arXiv AI
Characterizing Necessary Losers to Explain Tournaments Solutions
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arXiv AI
Aug 25
Characterizing Necessary Losers to Explain Tournaments Losers
arXiv:2608.23446v1 Announce Type: new Abstract: We study the problem of formally explaining why a candidate was not selected by a given tournament rule, by identifying sub-tournaments in which the ca...
arXiv Machine Learning
Sep 22
Algorithmic Collusion and the Complexity of Information-Value-Free Equilibria
arXiv:2609.22757v1 Announce Type: cross Abstract: A (coarse) correlated equilibrium (CE) is information-value-free (IVF) if a player can match the payoff obtained from recommendations by committing t...
arXiv AI
6d ago
Proportional Representation in Temporal Voting with Ranked Preferences
The paper investigates proportional representation in a temporal voting setting where a single candidate is chosen each round and voters submit ranked preferences that may evolve over time. It extends classic proportionality axioms—justified representation (JR), proportional JR (PJR), extended JR (EJR), and proportionality for solid coalitions (PSC)—to accommodate various ways of determining which top-ranked candidates are considered approved, ranging from a fixed common cutoff to individual, round‑specific cutoffs. The authors analyze which axioms can be guaranteed under different informational assumptions about future rounds, showing that while EJR is unattainable, JR, PJR, and PSC can be achieved with a fixed cutoff if all preferences are known in advance; varying cutoffs reduce guarantees, yet PJR can still be achieved efficiently for groups that agree in every round, and PSC can be satisfied without future knowledge. They also demonstrate that checking these axioms is often coNP‑complete, though some stronger axioms may be easier to verify.
arXiv Machine Learning
Sep 3
Towards Solving the Gilbert-Pollak Conjecture via Large Language Models
The paper announces a new lower bound of 0.8559 for the Steiner ratio, improving on the previous 0.824 bound for the Gilbert‑Pollak Conjecture. It introduces an AI system that uses large language models to generate rule‑constrained geometric lemmas, which are then turned into executable verification functions that certify the bound. The approach relies on only thousands of LLM calls, highlighting the feasibility of LLM‑based methods for advanced mathematical research.
arXiv AI
Jun 9
Discovering Expert-Level Nash Equilibrium Algorithms with Large Language Models
arXiv:2508. 11874v2 Announce Type: replace-cross Abstract: Designing polynomial-time algorithms for approximate Nash equilibria (ANE) with provable worst-case guarantees is a fundamental open problem in algorithmic game theory.
arXiv AI
Aug 25
Multi-Winner Voting with Argumentative Ballots
arXiv:2608.23247v1 Announce Type: cross Abstract: We introduce multi-winner voting with argumentative ballots (MVArg) and investigate theoretical properties. As our conceptual contribution, we genera...