Polynomial-Time Algorithm for Thiele Voting Rules with Voter Interval Preferences
We present a polynomial-time algorithm for computing an optimal committee of size $k$ under any given Thiele voting rule for elections on the Voter Interval domain (i.e., when voters can be ordered so that each candidate is approved by a consecutive voters). Our result extends to the Generalized Thiele rule, in which each voter has an individual weight (scoring) sequence. This resolves a 10-year-old open problem that was originally posed for Proportional Approval Voting and later extended to every Thiele rule (Elkind and Lackner, IJCAI 2015; Peters, AAAI 2018). Our main technical ingredient is a new structural result -- a concavity theorem for families of intervals. It shows that, given t...
| Authors | Pasin Manurangsi, Krzysztof Sornat |
|---|---|
| Primary category | cs.GT |
| Published | 7 April 2026 |
| Last updated at source | 7 April 2026 |
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