  The increasing application of machine learning techniques in everyday
decision-making processes has brought concerns about the fairness of
algorithmic decision-making. This paper concerns the problem of collider bias
which produces spurious associations in fairness assessment and develops
theorems to guide fairness assessment avoiding the collider bias. We consider a
real-world application of auditing a trained classifier by an audit agency. We
propose an unbiased assessment algorithm by utilising the developed theorems to
reduce collider biases in the assessment. Experiments and simulations show the
proposed algorithm reduces collider biases significantly in the assessment and
is promising in auditing trained classifiers.
