arXiv AI

MILP the Gap: An Automated Reasoning Approach to Condorcet's Paradox

arXiv AI
Sep 28

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.

By Noam Hazon, Leora Schmerler, Nicholas Teh
arXiv AI
Oct 2

Query-efficient winner prediction in district-based elections

The paper studies how to predict the winner of a district‑based election using as few queries to individual votes as possible. It introduces an adaptive randomized algorithm that, for any number of candidates and any error tolerance, correctly predicts the overall winner with probability at least 1‑δ using ≥O(1/ε² log m/δ log 1/δ) queries. This improves previous results for two candidates and balanced districts, and nearly matches a proven lower bound for constant‑size candidate sets.

By Koustav De, Debajyoti Kar, Swagato Sanyal
arXiv AI
Aug 26

Rules Before Oracles: Auditable, User-Configurable Argument Selection for Deliberative Polling

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.

By Muntaser Syed, Markus Zanker, Marius Silaghi
arXiv AI
Sep 10

Improving Randomized Metric Distortion to 2.1441

The paper announces an improved upper bound on the distortion of randomized voting rules in metric social choice, reducing it from the previous range of $[2.1126,2.5]$ to $2.1441$. It introduces the concept of random-size stable lotteries, proves their existence, and derives the new bound via a potential argument. The proofs were generated with GPT-5.6-Sol and subsequently verified and simplified by the author.

By Nisarg Shah
arXiv AI
Oct 2

Outer Diversity of Condorcet Domains

The paper investigates the outer diversity of Condorcet domains, which are sets of rankings ensuring a transitive majority relation for elections with an odd number of votes from the domain. It defines outer diversity as the expected swap distance from a random vote to the nearest domain vote and provides numerical analyses for maximal domains with few candidates. The authors also derive asymptotic behaviors for several special domains, yielding theoretical insights into this measure.

By Piotr Faliszewski, Jan Jabrocki, Mateusz S{\l}uszniak, Krzysztof Sornat, Stanis{\l}aw Szufa, Tomasz W\k{a}s