Fair Committee Selection under Ordinal Preferences and Limited Cardinal Information

Ameet Gadekar, Aristides Gionis, Suhas Thejaswi, Sijing Tu

Keywords: ordinal fair k-center, k-committee selection, metric distortion

Abstract:

We study the problem of fair $k$-committee selection under an egalitarian objective. Given $n$ agents partitioned into $m$ groups (e.g., demographic quotas), the goal is to aggregate their preferences to form a diverse committee of size $k$ that guarantees minimum representation from each group while minimizing the maximum cost incurred by any agent.
We model this setting as the ordinal fair $k$-center problem, where agents are embedded in an unknown metric space, and each agent reports a complete preference ranking (i.e., ordinal information) over all agents, consistent with the underlying distance metric (\ie, cardinal information). The quality of a solution is evaluated via the distortion metric, which measures the worst-case approximation compared to the optimal solution that has complete access to the underlying metric space.

When cardinal information is not available, no constant distortion is possible for the ordinal $k$-center problem, even without fairness, when $k\geq 3$ [Burkhardt et.al., AAAI'24].
To overcome this hardness, we allow limited access to cardinal information by querying the metric space. In this setting, our main contribution is a factor-$5$ distortion algorithm that requires only $O(k \log^2 k)$ queries. Along the way, we present an improved factor-$3$ distortion algorithm using
$O(k^2)$
queries.

Area: Game Theory and Economic Paradigms (GTEP)

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Submission Number: 1026