Table 2 Fairness evaluation index system...

Table 2

Fairness evaluation index system of marketing algorithm

Algorithm fairness evaluation perspective	Algorithm fairness criteria	Marketing algorithm fairness evaluation index calculation method
Marketing coverage fairness	Equality of Opportunity	${C E O A}_{i} = S - TPR = P (\hat{Y} = 1 \| S = i, Y = 1) = \frac{T P}{T P + F N}$ $CEOD = \sqrt{\sum_{i = 1}^{n} {({C E O A}_{i} - \bar{{C E O A}_{i}})}^{2} / n}$
Marketing coverage fairness	Disparate Mistreatment	${C D M A}_{i} = \frac{S - FPR + S - FNR}{2} = [P (\hat{Y} = 1 \| S = i, Y = 0) + P (\hat{Y} = 0 \| S = i, Y = 1)] / 2 = (\frac{F P}{T N + F P} + \frac{F N}{T P + F N}) / 2$ $CDMD = \sqrt{\sum_{i = 1}^{n} {({C D M A}_{i} - \bar{{C D M A}_{i}})}^{2} / n}$
Marketing intensity fairness	Demographic Parity	${E D P A}_{i} = \frac{\bar{Y (S = i)}}{\bar{Y}}$ ⁠, Y is the amount of red envelopes ${E D P D}_{j} = \sqrt{\sum_{i = 1}^{n} \frac{{({E D P A}_{i} - \bar{{E D P A}_{i}})}^{2}}{n}}$ $EDPD = \frac{{E DP D}_{j} - {E DP D}_{\min}}{{{E DP D}_{\max} - E DP D}_{\min}}$
Marketing intensity fairness	Demographic Parity	${D P J S}_{i j} = JS (S_{i} ‖ S_{j})$ $= \frac{1}{2} K L (S_{i} ‖ \frac{S_{i} + S_{j}}{2}) + \frac{1}{2} K L (S_{j} ‖ \frac{S_{i} + S_{j}}{2})$ $= \frac{1}{2} \sum s_{i} (x) \log \frac{2 s_{i} (x)}{s_{i} (x) + s_{j} (x)} + \frac{1}{2} \sum s_{j} (x) \log \frac{2 s_{j} (x)}{s_{i} (x) + s_{j} (x)}$ $DPJS = \frac{1}{n (n - 1)} \sum_{j} \sum_{i} {D P J S}_{i j}$
Marketing frequency fairness	Demographic Parity	${F D P A}_{i} = \bar{Y (S = i)} / \bar{Y}$ ⁠, Y is the number of times the user gets a red envelope in a period of time ${F DP D}_{j} = \sqrt{\sum_{i = 1}^{n} {({F D P A}_{i} - \bar{{F D P A}_{i}})}^{2} / n}$ $FDPD = \frac{{F DP D}_{j} - {F DP D}_{\min}}{{{F DP D}_{\max} - F DP D}_{\min}}$
Marketing frequency fairness	Demographic Parity	${D P J S}_{i j} = JS (S_{i} ‖ S_{j})$ $= \frac{1}{2} K L (S_{i} ‖ \frac{S_{i} + S_{j}}{2}) + \frac{1}{2} K L (S_{j} ‖ \frac{S_{i} + S_{j}}{2})$ $= \frac{1}{2} \sum s_{i} (x) \log \frac{2 s_{i} (x)}{s_{i} (x) + s_{j} (x)} + \frac{1}{2} \sum s_{j} (x) \log \frac{2 s_{j} (x)}{s_{i} (x) + s_{j} (x)}$ $DPJS = \frac{1}{n (n - 1)} \sum_{j} \sum_{i} {D P J S}_{i j}$

Algorithm fairness evaluation perspective	Algorithm fairness criteria	Marketing algorithm fairness evaluation index calculation method
Marketing coverage fairness	Equality of Opportunity	${C E O A}_{i} = S - TPR = P (\hat{Y} = 1 \| S = i, Y = 1) = \frac{T P}{T P + F N}$ $CEOD = \sqrt{\sum_{i = 1}^{n} {({C E O A}_{i} - \bar{{C E O A}_{i}})}^{2} / n}$
Marketing coverage fairness	Disparate Mistreatment	${C D M A}_{i} = \frac{S - FPR + S - FNR}{2} = [P (\hat{Y} = 1 \| S = i, Y = 0) + P (\hat{Y} = 0 \| S = i, Y = 1)] / 2 = (\frac{F P}{T N + F P} + \frac{F N}{T P + F N}) / 2$ $CDMD = \sqrt{\sum_{i = 1}^{n} {({C D M A}_{i} - \bar{{C D M A}_{i}})}^{2} / n}$
Marketing intensity fairness	Demographic Parity	${E D P A}_{i} = \frac{\bar{Y (S = i)}}{\bar{Y}}$ , Y is the amount of red envelopes ${E D P D}_{j} = \sqrt{\sum_{i = 1}^{n} \frac{{({E D P A}_{i} - \bar{{E D P A}_{i}})}^{2}}{n}}$ $EDPD = \frac{{E DP D}_{j} - {E DP D}_{\min}}{{{E DP D}_{\max} - E DP D}_{\min}}$
Marketing intensity fairness	Demographic Parity	${D P J S}_{i j} = JS (S_{i} ‖ S_{j})$ $= \frac{1}{2} K L (S_{i} ‖ \frac{S_{i} + S_{j}}{2}) + \frac{1}{2} K L (S_{j} ‖ \frac{S_{i} + S_{j}}{2})$ $= \frac{1}{2} \sum s_{i} (x) \log \frac{2 s_{i} (x)}{s_{i} (x) + s_{j} (x)} + \frac{1}{2} \sum s_{j} (x) \log \frac{2 s_{j} (x)}{s_{i} (x) + s_{j} (x)}$ $DPJS = \frac{1}{n (n - 1)} \sum_{j} \sum_{i} {D P J S}_{i j}$
Marketing frequency fairness	Demographic Parity	${F D P A}_{i} = \bar{Y (S = i)} / \bar{Y}$ , Y is the number of times the user gets a red envelope in a period of time ${F DP D}_{j} = \sqrt{\sum_{i = 1}^{n} {({F D P A}_{i} - \bar{{F D P A}_{i}})}^{2} / n}$ $FDPD = \frac{{F DP D}_{j} - {F DP D}_{\min}}{{{F DP D}_{\max} - F DP D}_{\min}}$
Marketing frequency fairness	Demographic Parity	${D P J S}_{i j} = JS (S_{i} ‖ S_{j})$ $= \frac{1}{2} K L (S_{i} ‖ \frac{S_{i} + S_{j}}{2}) + \frac{1}{2} K L (S_{j} ‖ \frac{S_{i} + S_{j}}{2})$ $= \frac{1}{2} \sum s_{i} (x) \log \frac{2 s_{i} (x)}{s_{i} (x) + s_{j} (x)} + \frac{1}{2} \sum s_{j} (x) \log \frac{2 s_{j} (x)}{s_{i} (x) + s_{j} (x)}$ $DPJS = \frac{1}{n (n - 1)} \sum_{j} \sum_{i} {D P J S}_{i j}$

Note(s): Among them, n is the number of categories of sensitive attribute S, i is the population of each category under a certain sensitive attribute, and j is each sensitive attribute

Source(s): Table by authors’

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