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Su et al. Intell Robot 2022;2(3):244­74 I http://dx.doi.org/10.20517/ir.2022.17 Page 252

ZipCode ZipCode ZipCode

Race Loan Race Loan Race Loan

Income Income Income
(a) (b) (c)

Figure 5. Two alternative graphs for the loan application system. (a) A causal graph of the loan application system, where Race is the
sensitive attribute and Loan is the decision. (b) A causal graph of the system after removing unresolved discrimination. (c) A causal graph
of the system that is free of proxy discrimination.

4.1.2. Path-specific fairness
The causal effect of sensitive attribute on the outcome can be divided into direct effect and indirect effect, and it
can be deemed fair or discriminatory by an expert. Direct discrimination can be captured by the causal effects
of on transmitted along the direct path from to , while indirect discrimination is measured using the
causal effect of on along causal paths from to that pass through redlining/proxy attributes.

Figure 5(a) represents the causal graph of a simple example of a toy model of loan decision AI model, where
Race is treated as the sensitive attribute and Loan is treated as the decision. Since ZipCode can reflect the in-
formation of Race, ZipCode is a proxy for the sensitive attribute, that is to say, ZipCode is a redline attribute.
Thus, the causal effects spreading along the path Race → Loan are then considered to be direct discrimina-
tion, and the causal effects spreading along the path Race → ZipCode → Loan are considered to be indirect
discrimination. Note that the causal effects spreading along the path Race → Income → Loan are explainable
bias since it is reasonable to deny a loan to an applicant if he (or she) has a low income. That is to say, the
partial difference in loan issuance across different race groups can be explained by the fact that some racial
groups in the collected data tend to be underpaid.

Path-specific effect [10] is a fine-grained assessment of causal effects, that is, it can evaluate the causal effect
transmitted along certain paths. Thus, it is used to distinguish among direct discrimination, indirect discrim-
ination, and explainable bias. For any set of paths , the -specific effect can be computed as below:

+ − − (5)
( ) = ( | ( | , | ¯ )) − ( | ( ))
where ( | , | ¯ ) denotes the distribution of = where the intervention ( ) (i.e., force had ) is only
+
+
−
+
transmitted along path while the intervention ( ) (i.e., actual world = ) is transferred along the other
−
−
paths (denoted by ¯ ). If contains all direct edge from to , ( ) measures the direct discrimination. If
contains all indirect paths from to that pass through redlining/proxy attributes, ( ) evaluates the
indirect discrimination. If contains all indirect paths from to that pass through explaining attributes,
( ) assesses the explainable bias.
4.1.3. No unresolved/proxy discrimination
No unresolved discrimination [28] is a fairness notion which is based on Pearl’s structural causal model frame-
work and aims to detect indirect discrimination. This criterion is satisfied if there is no directed path from the
sensitiveattribute totheoutcome whichisnotblockedbytheresolvingvariables. Aresolvingvariableisany
variable in a causal graph that is influenced by the sensitive attribute to a certain degree but accepted by practi-
tioners as nondiscriminatory, which is very similar to the use of explanatory attributes in the statistics-based
fairness notion. For example, Figure 5 shows three causal graphs of a simple loan example. There exists such
discrimination in the causal graph shown in Figure 5(a) since the effects of Race on Loan can be transmitted
along the causal paths Race → Loan and Race → ZipCode → Loan, while there is no unresolved discrimina-
tion, since the effects of Race on Loan can only be transmitted through resolved attribute Income along Race