Generalizing the Approval-Weighted Veto Core Tradeoff

Construct natural collective-consent solution concepts that interpolate between proportional veto power for small coalitions and a super-majority approval threshold of two-thirds, analogously to the Approval-Weighted Veto Core's interpolation between proportional veto power and majority threshold.

Background

The Approval-Weighted Veto Core (AWVC) is introduced as a Goldilocks solution concept: its veto power is close to proportional for small coalitions while it guarantees a majority approval threshold as coalitions approach half of the electorate. The authors explicitly leave unresolved whether comparable natural concepts exist for other target approval thresholds, giving a two-thirds super-majority threshold as an example.

References

Fourth, while AWVC naturally interpolates between $v(s) = \frac sn$ veto power for small $s$ and majority threshold for $s$ close to $\frac n2$, it remains open whether there are natural concepts that do the same for other parameter choices, for example, a super-majority threshold of $\frac 23$.

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