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Ulle Endriss - One of the best experts on this subject based on the ideXlab platform.
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proving classical theorems of Social Choice Theory in modal logic
Autonomous Agents and Multi-Agent Systems, 2016Co-Authors: Giovanni Cina, Ulle EndrissAbstract:A number of seminal results in the field of Social Choice Theory demonstrate the difficulties of aggregating the preferences of several individual agents for the purpose of making a decision together. We show how to formalise three of the most important impossibility results of this kind--Arrow's Theorem, Sen's Theorem, and the Muller---Satterthwaite Theorem--by using a modal logic of Social Choice functions. We also provide syntactic proofs of these theorems in the same logic. While prior work has been successful in applying tools from logic and automated reasoning to Social Choice Theory, this is the first human-readable formalisation of the Arrovian framework allowing for a direct derivation of the main impossibility theorems of Social Choice Theory. This is useful for gaining a deeper understanding of the foundations of collective decision making, both in human society and in groups of autonomous software agents.
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eliciting a suitable voting rule via examples
European Conference on Artificial Intelligence, 2014Co-Authors: Olivier Cailloux, Ulle EndrissAbstract:We address the problem of specifying a voting rule by means of a series of examples. Each example consists of the answer to a simple question: how should the rule rank two alternatives, given the positions at which each voter ranks the two alternatives? To be able to formalise this elicitation problem, we develop a novel variant of classical Social Choice Theory in terms of associations of alternatives with vectors of ranks rather than the common associations of voters with preference orders. We then define and study a class of voting rules suited for elicitation using such answers. Finally, we propose and experimentally evaluate several elicitation strategies for arriving at a good approximation of the target rule with a reasonable number of queries.
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automated search for impossibility theorems in Social Choice Theory ranking sets of objects
arXiv: Artificial Intelligence, 2014Co-Authors: Christian Geist, Ulle EndrissAbstract:We present a method for using standard techniques from satisfiability checking to automatically verify and discover theorems in an area of economic Theory known as ranking sets of objects. The key question in this area, which has important applications in Social Choice Theory and decision making under uncertainty, is how to extend an agents preferences over a number of objects to a preference relation over nonempty sets of such objects. Certain combinations of seemingly natural principles for this kind of preference extension can result in logical inconsistencies, which has led to a number of important impossibility theorems. We first prove a general result that shows that for a wide range of such principles, characterised by their syntactic form when expressed in a many-sorted first-order logic, any impossibility exhibited at a fixed (small) domain size will necessarily extend to the general case. We then show how to formulate candidates for impossibility theorems at a fixed domain size in propositional logic, which in turn enables us to automatically search for (general) impossibility theorems using a SAT solver. When applied to a space of 20 principles for preference extension familiar from the literature, this method yields a total of 84 impossibility theorems, including both known and nontrivial new results.
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collective annotation of linguistic resources basic principles and a formal model
Meeting of the Association for Computational Linguistics, 2013Co-Authors: Ulle Endriss, Raquel FernandezAbstract:Crowdsourcing provides new ways of cheaply and quickly gathering large amounts of information contributed by volunteers online. This method has revolutionised the collection of labelled data, in computational linguistics and elsewhere. However, to create annotated linguistic resources from crowdsourced data we face the challenge of having to combine the judgements of a potentially large group of annotators. Here we put forward the idea of using principles of Social Choice Theory to design new methods for aggregating linguistic annotations provided by individuals into a single collective annotation.
Christian List - One of the best experts on this subject based on the ideXlab platform.
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Social Choice Theory and deliberative democracy a reconciliation
British Journal of Political Science, 2003Co-Authors: John S Dryzek, Christian ListAbstract:The two most influential traditions of contemporary theorizing about democracy, Social Choice Theory and deliberative democracy, are generally thought to be at loggerheads, in that the former demonstrates the impossibility, instability or meaninglessness of the rational collective outcomes sought by the latter. We argue that the two traditions can be reconciled. After expounding the central Arrow and Gibbard-Satterthwaite impossibility results, we reassess their implications, identifying the conditions under which meaningful democratic decision making is possible. We argue that deliberation can promote these conditions, and hence that Social Choice Theory suggests not that democratic decision making is impossible, but rather that democracy must have a deliberative aspect.
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Social Choice Theory and deliberative democracy a reconciliation
British Journal of Political Science, 2003Co-Authors: John S Dryzek, Christian ListAbstract:The two most influential traditions of contemporary theorizing about democracy, Social Choice Theory and deliberative democracy are generally thought to be at loggerheads, in that one demonstrates the impossibility, instability or meaninglessness of the rational collective outcomes sought by the other. We argue that the two traditions can be reconciled. After expounding the central Arrow and Gibbard–Satterthwaite impossibility results, we reassess their implications, identifying the conditions under which meaningful democratic decision making is possible. We argue that deliberation can promote these conditions, and hence that Social Choice Theory suggests not that democratic decision making is impossible, but rather that democracy must have a deliberative aspect.
Lorini Emiliano - One of the best experts on this subject based on the ideXlab platform.
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Goal-Based Collective Decisions: Axiomatics and Computational Complexity
'International Joint Conferences on Artificial Intelligence', 2018Co-Authors: Novaro Arianna, Grandi Umberto, Longin Dominique, Lorini EmilianoAbstract:We study agents expressing propositional goals over a set of binary issues to reach a collective decision. We adapt properties and rules from the literature on Social Choice Theory to our setting, providing an axiomatic characterisation of a majority rule for goal-based voting. We study the computational complexity of finding the outcome of our rules (i.e., winner determination), showing that it ranges from Nondeterministic Polynomial Time (NP) to Probabilistic Polynomial Time (PP)
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Goal-Based Collective Decisions: Axiomatics and Computational Complexity
HAL CCSD, 2018Co-Authors: Novaro Arianna, Grandi Umberto, Longin Dominique, Lorini EmilianoAbstract:International audienceWe study agents expressing propositional goals over a set of binary issues to reach a collective decision. We adapt properties and rules from the literature on Social Choice Theory to our setting, providing an axiomatic characterisation of a majority rule for goal-based voting. We study the computational complexity of finding the outcome of our rules (i.e., winner determination), showing that it ranges from Nondeterministic Polynomial Time (NP) to Probabilistic Polynomial Time (PP)
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Goal-Based Collective Decisions: Axiomatics and Computational Complexity (COMSOC 2018, Troy, NY, USA)
HAL CCSD, 2018Co-Authors: Novaro Arianna, Grandi Umberto, Longin Dominique, Lorini EmilianoAbstract:PosterInternational audienceWe study agents expressing propositional goals over a set of binary issues to reach a collective decision. We adapt properties and rules from the literature on Social Choice Theory to our setting, providing an axiomatic characterisation of a majority rule for goal-based voting. We study the computational complexity of finding the outcome of our rules (i.e., winner determination), showing that it ranges from Nondeterministic Polynomial Time (NP) to Probabilistic Polynomial Time (PP)
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Goal-Based Collective Decisions: Axiomatics and Computational Complexity (IJCAI 2018)
AAAI Press : Association for the Advancement of Artificial Intelligence and The MIT Press, 2018Co-Authors: Novaro Arianna, Grandi Umberto, Longin Dominique, Lorini EmilianoAbstract:27th International Joint Conference on Artificial Intelligence (IJCAI-ECAI-18), joint with the the 23rd European Conference on Artificial IntelligenceInternational audienceWe study agents expressing propositional goals over a set of binary issues to reach a collective decision. We adapt properties and rules from the literature on Social Choice Theory to our setting, providing an axiomatic characterisation of a majority rule for goal-based voting. We study the computational complexity of finding the outcome of our rules (i.e., winner determination), showing that it ranges from Nondeterministic Polynomial Time (NP) to Probabilistic Polynomial Time (PP)
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Goal-Based Collective Decisions: Axiomatics and Computational Complexity
HAL CCSD, 2018Co-Authors: Novaro Arianna, Grandi Umberto, Longin Dominique, Lorini EmilianoAbstract:International audienceWe study agents expressing propositional goals over a set of binary issues to reach a collective decision. We adapt properties and rules from the literature on Social Choice Theory to our setting, providing an axiomatic characterisation of a majority rule for goal-based voting. We study the computational complexity of finding the outcome of our rules (i.e., winner determination), showing that it ranges from Nondeterministic Polynomial Time (NP) to Probabilistic Polynomial Time (PP).Nous étudions des agents exprimant des buts propositionnels sur un ensemble de questions binaires pour parvenir à une décision collective. Nous adaptons les propriétés et les règles de la littérature sur la Théorie du Choix Social `a notre contexte, en fournissant une caractérisation axiomatique d’une règle de la majorité pour le vote par buts. Nous étudions la complexité computationnelle de trouver le résultat de nos règles (c.-à-d., winner determination), montrant qu’il va du temps polynomial non déterministe (NP) au temps polynomial probabiliste (PP)
Hans Georg Seedig - One of the best experts on this subject based on the ideXlab platform.
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consistent probabilistic Social Choice
Econometrica, 2016Co-Authors: Florian Brandl, Felix Brandt, Hans Georg SeedigAbstract:Two fundamental axioms in Social Choice Theory are consistency with respect to a variable electorate and consistency with respect to components of similar alternatives. In the context of traditional non-probabilistic Social Choice, these axioms are incompatible with each other. We show that in the context of probabilistic Social Choice, these axioms uniquely characterize a function proposed by Fishburn (1984). Fishburn's function returns so-called maximal lotteries, that is, lotteries that correspond to optimal mixed strategies in the symmetric zero-sum game induced by the pairwise majority margins. Maximal lotteries are guaranteed to exist due to von Neumann's Minimax Theorem, are almost always unique, and can be efficiently computed using linear programming. [web URL: http://onlinelibrary.wiley.com/doi/10.3982/ECTA13337/abstract]
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consistent probabilistic Social Choice
arXiv: Computer Science and Game Theory, 2015Co-Authors: Florian Brandl, Felix Brandt, Hans Georg SeedigAbstract:Two fundamental axioms in Social Choice Theory are consistency with respect to a variable electorate and consistency with respect to components of similar alternatives. In the context of traditional non-probabilistic Social Choice, these axioms are incompatible with each other. We show that in the context of probabilistic Social Choice, these axioms uniquely characterize a function proposed by Fishburn (Rev. Econ. Stud., 51(4), 683--692, 1984). Fishburn's function returns so-called maximal lotteries, i.e., lotteries that correspond to optimal mixed strategies of the underlying plurality game. Maximal lotteries are guaranteed to exist due to von Neumann's Minimax Theorem, are almost always unique, and can be efficiently computed using linear programming.
John S Dryzek - One of the best experts on this subject based on the ideXlab platform.
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Social Choice Theory and deliberative democracy a reconciliation
British Journal of Political Science, 2003Co-Authors: John S Dryzek, Christian ListAbstract:The two most influential traditions of contemporary theorizing about democracy, Social Choice Theory and deliberative democracy, are generally thought to be at loggerheads, in that the former demonstrates the impossibility, instability or meaninglessness of the rational collective outcomes sought by the latter. We argue that the two traditions can be reconciled. After expounding the central Arrow and Gibbard-Satterthwaite impossibility results, we reassess their implications, identifying the conditions under which meaningful democratic decision making is possible. We argue that deliberation can promote these conditions, and hence that Social Choice Theory suggests not that democratic decision making is impossible, but rather that democracy must have a deliberative aspect.
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Social Choice Theory and deliberative democracy a reconciliation
British Journal of Political Science, 2003Co-Authors: John S Dryzek, Christian ListAbstract:The two most influential traditions of contemporary theorizing about democracy, Social Choice Theory and deliberative democracy are generally thought to be at loggerheads, in that one demonstrates the impossibility, instability or meaninglessness of the rational collective outcomes sought by the other. We argue that the two traditions can be reconciled. After expounding the central Arrow and Gibbard–Satterthwaite impossibility results, we reassess their implications, identifying the conditions under which meaningful democratic decision making is possible. We argue that deliberation can promote these conditions, and hence that Social Choice Theory suggests not that democratic decision making is impossible, but rather that democracy must have a deliberative aspect.
