New FJR+ algorithm ensures fair AI committee elections in polynomial time
FJR+ verifies fairness of AI-elected committees 100x faster than old methods...
Computer scientist Nicholas Teh has developed FJR+ (Full Justified Representation+), a significant advancement in proportionality axioms for approval-based committee elections. This new algorithm addresses the coNP-complete verification challenge of traditional FJR, which required exponential time to verify fairness in AI-elected committees. FJR+ introduces a polynomial-time verifiable and satisfiable solution that strengthens existing FJR and EJR+ models.
The core innovation lies in the Residual-Budget Greedy (RBG) algorithm, which selects partial committees such that every size-k completion satisfies FJR+. This enables sequential Phragmén to achieve priceable completions while maintaining FJR+ compliance and the sub-core property. The solution also extends to approval-based participatory budgeting with arbitrary project costs, offering a Droop-quota version of FJR+ and a project-specific RBG variant that computes these properties in polynomial time.
- FJR+ is a strict strengthening of FJR and EJR+ that verifies fairness in polynomial time, unlike traditional FJR (coNP-complete)
- Residual-Budget Greedy (RBG) algorithm enables priceable completions that always satisfy FJR+ and the sub-core
- Extends to approval-based participatory budgeting with arbitrary project costs via project-specific RBG variant
Why It Matters
This breakthrough ensures AI-elected committees are fair and verifiable in real-world applications like AI governance and participatory budgeting.