Papers › How should we aggregate ratings? Accounting for personal rating scales via Wasserstein...
How should we aggregate ratings? Accounting for personal rating scales via Wasserstein barycenters
Daniel Raban
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
A common method of comparing items is to collect numerical ratings on a linear scale and compare the average rating for each item. However, averaging ratings does not account for people rating according to differing personal rating scales. With this in mind, we investigate the problem of calculating aggregate numerical ratings from individual numerical ratings and propose a new, non-parametric model for the problem. We show that, with minimal modeling assumptions, the standard average is inconsistent for estimating the quality of items. Analyzing the problem of heterogeneous personal rating scales from the perspective of optimal transport, we derive an alternative rating estimator, which we show is asymptotically consistent almost surely and in L^p for estimating quality, with an optimal rate of convergence. Further, we generalize Kendall's W, a non-parametric coefficient of preference concordance between raters, from the special case of rankings to the more general case of arbitrary numerical ratings. Along the way, we prove Glivenko--Cantelli-type theorems for uniform convergence of the cumulative distribution functions and quantile functions for Wasserstein-2 barycenters on [0,1].
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections