The paper focuses on finding fair (according to demographic parity) representations in multitask settings, which is indeed an interesting problem of the fair ML community. The paper is well written and the contributions are signifiant. That said, as pointed out by the reviewers in the (post-rebuttal updated) feedback, the paper could significantly increase its impact and contributions with a more thorough experimental evaluation, and additional theoretical results addressing the model performance on new tasks (although such extension could be also studied in future work). I encourage the authors to incorporate the reviewers' feedback in the revised version of the paper, which should especially clarify the distinction of shifts in (X, Y) vs P(Y | X, S) (see comments by R1 and R2).