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4.2.2. Individual direct discrimination
Individual direct discrimination [29] is a situation testing-based technique [35] guided by the structural causal
model for analyzing the discrimination at the individual level. Situation testing is a legally grounded technique
to detect the discrimination against a target individual by comparing the outcome of the individuals similar
to the target one from both the advantaged group and the disadvantaged one in the same decision process. In
other words, for a target individual , select top- individuals most similar to from the group = (denoted
+
as ) and top- individuals most similar to from the group = (denoted as ), and then perform one-
+
−
−
to-one pairing according to the similarity ranking. The target individual is considered as discriminated if a
significant difference is observed between the rate of positive decisions for all pairs from and (typically,
+
−
higher than fair threshold ). The key issue for implementing situation testing is how to define a distance
function ( , ) to measure similarity between individuals.
′
For the individual direct discrimination criterion, the distance function ( , ) is defined not only by adopting
′
normalized Manhattan distance and overlap measurement but also by incorporating causal inference. Specifi-
cally, givenacausalgraph, onlythevariablesthataredirectparentnodesofthedecisionvariableareconsidered
to compute the similarity between individuals, which are denoted as X = ( ) \ { }. The formal definition
of ( , ) is as follows:
′
|X|
∑
( , ) = | ( , ) · ( , )| (8)
′
′
′

=1
where ( , ) represents the causal effect of each of the selected variables ( ∈ X) on the outcome
′

and ( , ) is a distance function proposed by Luong et al. [36] . Specifically, the normalized Manhattan
′

′
| − |

′
distance is employed for ordinal/interval variables (i.e., ( , ) = , where denotes the differ-

ence between the maximum and minimum of the variable ) and the overlap measurement is employed for
categorical variables (i.e., ( , ) = 0 if = , and ( , ) = 1 otherwise).
′
′
′

For each selected variable , the definition of ( , ) is as follows:
′

′ (9)
( ) = ( | (x)) − ( | ( ,x \ ))

′
where ( | (x)) is the effect of the intervention that forces X to take the set of values x, and ( | ( ,x \

)) is the effect of the intervention that forces to take value and other variables in X to take the same
′

values as x.
4.2.3. Equality of effort
Equality of effort fairness notion [30] detects bias by comparing the effort required to reach the same level of
outcome of individuals from advantaged and disadvantaged groups who are similar to the target individual.
That is to say, given a treatment variable , it quantifies how much this treatment variable should change to
make the individual achieve a certain outcome level in order to address the concerns of whether the efforts
required to achieve the same level of outcome for individuals from the advantaged and disadvantaged groups

are different. Following Rubin’s potential outcome model framework [37] , let be the potential outcome for

individual had been and E[ ] be the expectation of outcome for individual . Then, for individual , the

needed minimal value of treatment variable to achieve -level of outcome is defined as follows:

Ψ ( ) = ∈ E[ ] ⩾ (10)

Unfortunately, is not observable, which results in Ψ ( ) being uncomputable. Situation testing is then

used to estimate it, where the distance function ( , ) of equality of effort is the same as individual direct
′
discrimination mentioned in Section 4.2.2. Let and be the two sets of individuals with = and
+
−
+
= that are similar to the target individual , respectively, and E[ ] be the expected outcome under

−
+