Jannik Peters ties metric distortion to undominated committees for better voting
New bounds show size-5 committees can achieve distortion as low as 2.7384
In a new research note posted to arXiv, Jannik Peters (an independent researcher) bridges two well-studied topics in computational social choice: metric distortion and Condorcet winning sets (specifically, undominated committees). The paper, “Two Observations on Metric Distortion and Condorcet Winning Sets,” offers both a necessary and sufficient condition linking the two concepts, building on prior work by Bankhashem et al. (2026).
Peters first shows that any committee that is α-undominated for α ≤ 0.5−Ω(1) automatically achieves a bi-criteria metric distortion strictly less than 3−Ω(1). A direct corollary: a committee of just five members can attain a distortion of at most 2.7384, a concrete improvement over generic bounds. In the other direction, he proves that any committee with bi-criteria distortion strictly less than 3−Ω(1) must be (1−Ω(1))-undominated, creating a tight equivalence. These results clarify the structural relationship between winner-set stability and worst-case utility loss in voting systems.
The work is purely theoretical but has practical implications for designing small committees that are both representative (low distortion) and strategically robust (undominated). It suggests that algorithms seeking undominated committees automatically come with distortion guarantees, and vice versa. The paper is available under arXiv:2606.14144.
- Any α-undominated committee with α ≤ 0.5−Ω(1) has bi-criteria metric distortion strictly below 3, with a specific bound of 2.7384 for size‑5 committees
- Conversely, committees achieving distortion <3−Ω(1) must be (1−Ω(1))-undominated, establishing a tight two-way relationship
- Builds on Bankhashem et al. (2026) and provides explicit asymptotic constants missing in prior work
Why It Matters
Connects two core social choice concepts, enabling provable guarantees for small, stable committees in elections.