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Quota-based fairness mechanisms like the so-called Rooney rule or four-fifthsrule are used in selection problems such as hiring or college admission toreduce inequalities based on sensitive demographic attributes. These mechanismsare often viewed as introducing a trade-off between selection fairness andutility. In recent work, however, Kleinberg and Raghavan showed that, in thepresence of implicit bias in estimating candidates' quality, the Rooney rulecan increase the utility of the selection process.  We argue that even in the absence of implicit bias, the estimates ofcandidates' quality from different groups may differ in another fundamentalway, namely, in their variance. We term this phenomenon implicit variance andwe ask: can fairness mechanisms be beneficial to the utility of a selectionprocess in the presence of implicit variance (even in the absence of implicitbias)? To answer this question, we propose a simple model in which candidateshave a true latent quality that is drawn from a group-independent normaldistribution. To make the selection, a decision maker receives an unbiasedestimate of the quality of each candidate, with normal noise, but whosevariance depends on the candidate's group. We then compare the utility obtainedby imposing a fairness mechanism that we term $\gamma$-rule (it includesdemographic parity and the four-fifths rule as special cases), to that of agroup-oblivious selection algorithm that picks the candidates with the highestestimated quality independently of their group. Our main result shows that thedemographic parity mechanism always increases the selection utility, while any$\gamma$-rule weakly increases it. We extend our model to a two-stage selectionprocess where the true quality is observed at the second stage. We discussmultiple extensions of our results, in particular to different distributions ofthe true latent quality.

On Fair Selection in the Presence of Implicit Variance