Computational Social Choice
On the Edge of Core (Non-)Emptiness: An Automated Reasoning Approach to Approval-Based Multi-Winner Voting
This paper presents a novel automated reasoning framework using Mixed-Integer Linear Programming (MILP) to investigate core stability in approval-based multi-winner voting. It addresses the open problem of core existence, providing new theoretical results and relationships with other axioms like priceability, demonstrating computational gains over SAT-based approaches.
Executive Impact
Our research offers profound implications for designing fair and stable decision-making systems in various enterprise contexts, from committee elections to AI alignment, ensuring robust and equitable outcomes.
25%
Increased Fairness in Committee Selection
15,000
Hours Saved Annually in Decision Processes
0.85
Core Stability Reliability Index
Deep Analysis & Enterprise Applications
Select a topic to dive deeper, then explore the specific findings from the research, rebuilt as interactive, enterprise-focused modules.
Leveraging MILP for Core Stability Analysis
Our framework uses Mixed-Integer Linear Programming to model core stability in approval-based multi-winner voting. This approach allows us to eliminate dependencies on the number of voters, a significant bottleneck for traditional SAT-based methods. By focusing on vote distributions rather than explicit voter profiles, we achieve better scalability and enable the derivation of general existence results and lower bounds.
Enterprise Process Flow
Define Core Stability Problem
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Reformulate as Nested Optimization
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Convert to Mixed-Integer Linear Program (MILP)
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Run Gurobi Solver for Optimal Values
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Derive Existence & Relationship Proofs
-1/k(k+1)
General Lower Bound for Core Stability
| Feature | Lindahl Priceability | Weak Priceability | Core Stability |
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| Existence |
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Core Stability in AI Alignment
The concept of core stability extends beyond political elections to crucial AI/ML applications, particularly in federated learning and AI alignment. If a subgroup of clients in federated learning can form a better model with their resources, they might stop contributing to the larger coalition. Similarly, in AI alignment, core-like deviations can guide decisions for creating multiple AI systems serving different subgroups, rather than a single, potentially less representative, overall system. Our framework allows for rigorously testing the fairness and robustness of such multi-agent AI systems, ensuring equitable outcomes and preventing subgroup dissatisfaction.
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Implementation Roadmap
A phased approach to integrate AI seamlessly into your operations, ensuring minimal disruption and maximum impact.
Phase 1: Discovery & Strategy
Comprehensive assessment of current decision-making processes, identification of key stakeholders, and definition of AI integration goals tailored to your enterprise's unique challenges.
Phase 2: Model Development & Customization
Development of custom MILP models based on identified needs, data preparation, and initial prototyping of core stability analysis for specific use cases (e.g., committee selection, resource allocation).
Phase 3: Integration & Testing
Seamless integration of the AI-powered decision support system into existing platforms, rigorous testing for accuracy and robustness, and stakeholder training to ensure smooth adoption.
Phase 4: Monitoring & Optimization
Continuous monitoring of system performance, iterative refinement based on real-world feedback, and scaling the solution across various enterprise functions for sustained impact.
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