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The previous works would correct the decision making in such a way that males and
females would get on average the same income, say $ 20,000, leading to a reverse
discrimination as it would result in male employees being assigned a lower salary
than female for the same amount of working hours. In many real world cases, if the
difference in the decisions can be justified, it is not considered as illegal discrimina-
tion. Moreover, making the probabilities of acceptance equal for both would lead to
favoring the group which is being deprived, in this example females.
Ta b l e 8 . 1
Summary statistics of the Adult dataset (Asuncion and Newman, 2007)
hours per week annual income (K$)
female
36.4
10.9
male
42.4
30.4
all data
40.4
23.9
8.2.3
Discrimination in Decision Making
To analyze the effects of discrimination and design discrimination-free learning
techniques, a model describing how discrimination happens needs to be assumed.
We consider that discrimination happens in the following way in relation to ex-
perimental findings reported in (Hart, 2005). The historical data originates from
decision making by human experts. First the qualifications of a candidate are eval-
uated and a preliminary score is obtained. The qualifications are evaluated objec-
tively. Then the score is corrected with a discrimination bias by looking at, e.g.,
the gender of a candidate and either adding or subtracting a fixed (the same) bias
from the qualification score. The final acceptance decision is made by comparing
the score to a fixed acceptance threshold. If the score is higher than the threshold
then the candidate is accepted.
This discrimination model has two important implications. First, the decision bias
is more likely to affect the individuals whose objective score is close to the decision
threshold. If an individual has very good qualifications, adding or subtracting the
discriminatory bias would not change the acceptance decision.
Second, there may be attributes within the training data, however, that objectively
explain the score, but at the same time are correlated with the sensitive attribute.
When observing the decisions it would seem due to correlation that the decision
is using the sensitive attribute. Next we discuss how to quantify, which part of the
difference in decision across the sensitive groups is explainable and which is due to
discrimination bias.
It is important to mention here that this discrimination model does not guarantee
to cover the all possible scenarios that lead to discrimination, however, it covers the
most important and typical scenario.
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