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: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...
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.
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: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: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...
arXiv:2608. 09586v1 Announce Type: new Abstract: The Independent Chip Model (ICM) converts tournament chips into reference prize equity, and policies are routinely constructed against those values.
arXiv:2608. 09128v1 Announce Type: cross Abstract: LLM agents are increasingly deployed in multi-agent social settings where they must cooperate, negotiate, and adapt to other agents.
The paper proposes a transparent, user‑configurable rule for selecting arguments in deliberative polls, replacing opaque learned rankers. It formalises argument selection over bipolar justification sets, introduces seven civic recommender criteria, and presents a one‑hop reversed endorsement flow rule that meets them. Experiments on 17,000 simulated runs show the rule performs comparably to random on coverage but outperforms other methods on endorsement mass and robustness under adversarial pressure.
arXiv:2609.00706v1 Announce Type: new Abstract: The SAIR Mathematics Distillation Challenge on Equational Theories asks a solver to classify whether one magma identity implies another and, for either...
arXiv:2610.00577v1 Announce Type: cross Abstract: In a district-based election, N voters are partitioned into k districts, and each voter votes for one of m candidates. Each district elects a winner...
arXiv:2609.38375v1 Announce Type: new Abstract: Can a constant number of linear minimizations per round improve on the $T^{3/4}$ regret rate of online Frank-Wolfe on general convex sets? Weibel et al...