Individual Vs Group Fairness

Why Does This Exist?

Early teams tried the obvious fix: delete gender and race from the data and call the model fair. It failed twice. First, the model rebuilt the missing columns from stand-ins like zip code, school, and vocabulary, so blindness changed nothing. Second, even a genuinely blind model can land unevenly when groups start from different places, because the same rule applied to different distributions produces different rates.

Researchers then wrote down what fairness could mean, and two families emerged. Individual fairness says similar people get similar outcomes. Group fairness says groups get equal rates. Each sounds undeniable on its own. Together they contradict each other whenever the groups differ, which is nearly always, and that contradiction is mathematical rather than a matter of opinion.

This page teaches both definitions, the exact point where they collide, and how to choose. For the parent tour of metrics, read AI fairness first. For the legal yardstick that measures outcome gaps, disparate impact is next. For catching violations before launch, model auditing closes the loop.

Think of It Like This

How It Actually Works

Write each applicant as features $x$, with $x$ holding everything except the protected attribute, and write the model's decision as $M(x)$, which is 1 for admit and 0 for reject. Individual fairness constrains pairs. Group fairness constrains rates.

Individual fairness: similar in, similar out

Two people with distance $D(x_1, x_2)$ between them must get decisions no further apart than $L$ times that distance:

In plain words: $D$ measures how alike two applicants are, $M$ is the model's output, and $L$ caps how fast the output may change as people differ. Nearly identical files must get nearly identical answers. The entire battle hides inside $D$, because deciding which features count toward similarity is a judgment call. Include school quality and two applicants from different worlds look different; exclude it and they look the same. A flawed $D$ makes the model faithfully reproduce whoever defined similar.

Group fairness: equal rates across groups

Demographic parity ignores pairs and demands equal selection rates. With protected attribute $A$ marking the groups:

In plain words: the chance of admission must be the same in both groups. Stricter siblings split the rates further. Equalized odds demands equal true positive and false positive rates per group, so qualified applicants succeed equally often and unqualified ones fail equally often. The famous impossibility result says these group targets generally cannot all hold at once when base rates differ, which is the normal case, so teams pick the one matching the harm they most fear.

Worked example: one cutoff, two rates, no escape

Score twelve applicants. Group A scores $[45, 55, 62, 70, 76, 84]$ and group B scores $[68, 82, 88, 93, 97, 102]$. Apply one shared cutoff at 80, the individual-fairness choice.

Group A passes one of six, the 84, for a rate of $1 / 6 \approx 0.167$. Group B passes five of six, everything except the 68, for $5 / 6 \approx 0.833$. The ratio of the lower rate to the higher is $0.167 / 0.833 = 0.20$, far below the 0.8 four-fifths flag, so group fairness fails loudly. That is the top row of the diagram.

Now force parity at 3 of 6 each. Group A needs its cutoff at 70, passing 70, 76, and 84 for $3 / 6 = 0.50$. Group B needs its cutoff at 93, passing 93, 97, and 102 for $3 / 6 = 0.50$. Rates match, and individual fairness breaks on contact: an applicant scoring 76 passes as a member of A and fails as a member of B, and one scoring 82 does the reverse side of the same trick. Same score, different answer, with the protected attribute as the only difference. That pair is the amber callout in the bottom row. There is no third cutoff that fixes both rows, because the score distributions genuinely differ.

Code

Two threshold policies on the same twelve scores, in plain Python. One shared cutoff treats equal scores equally and splits the rates; per-group cutoffs equalize the rates and split equal scores.

1scores_a: list[int] = [45, 55, 62, 70, 76, 84]2scores_b: list[int] = [68, 82, 88, 93, 97, 102]3
4shared: int = 805pass_a: int = sum(1 for s in scores_a if s >= shared)6pass_b: int = sum(1 for s in scores_b if s >= shared)7print(f"{pass_a}/6 {pass_b}/6")  # -> 1/6 5/68
9cut_a: int = 7010cut_b: int = 9311par_a: int = sum(1 for s in scores_a if s >= cut_a)12par_b: int = sum(1 for s in scores_b if s >= cut_b)13print(f"{par_a}/6 {par_b}/6")  # -> 3/6 3/614
15split_76: tuple[int, int] = (1 if 76 >= cut_a else 0, 1 if 76 >= cut_b else 0)16print(split_76)  # -> (1, 0)

The outputs match the hand counts: 1 of 6 against 5 of 6 under one cutoff, 3 and 3 under split cutoffs, and a score of 76 that passes in A and fails in B.

Watch Out For

The Quick Version

• Individual fairness gives similar people similar outcomes under one shared rule.
• Group fairness gives groups equal rates, most simply demographic parity at equal selection probabilities.
• One cutoff at 80 on our twelve scores passes 1 of 6 in group A and 5 of 6 in group B, a ratio of 0.20.
• Forcing 3 and 3 needs cutoffs at 70 and 93, so a score of 76 passes in one group and fails in the other.
• Deleting the protected column does not fix this, because stand-in features rebuild it.
• Pick the definition that matches the stakes and document the choice, since the math forbids satisfying all of them.

What to Read Next

• AI Fairness
• Disparate Impact in AI Models
• Model Auditing