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Two-Sample Testing on Ranked Preference Data and the Role of Modeling Assumptions

Charvi Rastogi, Sivaraman Balakrishnan, Nihar B. Shah, Aarti Singh; 23(225):1−48, 2022.

Abstract

A number of applications require two-sample testing on ranked preference data. For instance, in crowdsourcing, there is a long-standing question of whether pairwise-comparison data provided by people is distributed identically to ratings-converted-to-comparisons. Other applications include sports data analysis and peer grading. In this paper, we design twosample tests for pairwise-comparison data and ranking data. For our two-sample test for pairwise-comparison data, we establish an upper bound on the sample complexity required to correctly test whether the distributions of the two sets of samples are identical. Our test requires essentially no assumptions on the distributions. We then prove complementary lower bounds showing that our results are tight (in the minimax sense) up to constant factors. We investigate the role of modeling assumptions by proving lower bounds for a range of pairwise-comparison models (WST, MST, SST, parameter-based such as BTL and Thurstone). We also provide tests and associated sample complexity bounds for partial (or total) ranking data. Furthermore, we empirically evaluate our results via extensive simulations as well as three real-world data sets consisting of pairwise-comparisons and rankings. By applying our two-sample test on real-world pairwise-comparison data, we conclude that ratings and rankings provided by people are indeed distributed differently.

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