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comparison is made against the overall population of that city. The extended lift of
such a rule can be read as the ratio of the refusal rate of black people in the ZIP
over the mean refusal rate of the whole city. A lower bound for the confidence p 1 of
the classification rule (
) can be obtained as p 1
γ ) / β =
9875 (for details, see Ruggieri et al., 2010a). Intuitively, even in the extreme case
that the whole 1% of people in the area who were admitted are blacks, the ratio
of un-admitted blacks cannot be lower than 98.75%. By knowing that the average
admission rate for the generality of people from Liverpool is 9%, the lower bound
for the elift measure of (
97 - and extremely high
ratio stating that black people from that area had at least 10.97 times the average
chance (of a Liverpool applicant) of seeing their application refused.
We conclude by mentioning that the redlining inference strategy is one possible
inference reasoning for deducing unknown discriminatory effects from observed,
apparently non-discriminatory, ones. Additional inference strategies are proposed
in (Ruggieri et al., 2010a). In general, an inference strategy consists of deriving
lower bounds for a discrimination measure of an unavailable PD rule starting from:
assumptions on the form of the premise of the rule; and some background knowl-
edge, which in our framework is coded in the form of association rules. The situation
resembles here what occurs in privacy-preserving data mining (Agrawal & Srikant,
2000; Sweeney, 2001), where coupling an anonymized dataset with external knowl-
edge might allow for the inference of the identity of individuals through some attack
)is p 1
Consider a PD classification rule denying some benefit:
that has been unveiled, either directly or indirectly. In a case before a court,
such a rule supports the complainant position if she belongs to the disadvantaged
group A , she satisfies the context conditions B and the rule is a -directly dis-
criminatory where a is a threshold stated in law, regulations or past sentences.
Showing that no rule satisfies those conditions supports the respondent position.
However, this is an exceptional case. When one or more such rules exist, the
respondent is then required to prove that the “provision, criterion or practice is ob-
jectively justified by a legitimate aim and the means of achieving that aim are ap-
propriate and necessary” (see Ellis, 2005). A typical example in the literature is the
one of the “genuine occupational requirement”, also called “business necessity” by
the (U.S. Federal Legislation, 2011, (f)). For instance, assume that the complainant
claims for discrimination against women among applicants to a job position. A clas-
sification rule SEX = FEMALE , CITY =NYC
HIRE = NO with high extended lift
supports her position. The respondent might argue that the rule is an instance of a
more general rule DRIVE TRUCK = FALSE , CITY =NYC
HIRE = NO .Sucharule
is legitimate, since the requirement that prospect workers are able to drive trucks
can be considered a genuine occupational requirement (for some specific job). Let
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