Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
The Core of Approval-Based Committee Elections with Few Seats
Authors: Dominik Peters
IJCAI 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | These results are obtained with the help of computer search using linear programs. The computations establishing Theorem 5.3 can be verified based on Farkas certificates: the code repository includes, for each history and each possible extension of the history that induces an infeasible system of linear inequalities, a Farkas witness. |
| Researcher Affiliation | Academia | Dominik Peters CNRS, LAMSADE, Universit e Paris Dauphine PSL EMAIL |
| Pseudocode | Yes | Algorithm 1 Recursive PAV rule Algorithm 2 Finding all histories |
| Open Source Code | Yes | Code for these tasks is available at https://github.com/DominikPeters/core-few-candidates/. |
| Open Datasets | No | The paper focuses on theoretical proofs of existence for core committees using computational search with linear programs based on constructed 'profiles' of voter preferences, rather than analyzing external, publicly available datasets. |
| Dataset Splits | No | The paper does not involve traditional datasets that would require training, test, or validation splits. Its methodology relies on theoretical analysis and computational searches on abstract voter profiles. |
| Hardware Specification | Yes | Gurobi solves m=7, k=5, in 450s, but did not solve m=7, k=4 after 134 000s (37h) on 8 cores. Verifying their validity using a simple script [available on Git Hub] that performs exact fractional computations (without calling a solver) takes about 4 hours on 8 cores |
| Software Dependencies | No | I have used Gurobi and the cvc5 solver [Barbosa et al., 2022] in this work. However, specific version numbers for these solvers are not provided. |
| Experiment Setup | Yes | We show via linear programs that PAV always selects a core-stable committee when k <= 7, and that it always selects at least one core-stable committee when k= 8. The optimal solutions to all these programs is 1/4. The optimal solutions to these two programs are 1/12. By running Algorithm 2 for m=15 and k=9, . . . , 13, we obtain the following result. |