On the Edge of Core (Non-)Emptiness: An Automated Reasoning Approach to Approval-Based Multi-Winner Voting
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908720420618240 |
|---|---|
| author | Berker, Ratip Emin Tewolde, Emanuel Conitzer, Vincent Guo, Mingyu Heule, Marijn Xia, Lirong |
| author_facet | Berker, Ratip Emin Tewolde, Emanuel Conitzer, Vincent Guo, Mingyu Heule, Marijn Xia, Lirong |
| contents | Core stability is a natural and well-studied notion for group fairness in multi-winner voting, where the task is to select a committee from a pool of candidates. We study the setting where voters either approve or disapprove of each candidate; here, it remains a major open problem whether a core-stable committee always exists. In this work, we develop an approach based on mixed-integer linear programming for deciding whether and when core-stable committees are guaranteed to exist. In contrast to SAT-based approaches popular in computational social choice, our method can produce proofs for a specific number of candidates independent of the number of voters. In addition to these computational gains, our program lends itself to a novel duality-based reformulation of the core stability problem, from which we obtain new existence results in special cases. Further, we use our framework to reveal previously unknown relationships between core stability and other desirable properties, such as notions of priceability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16895 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Edge of Core (Non-)Emptiness: An Automated Reasoning Approach to Approval-Based Multi-Winner Voting Berker, Ratip Emin Tewolde, Emanuel Conitzer, Vincent Guo, Mingyu Heule, Marijn Xia, Lirong Computer Science and Game Theory 91B12, 91B14, 68Q25, 68T01, 68V05, 90C11 F.2; I.2; J.4 Core stability is a natural and well-studied notion for group fairness in multi-winner voting, where the task is to select a committee from a pool of candidates. We study the setting where voters either approve or disapprove of each candidate; here, it remains a major open problem whether a core-stable committee always exists. In this work, we develop an approach based on mixed-integer linear programming for deciding whether and when core-stable committees are guaranteed to exist. In contrast to SAT-based approaches popular in computational social choice, our method can produce proofs for a specific number of candidates independent of the number of voters. In addition to these computational gains, our program lends itself to a novel duality-based reformulation of the core stability problem, from which we obtain new existence results in special cases. Further, we use our framework to reveal previously unknown relationships between core stability and other desirable properties, such as notions of priceability. |
| title | On the Edge of Core (Non-)Emptiness: An Automated Reasoning Approach to Approval-Based Multi-Winner Voting |
| topic | Computer Science and Game Theory 91B12, 91B14, 68Q25, 68T01, 68V05, 90C11 F.2; I.2; J.4 |
| url | https://arxiv.org/abs/2512.16895 |