Demographic Parity (Statistical Parity)

Demographic parity — also called statistical parity — asks that the decision be independent of the protected attribute:

\[ P(\hat{Y} = 1 \mid A = a) = P(\hat{Y} = 1 \mid A = b) \quad \forall \, a, b \]

If a hiring model interviews 60% of one group and 40% of another, demographic parity is violated. Unlike label-conditioned criteria in the fairness parity family, it does not use the true outcome label. Here A identifies the group and Ŷ=1 denotes a positive decision. The denominator is everyone in the relevant group, not only qualified applicants or selected people.

Equal shares do not identify who benefits

Suppose a process selects 40 of 100 applicants in group A and 80 of 200 in group B. Both selection rates are 40%, so demographic parity holds even though the numbers selected differ. Equal counts would answer another question: selecting 40 people from each group would give rates of 40% and 20%. Define the eligible population and time period before comparing shares.

The parity calculation cannot tell whether the selected applicants are qualified. A policy selecting 40% uniformly at random has a population selection probability of 40% in each group while ignoring qualifications. Independent random draws need not produce exactly equal observed rates in finite samples. A policy selecting exactly 40% from each group can achieve the sample rates by construction. Neither mechanism guarantees useful selections.

This limitation does not make the distributional question unimportant. If an interview is a valuable opportunity, a persistent difference in access deserves investigation even when a model is accurate overall. Conversely, equal interview rates do not establish equal access to application channels, equal treatment during interviews, or equal final hiring rates. The decision stage being measured matters.

How a threshold affects parity

A threshold converts a score into a decision: applicants above the cutoff are selected. Lowering it selects more people; raising it selects fewer. If groups have different score distributions, a common cutoff can produce different selection rates. Group-specific cutoffs can target a common rate when the score distributions and available decision rules permit it. Ties and discrete scores can prevent an exact rate without an additional tie-breaking rule.

Changing the cutoff also changes who is selected. For a calibrated score predicting a desirable outcome, adding lower-scoring people generally lowers expected precision among those selected. That is a consequence of the score and the selected population, not a universal cost of demographic parity. Improvements to measurement, access or model quality may change which trade-offs are feasible. A common cutoff can already satisfy parity if the relevant score distributions agree.

Interpret errors in the context of the action. An extra interview consumes capacity; an unsuitable credit offer can impose financial harm; an unnecessary investigation can burden the person flagged. Even a beneficial allocation has costs and constraints, so false positives are not automatically harmless. Record both access and downstream consequences when evaluating a policy.

Measuring the gap

A difference subtracts one group’s selection rate from another; a ratio divides them. If the rates are 30% and 50%, the difference is 20 percentage points and the lower-to-higher ratio is 0.60. With more than two groups, state the reference or use a clearly defined maximum pairwise gap. If the reference rate is zero, a ratio is undefined; report the counts rather than silently substituting a value.

The US Uniform Guidelines on Employee Selection Procedures use a rate below four-fifths of the highest group’s rate as a rule of thumb for adverse impact. The EEOC guidance explains that the arithmetic is not a legal definition: context, statistical and practical significance, and small samples can change the interpretation. It is an employment-selection rule of thumb, not a universal fairness target. Report each group’s counts, rates and uncertainty alongside any ratio.

Where it belongs

Demographic parity is relevant when the distribution of the outcome is itself what is at stake, when the recorded label is not trustworthy enough to build a criterion on — historical hiring decisions, arrest records, prior approvals — or when a legal standard is framed in terms of selection rates, as the Uniform Guidelines are.

When the concern is missed positives or wrongful flags, equal opportunity and equalized odds ask about the relevant error rates. Demographic parity can also coexist with predictive parity at unequal base rates: if both groups select 20% with precision 50%, different true-positive and false-positive rates can accommodate different prevalences. State the exact combination of criteria before claiming that it cannot be satisfied.

References

• EEOC, Questions and Answers on the Uniform Guidelines — adverse impact
• Hardt, Price & Srebro, Equality of Opportunity in Supervised Learning, NeurIPS 2016
• Kleinberg, Mullainathan & Raghavan, Inherent Trade-Offs in the Fair Determination of Risk Scores, ITCS 2017