FJR+ Strengthens Proportionality in Committee Elections
A recent paper on arXiv presents FJR+, an enhanced version of the full justified representation (FJR) axiom tailored for approval-based committee elections, which can be verified and fulfilled in polynomial time. The study, titled 'Strengthening Full Justified Representation: Efficient Verification and Computation' (arXiv:2608.11500), examines the Residual-Budget Greedy (RBG) algorithm, demonstrating that it can form a partial committee where every size-k completion adheres to FJR+. This enables the application of sequential Phragmén to achieve a priceable completion. The established rule consistently meets FJR+ and the sub-core requirements, being priceable when at least k candidates are approved. Additionally, the paper introduces a Droop-quota variant of FJR+ and broadens FJR+ to include approval-based participatory budgeting with varying project costs.
Key facts
- FJR+ is a strict strengthening of FJR and EJR+ that can be verified and satisfied in polynomial time.
- The Residual-Budget Greedy (RBG) algorithm selects a partial committee such that every size-k completion satisfies FJR+.
- Sequential Phragmén can be used to obtain a priceable completion.
- The resulting rule always satisfies FJR+ and the sub-core.
- The rule is priceable whenever at least k candidates receive an approval.
- A Droop-quota version of FJR+ is also obtained.
- FJR+ is extended to approval-based participatory budgeting with arbitrary project costs.
- The paper is available on arXiv with identifier 2608.11500.
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- arXiv