What was already known
The voter-interval case was open for Proportional Approval Voting and later for all Thiele rules; earlier tractability results concerned other domains or special rules.
AI involvement
Gemini proposed the retained Lagrangian approach and a concavity proof. Manurangsi and Sornat directed, repaired, verified and generalized the argument.
Gemini generated the two central retained ideas, while the human authors directed the problem, repaired the flawed version and proved the general algorithm.
Importance
Resolves a decade-old winner-determination question for this restricted election domain.
Limitations
Manurangsi and Sornat corrected an initial model error, generalized the concavity proof and verified the final algorithm. The guarantee is specific to voter-interval profiles.
Technical verification
The two named authors explicitly report fully verifying and adapting the model's Lagrangian idea and concavity proof for the final theorem, with a complete proof supplied in the paper. This is source-reported human proof checking, not a machine formalization or a check reproduced here.
Formal checking
Manurangsi and Sornat report fully verifying and adapting the model ideas for the final concavity theorem and polynomial-time algorithm.
- Checker
- Pasin Manurangsi and Krzysztof Sornat
- Scope
- Final concavity theorem and polynomial-time Generalized Thiele algorithm on voter-interval profiles
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The authors explain why the interval concavity theorem repairs the failed model proof and how it yields the Lagrangian algorithm, including the overlap case the model did not handle.
Correction and publication history
Resolves a decade-old winner-determination question for this restricted election domain.
Read this published revision