Computing or Approximating Infinite-Candidate Veto Cores

Develop algorithms to compute or approximate the entire proportional veto core and disapproval veto-core variants for infinite candidate spaces.

Background

The paper studies the proportional veto core and its approval-sensitive variants, including the Disapproval Veto Core (DVC), as mechanisms for protecting minorities in collective-consent decisions. For finite candidate sets, the paper provides polynomial-time computational procedures based on flow and minimum-cut techniques. The authors explicitly identify the corresponding computational problem for infinite candidate spaces as unresolved, asking for methods that can compute or approximate the complete solution sets rather than merely test individual candidates.

References

Second, an important open problem is the computation or approximation of the entire proportional veto core and DVC-variations for infinite $C$.

— Where Should Society Draw the Line? A Social Choice Approach to Collective Consent  (2609.10759 - Dong et al., 9 Sep 2026) in Section Discussion

The boundary shapes of the sets selected by these concepts appear to be intricate, e.g., for DVC they can be non-convex, so even the question of whether they can be represented concisely is open.

— Where Should Society Draw the Line? A Social Choice Approach to Collective Consent  (2609.10759 - Dong et al., 9 Sep 2026) in Section Discussion