Confused by how's C_0, C_1 being calculated in paper

[LittleLittleCloud]

Hi fairlearn team, I am reading this paper and am confused on how C_0, C_1 is calculated for DP in signed_weight function

The generic fomular for C_0 and C_1 is

but for DP, according to paper, it's

Just wondering how's the second term for C_0 disappear and how's C_1's second term being transform to the given format.

Regards

[romanlutz]

Adding @MiroDudik who is one of the authors of the paper.

If I remember this correctly, the function g just evaluates to h(X), so in the C_0 case that 0, and in the C_1 case that's 1. Hence, the entire term on the right is 0.

My personal notes from quite some time ago have this little note (which is not from the paper, but rather my derivation of this result, so take it with a grain of salt):