Applications of Logic in Social Choice Theory

Endriss, Ulle

doi:10.1007/978-3-642-22359-4_7

Cited by 11 publications

(21 citation statements)

References 8 publications

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“…Arguably, SCF's (returning a top alternative rather than a full ranking of all alternatives) are relevant to a wider range of applications. In any case, known techniques to prove either version of the theorem are very similar [12,35]. Thus, our work also suggests how one might construct a similar syntatcic proof of Arrow's Theorem for social welfare functions, using, for instance, a logic such as that of Ågotnes et al [1].…”

Section: Introductionmentioning

confidence: 92%

“…However, the full original logic of Troquard et al [37] can model these two layers of preferences-indeed, this is the main objective it had been designed for originally. Our work, together with the fact that the Gibbard-Satterthwaite Theorem may be considered a relatively simple corollary to the Muller-Satterthwaite Theorem requiring only a proof showing that strategy-proofness implies strong monotonicity [12], therefore strongly suggests that proving the Gibbard-Satterthwaite Theorem in the full logic of Troquard et al using an extension of our approach is possible in principle.…”

Section: Introductionmentioning

confidence: 99%

“…As we are designing ever more specialised social choice mechanisms for novel types of tasks, better tools to analyse the formal properties of these mechanisms are needed. Specifically, there is now a growing literature on the formal verification of social choice mechanisms by means of logical modelling and the use of techniques from automated reasoning [1,5,9,12,13,16,24,34,37,38]. (We will review some of the contributions to this field in Sect.…”

Section: Introductionmentioning

confidence: 99%

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Proving classical theorems of social choice theory in modal logic

Cinà

Endriss

2016

Auton Agent Multi-Agent Syst

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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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Section: Introductionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Proving classical theorems of social choice theory in modal logic

Cinà

Endriss

2016

Auton Agent Multi-Agent Syst

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“…Perhaps the most famous one is Arrow's Theorem [2]; it states that it is impossible to aggregate the preferences of a finite set of individuals in a manner that would satisfy a small number of natural properties. In recent years there has been a growing interest in applications of logic to social choice theory [11]. In this paper we present a formalisation of several results from social choice theory in classical first-order logic (FOL).…”

Section: Introductionmentioning

confidence: 99%

First-Order Logic Formalisation of Impossibility Theorems in Preference Aggregation

Grandi

Endriss

2012

J Philos Logic

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In preference aggregation a set of individuals express preferences over a set of alternatives, and these preferences have to be aggregated into a collective preference. When preferences are represented as orders, aggregation procedures are called social welfare functions. Classical results in social choice theory state that it is impossible to aggregate the preferences of a set of individuals under different natural sets of axiomatic conditions. We define a first-order language for social welfare functions and we give a complete axiomatisation for this class, without having the number of individuals or alternatives specified in the language. We are able to express classical axiomatic requirements in our first-order language, giving formal axioms for three classical theorems of preference aggregation by Arrow, by Sen, and by Kirman and Sondermann. We explore to what extent such theorems can be formally derived from our axiomatisations, obtaining positive results for Sen's Theorem and the Kirman-Sondermann Theorem. For the case of Arrow's Theorem, which does not apply in the case of infinite societies, we have to resort to fixing the number of individuals with an additional axiom. In the long run, we hope that our approach to formalisation can serve as the basis for a fully automated proof of classical and new theorems in social choice theory.

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“…This can be done by looking for an aggregation procedure: a process through which the individual preferences are combined into a single one. As stated in Endriss [42], "when a group needs to make a decision, we are faced with the problem of aggregating the views of the individual members of that group into a single collective view that adequately reflects the 'will of the people' ". Finding appropriate aggregation procedures is the fundamental aim of research fields as social choice theory [4; 5; 6] as well as preference/belief change/merge/aggregation (e.g., Konieczny and Pino Pérez [75,76]; Grüne-Yanoff and Hansson [64]; Gabbay et al [49]; Liu [88]; Konieczny and Pino Pérez [77]).…”

Section: Introductionmentioning

confidence: 99%

Reliability-based preference dynamics: lexicographic upgrade

Velázquez–Quesada¹

2017

Journal of Logic and Computation

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This paper models collective decision-making scenarios by using a priority-based aggregation procedure, the so-called lexicographic method, in order to represent a form of reliability-based 'deliberation'. More precisely, it considers agents with a preference ordering over a set of objects and a reliability ordering over the agents themselves, providing a logical framework describing the way in which the public and simultaneous announcement of the individual preferences leads to individual preference upgrade. The main results are the definitions of this lexicographic upgrade for diverse types of reliability relations (in particular, the preorder and total preorder cases), a sound and complete axiom system for a language describing the effects of such upgrades, and the definitions for non-public variations.

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Applications of Logic in Social Choice Theory

Cited by 11 publications

References 8 publications

Proving classical theorems of social choice theory in modal logic

Proving classical theorems of social choice theory in modal logic

First-Order Logic Formalisation of Impossibility Theorems in Preference Aggregation

Reliability-based preference dynamics: lexicographic upgrade

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