Proving classical theorems of social choice theory in modal logic

Cinà, Giovanni; Endriss, Ulle

doi:10.1007/s10458-016-9328-6

Cited by 10 publications

(9 citation statements)

References 33 publications

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“…The third direction of research we are interested in, is quantum logic for social choice. Modal logic has been used as a powerful tool to model and reason about social choice [25][26][27][28]. It is both natural and valuable to develop a quantum logic to model and reason about quantum social choice.…”

Section: Discussionmentioning

confidence: 99%

Schrödinger’s Ballot: Quantum Information and the Violation of Arrow’s Impossibility Theorem

Sun

Kulicki³

et al. 2021

Entropy

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We study Arrow’s Impossibility Theorem in the quantum setting. Our work is based on the work of Bao and Halpern, in which it is proved that the quantum analogue of Arrow’s Impossibility Theorem is not valid. However, we feel unsatisfied about the proof presented in Bao and Halpern’s work. Moreover, the definition of Quantum Independence of Irrelevant Alternatives (QIIA) in Bao and Halpern’s work seems not appropriate to us. We give a better definition of QIIA, which properly captures the idea of the independence of irrelevant alternatives, and a detailed proof of the violation of Arrow’s Impossibility Theorem in the quantum setting with the modified definition.

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Section: Discussionmentioning

confidence: 99%

Schrödinger’s Ballot: Quantum Information and the Violation of Arrow’s Impossibility Theorem

Sun

Kulicki³

et al. 2021

Entropy

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“…an axiom satisfied by all rules that are not a dictatorship of some agent i). Moreover, a translation of the preference aggregation axioms for strong monotonicity, independence of irrelevant alternatives and dictatorship is expressed in the Logic for Social Choice Functions by [9].…”

Section: Related Work On Logic and Judgment Aggregationmentioning

confidence: 99%

“…Similar concerns about implementation have been addressed with respect to the Logic for Social Choice Functions as well [9], though in that case the focus was on preference aggregation rather than judgment aggregation. Interestingly, this logic has indeed been implemented by [44] in the Common Lisp language, however focusing on game theoretical notions for positional scoring rules (e.g.…”

Section: Automated Reasoningmentioning

confidence: 99%

Judgment aggregation in dynamic logic of propositional assignments

Novaro

Grandi

Herzig

2018

Journal of Logic and Computation

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Judgment aggregation models a group of agents having to collectively decide over a number of logically interconnected issues starting from their individual opinions. In recent years, a growing literature has focused on the design of logical systems for social choice theory, and for judgment aggregation in particular, making use of logical languages designed ad hoc for this purpose. In this paper we deploy the existing formalism of Dynamic Logic of Propositional Assignments (DL-PA), an instance of Propositional Dynamic Logic where atomic programs affect propositional valuations. We show that DL-PA is a well-suited formalism for modeling the aggregation of binary judgments from multiple agents, by providing logical equivalences in DL-PA for some of the best-known aggregation procedures, desirable axioms coming from the literature on judgment aggregation and properties for the safety of the agenda problem.

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“…Early work using logical methods in social choice theory includes Murakami's [28] application of results about three-valued logic to the analysis of voting rules, Rubinstein's [34] proof of the equivalence between multi-profile and single-profile approaches to social choice, and Parikh's [31] development of a logic of games to study social procedures. There is now a rich literature developing logical systems that can formalize results in social choice theory (see, e.g., [32,1,29,37,40,16,21,12,30,23]).…”

Section: Introductionmentioning

confidence: 99%

Voting Theory in the Lean Theorem Prover

Holliday

Norman

Pacuit

2021

Lecture Notes in Computer Science

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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 (using Isabelle/HOL and Mizar) have focused on the verification of impossibility theorems, we aim to cover a variety of results ranging from impossibility theorems to the verification of properties of specific voting methods (e.g., Condorcet consistency, independence of clones, etc.). In order to formalize voting theoretic axioms concerning adding or removing candidates and voters, we work in a variable-election setting whose formalization makes use of dependent types in Lean.

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Proving classical theorems of social choice theory in modal logic

Cited by 10 publications

References 33 publications

Schrödinger’s Ballot: Quantum Information and the Violation of Arrow’s Impossibility Theorem

Schrödinger’s Ballot: Quantum Information and the Violation of Arrow’s Impossibility Theorem

Judgment aggregation in dynamic logic of propositional assignments

Voting Theory in the Lean Theorem Prover

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