# Standardization of Weighted Ranking Correlation Coefficients

arXiv: https://arxiv.org/abs/2504.08428 · HTML: https://mlsanity.com/paper/2504.08428/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 29 references that are in the map.
- First posted on arXiv 11 Apr 2025.

## Builds on (most cited first, 4 of 4)

- [A Weighted Correlation Index for Rankings with Ties](https://mlsanity.com/paper/1404.3325/) (2014)
- [A Deep Architecture for Semantic Matching with Multiple Positional Sentence Representations](https://mlsanity.com/paper/1511.08277/) (2015)
- [Comparing the Pearson and Spearman Correlation Coefficients Across Distributions and Sample Sizes: A Tutorial Using Simulations and Empirical Data](https://mlsanity.com/paper/2408.15979/) (2024)
- [Top-Rank-Focused Adaptive Vote Collection for the Evaluation of Domain-Specific Semantic Models](https://mlsanity.com/paper/2010.04486/) (2020)

## Built on by (most cited first, 1 of 1)

- [Cost-Sensitive Evaluation for Binary Classifiers](https://mlsanity.com/paper/2510.22016/) (2025)

## Abstract (arXiv)

A fundamental problem in statistics is measuring the correlation between two rankings of a set of items. Kendall's τ and Spearman's ρ are well established correlation coefficients whose symmetric structure guarantees zero expected value between two rankings randomly chosen with uniform probability. In many modern applications, however, greater importance is assigned to top-ranked items, motivating weighted variants of these coefficients. Such weighting schemes generally break the symmetry of the original formulations, resulting in a non-zero expected value under independence and compromising the interpretation of zero correlation. We propose a general standardization function g(·) that transforms a ranking correlation coefficient Gamma into a standardized form g(Gamma) with zero expected value under randomness. The transformation preserves the domain [-1,1], satisfies the boundary conditions, is continuous and increasing, and reduces to the identity for coefficients that already satisfy the zero-expected-value property. The construction of g(x) depends on three distributional parameters of Gamma: its mean, variance, and left variance; since their exact calculation becomes infeasible for large ranking lengths n, we develop accurate numerical estimates based on Monte Carlo sampling combined with polynomial regression to capture their dependence on n.