Sensitivity index to measure dependence on parameters for rankings and top- k rankings

In a multivariate framework, ranking a data set can be done by using an aggregation function in order to obtain a global score for each individual, and then by using these scores to rank the individuals. 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 sensitivity of the data set ranking up to a change of weights. This index is investigated in the general case and in the restricted case of top-k rankings. We also illustrate the interest to use such an index to analyse ranked data sets.