Group Fairness in Committee Selection

In this paper, we study fairness in committee selection problems. We consider a general notion of fairness via stability: A committee is stable if no coalition of voters can deviate and choose a committee of proportional size, so that all these voters strictly prefer the new committee to the existing one. Our main contribution is to extend this definition to stability of a distribution (or lottery) over committees. We consider two canonical voter preference models: the Approval Set setting where each voter approves a set of candidates and prefers committees with larger intersection with this set; and the Ranking setting where each voter ranks committees based on how much she likes her favorite candidate in a committee. Our main result is to show that stable lotteries always exist for these canonical preference models. Interestingly, given preferences of voters over committees, the procedure for computing an approximately stable lottery is the same for both models and therefore extends to the setting where some voters have the former preference structure and others have the latter. Our existence proof uses the probabilistic method and a new large deviation inequality that may be of independent interest.

💡 Research Summary

The paper addresses the problem of fairness in multi‑winner elections (committee selection) by introducing a novel notion of “stability”. A committee S of size K is called stable if no coalition of voters can afford to purchase an alternative committee S′ of proportional size such that every member of the coalition strictly prefers S′ to S. Formally, the coalition’s size must be at least |S′|·K·n, where n is the number of voters, and the coalition must contain at least that many voters who strictly prefer S′ (the capture count V(S, S′)). If this condition holds, S′ “blocks” S, and S is not stable.

Because deterministic stable committees may not exist—especially under the Ranking preference model where cyclic preferences can create unavoidable blocking—the authors extend the concept to randomized outcomes, i.e., lotteries (probability distributions) Δ over committees of size K. A lottery is L‑stable (1 ≤ L ≤ K) if for every committee S′ of size at most L the expected capture count under Δ satisfies
E_{S∼Δ}