Fair Income Distribution Eval

---
name: fair-income-distribution-eval
description: Assesses the fairness of a country's income distribution by comparing its Gini index and quintile income shares against a theoretical benchmark derived from professional sports salary allocations. The benchmark assumes that sports salaries, determined by performance and transparent rules, represent a procedurally and distributively fair standard. Use when the user wants to benchmark on World Bank Income Data, or asks about evaluating this task. Reports percentage deviation.
metadata:
  skill_kind: dataset_eval
  source_arxiv: 2202.00917
  bibtex_key: [REDACTED]
  confidence: high
---

# fair-income-distribution-eval

> A quantitative method for benchmarking fair income distribution — Sitthiyot et al. (2022) (arXiv:2202.00917, 2022)

## What this evaluates

Assesses the fairness of a country's income distribution by comparing its Gini index and quintile income shares against a theoretical benchmark derived from professional sports salary allocations. The benchmark assumes that sports salaries, determined by performance and transparent rules, represent a procedurally and distributively fair standard.

## Datasets

- **World Bank Income Data** — total 75; splits: test (75)

## Metrics

- `percentage deviation` **(primary)** — range: percent
  - The absolute percentage difference between a country's actual income share in a given quintile and the benchmark's predicted fair share for that quintile, conditional on the country's Gini index. Formula: 100 * |Q_actual - Q_fair(Gini)| / Q_fair(Gini).

## Input / output format

**Input**: A country's Gini index and its income shares by quintile (Q1 to Q5) in decimal form.

**Output**: Percentage deviation score for each quintile, indicating the degree of unfairness relative to the sports-derived benchmark.

## Scoring recipe

```python
def compute_fairness_deviation(gini, q_actual):
    q_fair = [
        0.1956*gini**4 - 0.6612*gini**3 + 0.9356*gini**2 - 0.6700*gini + 0.20,
        -0.4914*gini**4 + 1.3968*gini**3 - 1.1195*gini**2 + 0.0141*gini + 0.20,
        0.2545*gini**4 + 0.0508*gini**3 - 0.6650*gini**2 + 0.1597*gini + 0.20,
        1.9481*gini**4 - 3.3533*gini**3 + 1.0625*gini**2 + 0.1428*gini + 0.20,
        -1.9067*gini**4 + 2.5669*gini**3 - 0.2136*gini**2 + 0.3534*gini + 0.20
    ]
    deviations = [100 * abs(q_a - q_f) / q_f for q_a, q_f in zip(q_actual, q_fair)]
    return deviations
```

## Common pitfalls

- The benchmark relies on the assumption that professional sports salaries are perfectly fair, which may not generalize to national economies.
- The polynomial equations are fitted to sports data with Gini indices between 0.247 and 0.873; extrapolating to countries with Gini indices outside this range may produce invalid or negative shares.
- The metric computes deviation per quintile; the paper does not specify a standardized aggregation method (e.g., mean or max) for an overall country-level fairness score.

## Evidence (verbatim from paper)

> we measure the degree of fairness by calculating the percentage deviation (in absolute value) of a country's income share in each quintile from the fair income share based on our benchmark derived from the relationship between the salary shares of the athlete in each quintile and the Gini index for the athlete's salary from 11 professional sports.

## Citation

```bibtex
@misc{sitthiyot2022fair,
  title={A quantitative method for benchmarking fair income distribution},
  author={Sitthiyot et al. (2022)},
  year={2022},
  note={arXiv:2202.00917}
}
```

- arXiv: 2202.00917