Table 1 Summary table of fairness... | Emerald Publishing

Table 1

Summary table of fairness standard definition

Fairness criterion	Definition and calculation formula of fairness standard
Demographic Parity, its essence is the comparison between $P (\hat{Y} \| S = 0)$ and $P (\hat{Y} \| S = 1) .$	(1) If the predicted value Y satisfies $P (\hat{Y} \| S = 0) = P (\hat{Y} \| S = 1)$ ⁠, then the algorithm achieves demographic parity (2) Or the ratio of the two groups can be compared $\frac{P (\hat{Y} \| S = 0)}{P (\hat{Y} \| S = 1)}$
Individual fairness	If an algorithm predicts the same results for similar individuals, it is said to achieve individual fairness. The calculation method is the same as Demographic Parity, but the refinement is specific to each person
Equality of opportunity	if the predicted value $\hat{Y}$ satisfies $P (\hat{Y} = 1 \| S = 0, Y = 1) = P (\hat{Y} = 1 \| S = 1, Y = 1)$ ⁠,the algorithm achieves equal opportunity. Concretely speaking, S-TPR(True Positive Rate) = $P (\hat{Y} = 1 \| S = s, Y = 1) = \frac{T P}{T P + F N}$
Equality of odds	On the basis of Equality of Opportunity, TNR, FPR and FNR are also required to be equal S-TPR (True Positive Rate) = $P (\hat{Y} = 1 \| S = s, Y = 1) = \frac{T P}{T P + F N}$ S-TNR (True Negative Rate) = $P (\hat{Y} = 0 \| S = s, Y = 0) = \frac{T N}{T N + F P}$ S-FPR (False Positive Rate) = $P (\hat{Y} = 1 \| S = s, Y = 0) = \frac{F P}{T N + F P}$ S-FNR (False Negative Rate) = $P (\hat{Y} = 0 \| S = s, Y = 1) = \frac{F N}{T P + F N}$
Disparate mistreatment	S-FPR + S-FNR = $P (\hat{Y} = 1 \| S = s, Y = 0) + P (\hat{Y} = 0 \| S = s, Y = 1)$ is equal
Predictive rate parity	$P (Y = 1 \| S = s, \hat{Y} = 1) = \frac{T P}{T P + F P}$ is equal

Fairness criterion	Definition and calculation formula of fairness standard
Demographic Parity, its essence is the comparison between $P (\hat{Y} \| S = 0)$ and $P (\hat{Y} \| S = 1) .$	(1) If the predicted value Y satisfies $P (\hat{Y} \| S = 0) = P (\hat{Y} \| S = 1)$ , then the algorithm achieves demographic parity (2) Or the ratio of the two groups can be compared $\frac{P (\hat{Y} \| S = 0)}{P (\hat{Y} \| S = 1)}$
Individual fairness	If an algorithm predicts the same results for similar individuals, it is said to achieve individual fairness. The calculation method is the same as Demographic Parity, but the refinement is specific to each person
Equality of opportunity	if the predicted value $\hat{Y}$ satisfies $P (\hat{Y} = 1 \| S = 0, Y = 1) = P (\hat{Y} = 1 \| S = 1, Y = 1)$ ,the algorithm achieves equal opportunity. Concretely speaking, S-TPR(True Positive Rate) = $P (\hat{Y} = 1 \| S = s, Y = 1) = \frac{T P}{T P + F N}$
Equality of odds	On the basis of Equality of Opportunity, TNR, FPR and FNR are also required to be equalS-TPR (True Positive Rate) = $P (\hat{Y} = 1 \| S = s, Y = 1) = \frac{T P}{T P + F N}$ S-TNR (True Negative Rate) = $P (\hat{Y} = 0 \| S = s, Y = 0) = \frac{T N}{T N + F P}$ S-FPR (False Positive Rate) = $P (\hat{Y} = 1 \| S = s, Y = 0) = \frac{F P}{T N + F P}$ S-FNR (False Negative Rate) = $P (\hat{Y} = 0 \| S = s, Y = 1) = \frac{F N}{T P + F N}$
Disparate mistreatment	S-FPR + S-FNR = $P (\hat{Y} = 1 \| S = s, Y = 0) + P (\hat{Y} = 0 \| S = s, Y = 1)$ is equal
Predictive rate parity	$P (Y = 1 \| S = s, \hat{Y} = 1) = \frac{T P}{T P + F P}$ is equal

Source(s): Table by authors