arXiv subjects

Sheldon H. Jacobson

Publications and source records attributed to Sheldon H. Jacobson.

4 recordsLinked to original sources

arXiv2026

Simpler Than You Think: The Practical Dynamics of Ranked Choice Voting

Ranked Choice Voting (RCV) adoption is expanding across U.S. elections, but faces persistent criticism for complexity, strategic manipulation, and ballot exhaustion. We empirically test these concerns on real election data, across three diverse contexts: New York City's 2021 Democratic primaries (54 races), Alaska's 2024 primary-infused statewide elections (52 races), and Portland's 2024 multi-winner City Council elections (4 races). Our algorithmic approach circumvents computational complexity barriers by reducing election instance sizes (via candidate elimination). Our findings reveal that despite its intricate multi-round process and theoretical vulnerabilities, RCV consistently exhibits simple and transparent dynamics in practice, closely mirroring the interpretability of plurality elections. Following RCV adoption, competitiveness increased substantially compared to prior plurality elections, with average margins of victory declining by 9.2 percentage points in NYC and 11.4 points in Alaska. Empirically, complex ballot-addition strategies are not more efficient than simple ones, and ballot exhaustion has minimal impact, altering outcomes in only 3 of 110 elections. These findings demonstrate that RCV delivers measurable democratic benefits while proving robust to ballot-addition manipulation, resilient to ballot exhaustion effects, and maintaining transparent competitive dynamics in practice. The computational framework offers election administrators and researchers tools for immediate election-night analysis and facilitating clearer discourse around election dynamics.

cs.CY↗

arXiv2026

Strategic AI in Cournot Markets

As artificial intelligence increasingly automates decision-making in competitive markets, understanding the resulting dynamics and ensuring fair market mechanisms is essential. We investigate the multi-faceted decision-making of large language models (LLMs) in oligopolistic Cournot markets, showing that LLMs not only grasp complex market dynamics--demonstrating their potential as effective economic planning agents--but also engage in sustained tacit collusion, driving prices up to 200% above Nash equilibrium levels. Our analysis examines LLM behavior across three dimensions-(1) decision type, (2) opponent strategies, and (3) market composition--revealing how these factors may shape the competitiveness of LLM-based decision-makers. Furthermore, we show that regulating a few dominant agents by enforcing best-response strategies effectively disrupts collusion and helps restore competitive pricing. Our findings identify potential concerns associated with AI integration in competitive market environments and provide regulatory policy recommendations for the era of automation.

cs.GT↗

arXiv2024

Highly Connected Graph Partitioning: Exact Formulation and Solution Methods

Graph partitioning (GP) and vertex connectivity have traditionally been two distinct fields of study. This paper introduces the highly connected graph partitioning (HCGP) problem, which partitions a graph into compact, size balanced, and $Q$-(vertex) connected parts for any $Q\geq 1$. This problem is valuable in applications that seek cohesion and fault-tolerance within their parts, such as community detection in social networks and resiliency-focused partitioning of power networks. Existing research in this fundamental interconnection primarily focuses on providing theoretical existence guarantees of highly connected partitions for a limited set of dense graphs, and do not include canonical GP considerations such as size balance and compactness. This paper's key contribution is providing a general modeling and algorithmic approach for HCGP, inspired by recent work in the political districting problem, a special case of HCGP with $Q=1$. This approach models $Q$-connectivity constraints as mixed integer programs for any $Q\geq 1$ and provides an efficient branch-and-cut method to solve HCGP. When solution time is a priority over optimality, this paper provides a heuristic method specifically designed for HCGP with $Q=2$. A computational analysis evaluates these methods using a test bed of instances from various real-world graphs. In this analysis, the branch-and-cut method finds an optimal solution within one hour in $82.8\%$ of the instances solved. For $Q=2$, small and sparse instances are challenging for the heuristic, whereas large and sparse instances are challenging for the exact method. Furthermore, this study quantifies the computational cost of ensuring higher connectivity using the branch-and-cut approach, compared to a baseline of ensuring $1$-connectivity. Overall, this work serves as an effective tool to partition a graph into resilient and cohesive parts.

cs.DM↗

arXiv2015

Solving the Pricing Problem in a Branch-and-Price Algorithm for Graph Coloring using Zero-Suppressed Binary Decision Diagrams

Branch-and-price algorithms combine a branch-and-bound search with an exponentially-sized LP formulation that must be solved via column generation. Unfortunately, the standard branching rules used in branch-and-bound for integer programming interfere with the structure of the column generation routine; therefore, most such algorithms employ alternate branching rules to circumvent this difficulty. This paper shows how a zero-suppressed binary decision diagram (ZDD) can be used to solve the pricing problem in a branch-and-price algorithm for the graph coloring problem, even in the presence of constraints imposed by branching decisions. This approach facilitates a much more direct solution method, and can improve convergence of the column generation subroutine.

cs.DS↗