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Let n respondents rank order d items, and suppose that d << n. Our main taskis to uncover and display the structure of the observed rank data by anexploratory riffle shuffling procedure which sequentially decomposes the nvoters into a finite number of coherent groups plus a noisy group : where thenoisy group represents the outlier voters and each coherent group is composedof a finite number of coherent clusters. We consider exploratory riffleshuffling of a set of items to be equivalent to optimal two blocks seriation ofthe items with crossing of some scores between the two blocks. A riffleshuffled coherent cluster of voters within its coherent group is essentiallycharacterized by the following facts : a) Voters have identical first TCAfactor score, where TCA designates taxicab correspondence analysis, an L1variant of correspondence analysis ; b) Any preference is easily interpreted asriffle shuffling of its items ; c) The nature of different riffle shuffling ofitems can be seen in the structure of the contingency table of the first-ordermarginals constructed from the Borda scorings of the voters ; d) The first TCAfactor scores of the items of a coherent cluster are interpreted as Borda scaleof the items. We also introduce a crossing index, which measures the extent ofcrossing of scores of voters between the two blocks seriation of the items. Thenovel approach is explained on the benchmarking SUSHI data set, where we showthat this data set has a very simple structure, which can also be communicatedin a tabular form.

Uncovering and Displaying the Coherent Groups of Rank Data by Exploratory Riffle Shuffling