Used to show no proposed fairness criteria besides CWG are genuine requirements of fairness by showing a perfectly fair algorithm violates all fairness criteria.
Thought Experiment
- 40 individuals each given a coin with some bias probability of landing heads between 0 and 1. Each coin has a bias written on it
- Individuals randomly assigned two rooms, Room A or B
- Aim is to predict for each individual, if their coin will land heads or tails and assign them a score representing this likelihood
- Assume we use the algorithm that we only predict heads if the number of the coin is greater than 0.5
- Suppose random assignment produces following result:
| Heads Probaability | Room A | Room B |
|---|---|---|
| 75% | 12 | |
| 12.5% | 8 | |
| 60% | 10 | |
| 40% | 10 |
- This violates every fairness criteria except CWG because A’s have more extreme probabilities than Bs