About

Eric Pacuit is a professor in the Department of Philosophy at the University of Maryland. His primary research interests are in logic (especially modal logic), social choice theory, game theory, formal and social epistemology, and problems that arise in AI and ethics. His research has been funded by the Natural Science Foundation and a Vidi grant from the Dutch science foundation (NWO).

Research topics

• Computer Science
• Political Science
• Law
• Machine Learning
• Mathematics
• Mathematical economics
• Statistics
• Algorithm

Selected publications

• Stable Voting and the Splitting of Cycles

  Proceedings of the AAAI Conference on Artificial Intelligence · 2026-03-14

  articleOpen access

  Algorithms for resolving majority cycles in preference aggregation have been studied extensively in computational social choice. Several sophisticated cycle-resolving methods, including Tideman's Ranked Pairs, Schulze's Beat Path, and Heitzig's River, are refinements of the Split Cycle (SC) method that resolves majority cycles by discarding the weakest majority victories in each cycle. Recently, Holliday and Pacuit proposed a new refinement of Split Cycle, dubbed Stable Voting, and a simplification thereof, called Simple Stable Voting (SSV). They conjectured that SSV is a refinement of SC whenever no two majority victories are of the same size. In this paper, we prove the conjecture up to 6 alternatives and refute it for more than 6 alternatives. While our proof of the conjecture for up to 5 alternatives uses traditional mathematical reasoning, our 6-alternative proof and 7-alternative counterexample were obtained with the use of SAT solving. The SAT encoding underlying this proof and counterexample is applicable far beyond SC and SSV: it can be used to test properties of any voting method whose choice of winners depends only on the ordering of margins of victory by size.

  PublisherDOI

• Stable Voting and the Splitting of Cycles

  Open MIND · 2026-01-07

  otherOpen access

  Algorithms for resolving majority cycles in preference aggregation have been studied extensively in computational social choice. Several sophisticated cycle-resolving methods, including Tideman's Ranked Pairs, Schulze's Beat Path, and Heitzig's River, are refinements of the Split Cycle (SC) method that resolves majority cycles by discarding the weakest pairwise majority victories in each cycle. Recently, Holliday and Pacuit proposed a new refinement of Split Cycle, dubbed Stable Voting, and a simplification thereof, called Simple Stable Voting (SSV). They conjectured that SSV is a refinement of SC whenever no two pairwise majority victories are of the same size. In this paper, we prove the conjecture up to 6 alternatives and refute it for more than 6 alternatives. While our proof of the conjecture for up to 5 alternatives uses traditional mathematical reasoning, our 6-alternative proof and 7-alternative counterexample were obtained with the use of SAT solving. The SAT encoding underlying this proof and counterexample is applicable far beyond SC and SSV: it can be used to test properties of any voting method whose choice of winners depends only on the ordering of margins of victory between alternatives by size.

  OA PDFDOI

• An extension of May’s Theorem to three alternatives: axiomatizing Minimax voting

  Social Choice and Welfare · 2025-06-13 · 1 citations

  articleOpen accessSenior authorCorresponding

  Abstract May’s Theorem [K. O. May, Econometrica 20 (1952) 680-684] characterizes majority voting on two alternatives as the unique preferential voting method satisfying several simple axioms. Here we show that by adding some desirable axioms to May’s axioms, we can uniquely determine how to vote on three alternatives (setting aside tiebreaking). In particular, we add two axioms stating that the voting method should mitigate spoiler effects and the so-called strong no show paradox . We prove a theorem stating that any preferential voting method satisfying our enlarged set of axioms, which includes some weak homogeneity and preservation axioms, must choose from among the Minimax winners in all three-alternative elections. When applied to more than three alternatives, our axioms also distinguish Minimax from other known voting methods that coincide with or refine Minimax for three alternatives.

  PublisherOA PDFDOI

• Learning to Manipulate Under Limited Information

  Proceedings of the AAAI Conference on Artificial Intelligence · 2025-04-11 · 1 citations

  articleOpen accessSenior author

  By classic results in social choice theory, any reasonable preferential voting method sometimes gives individuals an incentive to report an insincere preference. The extent to which different voting methods are more or less resistant to such strategic manipulation has become a key consideration for comparing voting methods. Here we measure resistance to manipulation by whether neural networks of varying sizes can learn to profitably manipulate a given voting method in expectation, given different types of limited information about how other voters will vote. We trained over 100,000 neural networks of 26 sizes to manipulate against 8 different voting methods, under 6 types of limited information, in committee-sized elections with 5-21 voters and 3-6 candidates. We find that some voting methods, such as Borda, are highly manipulable by networks with limited information, while others, such as Instant Runoff, are not, despite being quite profitably manipulated by an ideal manipulator with full information. For the three probability models for elections that we use, the overall least manipulable of the 8 methods we study are Condorcet methods, namely Minimax and Split Cycle.

  PublisherOA PDFDOI

• The irrationality of the California gubernatorial recall system

  The Mathematics Enthusiast · 2025-09-09

  articleOpen accessSenior author

  We analyze California’s gubernatorial recall system using basic ideas from the mathematical theory of social choice. We expose some pathologies of the system, use computer simulations to explore how often these pathologies might occur, investigate the effects of strategic voting on the analysis, and suggest changes to the system that cure the pathologies.

  PublisherOA PDFDOI

• pref_voting: The Preferential Voting Tools package for Python

  The Journal of Open Source Software · 2025-01-28 · 2 citations

  articleOpen accessSenior author

  and for practical applications of the theory.The basic problem of voting theory concerns how to combine "inputs" from multiple individual voters into a single social "output".For example, a common type of input from each voter is a ranking of some set of candidates, while a common type of social output is the selection of a winning candidate (or perhaps a set of candidates tied for winning).A voting method is then a function that takes in a ranking from each voter and outputs a winning candidate (or set of tied candidates).Other functions may instead output a social ranking of the candidates (Arrow, 1963) or a probability distribution over the candidates (Brandt, 2017), and other input types are also possible, such as sets of approved candidates (Brams & Fishburn, 2007), or assignments of grades to candidates (Balinski & Laraki, 2010), or real-valued functions on the set of candidates (d'Aspremont & Gevers, 2002;Sen, 2017).Faced with a function of any of these types, voting theorists study the function from several perspectives, including the general principles or "axioms" it satisfies (Felsenthal, 2012;Nurmi, 1987Nurmi, , 1999)), its susceptibility to manipulation by strategic voters (Taylor, 2005), its statistical behavior according to probability models for generating voter inputs (Green-Armytage et al., 2016;Merrill, 1988), the complexity of the function and related computational problems (e.g., the problem of determining if the function can be manipulated in a given election) (Faliszewski et al., 2009), and more.These studies are greatly facilitated by the implementation of algorithms for computing the relevant functions and checking their properties, which are provided in pref_voting.

  PublisherOA PDFDOI

• Common p-Belief with Plausibility Measures: Extended Abstract

  Electronic Proceedings in Theoretical Computer Science · 2025-11-25

  articleOpen access1st authorCorresponding

  An epistemic probability model has a common prior if P i = P j for all i, j A .To simplify notation, we write W, ( i ) iA , F , P when P is the common prior.Remark 2.2.We could also allow a different -algebra F i for each P i , but this complexity is unnecessary for the purpose of this paper.Given a state w and an agent i A , the set i (w) represents i's information at state w.With this interpretation in mind, we can now define the agents' knowledge and posterior beliefs.Definition 2.3 (Knowledge).Suppose that W, ( i ) iA , F , (P i ) iA is an epistemic probability model.The knowledge operator for agent i A is the function K i : (W ) (W ) where: for all E W ,If w K i (E) we say that agent i knows that E in w. 3 Definition 2.4 (Posterior Belief).Given an epistemic probability model W, ( i ) iA , F , (P i ) iA .The posterior belief for i at state w is the (possibly partial) function P i,w : (W ) [0, 1] where: for all E W ,Suppose that W, ( i ) iA , F , (P i ) iA is an epistemic-probability model.We write K(E) for the event that everyone knows E, and C(E) for the event that E is common knowledge. 4Formally, everyone knows is a function K : (W ) (W ) where: for all E W ,

  PublisherOA PDFDOI

• Stable Voting and the Splitting of Cycles

  ArXiv.org · 2025-11-29

  preprintOpen access

  Algorithms for resolving majority cycles in preference aggregation have been studied extensively in computational social choice. Several sophisticated cycle-resolving methods, including Tideman's Ranked Pairs, Schulze's Beat Path, and Heitzig's River, are refinements of the Split Cycle (SC) method that resolves majority cycles by discarding the weakest majority victories in each cycle. Recently, Holliday and Pacuit proposed a new refinement of Split Cycle, dubbed Stable Voting, and a simplification thereof, called Simple Stable Voting (SSV). They conjectured that SSV is a refinement of SC whenever no two majority victories are of the same size. In this paper, we prove the conjecture up to 6 alternatives and refute it for more than 6 alternatives. While our proof of the conjecture for up to 5 alternatives uses traditional mathematical reasoning, our 6-alternative proof and 7-alternative counterexample were obtained with the use of SAT solving. The SAT encoding underlying this proof and counterexample is applicable far beyond SC and SSV: it can be used to test properties of any voting method whose choice of winners depends only on the ordering of margins of victory by size.

  PublisherOA PDFDOI

• The Social Utility of Voting Revisited

  SSRN Electronic Journal · 2025-01-01 · 1 citations

  preprintOpen accessSenior author
  PublisherDOI

• Characterizations of voting rules based on majority margins

  arXiv (Cornell University) · 2025-01-15

  preprintOpen accessSenior author

  In the context of voting with ranked ballots, an important class of voting rules is the class of margin-based rules (also called pairwise rules). A voting rule is margin-based if whenever two elections generate the same head-to-head margins of victory or loss between candidates, the voting rule yields the same outcome in both elections. Although this is a mathematically natural invariance property to consider, whether it should be regarded as a normative axiom on voting rules is less clear. In this paper, we address this question for voting rules with any kind of output, whether a set of candidates, a ranking, a probability distribution, etc. We prove that a voting rule is margin-based if and only if it satisfies some axioms with clearer normative content. A key axiom is what we call Preferential Equality, stating that if two voters both rank a candidate $x$ immediately above a candidate $y$, then either voter switching to rank $y$ immediately above $x$ will have the same effect on the election outcome as if the other voter made the switch, so each voter's preference for $y$ over $x$ is treated equally.

  PublisherOA PDFDOI

Frequent coauthors

• Wesley H. Holliday

  25 shared

• Johan van Benthem

  20 shared

• Rohit Parikh

  City University of New York

  11 shared

• Benedikt Löwe

  8 shared

• Olivier Roy

  University of Bayreuth

  8 shared

• Andreas Witzel

  7 shared

• Jan‐Willem Romeijn

  Case Western Reserve University

  7 shared

• Samer Salame

  6 shared

Labs

• Eric Pacuit LabPI

Education

• PhD, Computer Science

  City University of New York

  2015

• Masters, Mathematics

  Case Western Reserve

  2000