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28Evidence Logic: A New Look at Neighborhood StructuresIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 97-118. 1998.
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28Changing Types: Information Dynamics for Qualitative Type SpacesStudia Logica 102 (2): 297-319. 2014.Many different approaches to describing the players’ knowledge and beliefs can be found in the literature on the epistemic foundations of game theory. We focus here on non-probabilistic approaches. The two most prominent are the so-called Kripkeor Aumann- structures and knowledge structures (non-probabilistic variants of Harsanyi type spaces). Much of the recent work on Kripke structures has focused on dynamic extensions and simple ways of incorporating these. We argue that many of these ideas c…Read more
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28Stable VotingConstitutional Political Economy. forthcoming.We propose a new single-winner voting system using ranked ballots: Stable Voting. The motivating principle of Stable Voting is that if a candidate A would win without another candidate B in the election, and A beats B in a head-to-head majority comparison, then A should still win in the election with B included (unless there is another candidate A' who has the same kind of claim to winning, in which case a tiebreaker may choose between such candidates). We call this principle Stability for Winne…Read more
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25First-Order Classical Modal LogicStudia Logica 84 (2): 171-210. 2006.The paper focuses on extending to the first order case the semantical program for modalities first introduced by Dana Scott and Richard Montague. We focus on the study of neighborhood frames with constant domains and we offer in the first part of the paper a series of new completeness results for salient classical systems of first order modal logic. Among other results we show that it is possible to prove strong completeness results for normal systems without the Barcan Formula (like FOL + K)in …Read more
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23Axioms for Defeat in Democratic ElectionsJournal of Theoretical Politics 33 (4). 2021.We propose six axioms concerning when one candidate should defeat another in a democratic election involving two or more candidates. Five of the axioms are widely satisfied by known voting procedures. The sixth axiom is a weakening of Kenneth Arrow's famous condition of the Independence of Irrelevant Alternatives (IIA). We call this weakening Coherent IIA. We prove that the five axioms plus Coherent IIA single out a method of determining defeats studied in our recent work: Split Cycle. In partic…Read more
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22Measuring Violations of Positive Involvement in VotingElectronic Proceedings in Theoretical Computer Science 335 189-209. 2021.In the context of computational social choice, we study voting methods that assign a set of winners to each profile of voter preferences. A voting method satisfies the property of positive involvement (PI) if for any election in which a candidate x would be among the winners, adding another voter to the election who ranks x first does not cause x to lose. Surprisingly, a number of standard voting methods violate this natural property. In this paper, we investigate different ways of measuring the…Read more
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22Voting Theory in the Lean Theorem ProverIn Sujata Ghosh & Thomas Icard (eds.), Logic, Rationality, and Interaction: 8th International Workshop, Lori 2021, Xi’an, China, October 16–18, 2021, Proceedings, Springer Verlag. pp. 111-127. 2021.There is a long tradition of fruitful interaction between logic and social choice theory. In recent years, much of this interaction has focused on computer-aided methods such as SAT solving and interactive theorem proving. In this paper, we report on the development of a framework for formalizing voting theory in the Lean theorem prover, which we have applied to verify properties of a recently studied voting method. While previous applications of interactive theorem proving to social choice have…Read more
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15The Tree of Knowledge in Action: Towards a Common PerspectiveIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 87-106. 1998.
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14By 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 differen…Read more
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14Logics of informational attitudes and informative actionsJournal of the Indian Council of Philosophical Research 27 (2): 37. 2010.
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12Merging Frameworks for InteractionJournal of Philosophical Logic 38 (5): 491-526. 2009.A variety of logical frameworks have been developed to study rational agents interacting over time. This paper takes a closer look at one particular interface, between two systems that both address the dynamics of knowledge and information flow. The first is Epistemic Temporal Logic (ETL) which uses linear or branching time models with added epistemic structure induced by agents’ different capabilities for observing events. The second framework is Dynamic Epistemic Logic (DEL) that describes int…Read more
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8Split Cycle: a new Condorcet-consistent voting method independent of clones and immune to spoilersPublic Choice 197 1-62. 2023.We propose a Condorcet-consistent voting method that we call Split Cycle. Split Cycle belongs to the small family of known voting methods satisfying the anti-vote-splitting criterion of independence of clones. In this family, only Split Cycle satisfies a new criterion we call immunity to spoilers, which concerns adding candidates to elections, as well as the known criteria of positive involvement and negative involvement, which concern adding voters to elections. Thus, in contrast to other clone…Read more
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8The Tree of Knowledge in Action: Towards a Common PerspectiveIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 87-106. 1998.
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6Games, Norms and Reasons: Logic at the Crossroads (edited book)Springer. 2011.Games, Norms, and Reasons: Logic at the Crossroads provides an overview of modern logic focusing on its relationships with other disciplines, including new interfaces with rational choice theory, epistemology, game theory and informatics. This book continues a series called "Logic at the Crossroads" whose title reflects a view that the deep insights from the classical phase of mathematical logic can form a harmonious mixture with a new, more ambitious research agenda of understanding and enhanci…Read more
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5May'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. In particular, we add two axioms stating that the voting method should mitigate spoiler effects and avoid the so-called strong no show paradox. We prove a theorem stating that any preferent…Read more
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Focusing on CampaignsIn Ramaswamy Ramanujam, Lawrence Moss & Can Başkent (eds.), Rohit Parikh on Logic, Language and Society, Springer Verlag. 2017.One of the important lessons to take away from Rohit Parikh’s impressive body of work is that logicians and computer scientists have much to gain by focusing their attention on the intricacies of political campaigns. Drawing on recent work developing a theory of expressive voting, we study the dynamics of voters’ opinions during an election. In this paper, we develop a model in which the relative importance of the different issues that concern a voter may change either in response to candidates’…Read more
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Foundations of the Formal Sciences Vi: Probabilistic Reasoning and Reasoning With Probabilities. Studies in Logic (edited book)College Publication. 2008.
College Park, Maryland, United States of America
Areas of Specialization
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Logic and Philosophy of Logic |
Social Choice Theory |
Game Theory |
Philosophy of Artificial Intelligence |
Formal Social Epistemology |
Epistemic Logic |