a first step, an accurate set of evaluation criteria should be identified. Then data are collected in order to obtain a value for each individual on each criterion (which will be called " variable " in this paper, with a statistical point of view). Last, these informations are aggre-gated into a single score in order to obtain a general ranking which is, mathematically speaking, a total pre-order (i.e. a complete order on the set of individuals possibility including ex-aequo). We focus in this paper in the last step of the rank construction, i.e. the aggregation process. We are very aware that the choice and construction of the set of variables for a composite index is a very touchy issue [5, 6, 13]. Moreover, quality, precision, availability of the data are also crucial issues that can greatly influence the accuracy of the final ranking. However, with an optimistic point of view, we suppose that all difficulties pointed out have been overcome. An unique synthesized score from several variables can be obtained through the use of an aggregation function. Even if a great number of aggregation functions have been identified [1, 9, 10], we choose in this paper CONTACT
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Antoine Rolland, Jairo Cugliari. Ranking and top-k ranking robustness index to measure dependence to parameters. 2018. ⟨hal-01811360⟩

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