# Ranking items given positive and negative ratings

Lower bound of the Wilson interval, see confidence interval https://www.evanmiller.org/how-not-to-sort-by-average-rating.html

Zhang 2011, How to Count Thumb-Ups and Thumb-Downs Model as information retrieval and evaluate using economic axioms

- law of increasing total utility, i.e. more up/dowm, leads to higher/lower score
- low of diminishing marginal utility, i.e. difference each up/down makes decreases when the number of up/down increase

Only Dirichlet Prior Smoothing and its special cases satisfied both axioms.

Schumacher also reached the same conclusion as Zhang 2011, recommends Laplace smoothing

Talton 2019, How do People Sort by Ratings?

- Recommends Laplace smoothing
- Suggest using number of up votes/down votes format to minimize contention

See https://en.wikipedia.org/wiki/Additive_smoothing “plus four rule”, (n_s + 2) / (n + 4)