Corrigendum to "An Information-Flow Perspective on Algorithmic Fairness"

Following up on the publication of our AAAI 2024 paper “An Information-Flow Perspective on Algorithmic Fairness”, Marco Favier kindly notified us about a mistake in our publication:
Section 3.2, in particular Lemma 2, states that Restricted Information Flow can be used to prove conditional demographic parity. This Lemma is wrong, as there exists a counterexample (provided by Marco Favier): For $G=\left\{A,B\right\}$ and $U=\left\{0,1\right\}$ both uniformly distributed, we could analyze Restricted Information Flow w.r.t. the restricted classification $R\left(A,0\right)=R\left(B,1\right)=0$ and $R\left(A,1\right)=R\left(B,0\right)=1$. In this case, we can show noninterference for the following program:

1. Jan 0001