Disparate Impact (DI)
The difference in positive proportions in the predicted labels metric can be assessed in the form of a ratio.
The comparison of positive proportions in predicted labels metric can be assessed in the form of a ratio instead of as a difference, as it is with the Difference in Positive Proportions in Predicted Labels (DPPL). The disparate impact (DI) metric is defined as the ratio of the proportion of positive predictions (y’ = 1) for facet a over the proportion of positive predictions (y’ = 1) for facet d. For example, if the model predictions grant loans to 60% of a middleaged group (facet a) and 50% other age groups (facet d), then DI = .5/.6 = 0.8, which indicates a positive bias and an adverse impact on facet d.
The formula for the ratio of proportions of the predicted labels:
DI = q'_{d}/q'_{a}
Where:

q'_{a} = n'_{a}^{(1)}/n_{a} is the predicted proportion of facet a who get a positive outcome of value 1. In our example, the proportion of a middleaged facet predicted to get granted a loan. Here n'_{a}^{(1)} represents the number of members of facet a who get a positive predicted outcome and n_{a} the is number of members of facet a.

q'_{d} = n'_{d}^{(1)}/n_{d} is the predicted proportion of facet d a who get a positive outcome of value 1. In our example, a facet of older and younger people predicted to get granted a loan. Here n'_{d}^{(1)} represents the number of members of facet d who get a positive predicted outcome and n_{d} the is number of members of facet d.
For binary, multicategory facet, and continuous labels, the DI values range over the interval [0, ∞).

Values less than 1 indicate that facet a has a higher proportion of predicted positive outcomes than facet d. This is referred to as positive bias.

A value of 1 indicates demographic parity.

Values greater than 1 indicate that facet d has a higher proportion of predicted positive outcomes than facet a. This is referred to as negative bias.