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Dependence Logic pp 235-260

# Dependence and Independence in Social Choice: Arrow’s Theorem

Chapter

## Abstract

One of the goals of social choice theory is to study the group decision methods that satisfy two types of desiderata. The first type ensures that the group decision depends in the right way on the voters’ opinions. The second type ensures that the voters are free to express any opinion, as long as it is an admissible input to the group decision method. Impossibility theorems, such as Arrow’s Theorem, point to an interesting tension between these two desiderata. In this paper, we argue that dependence and independence logic offer an interesting new perspective on this aspect of social choice theory. To that end, we develop a version of independence logic that can express Arrow’s properties of preference aggregation functions. We then prove that Arrow’s Theorem is derivable in a natural deduction system for the first-order consequences of our logic.

## Keywords

Social Choice Group Decision Social Ranking Social Choice Function Social Choice Theory
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer International Publishing Switzerland 2016

## Authors and Affiliations

1. 1.Department of PhilosophyUniversity of MarylandCollege ParkUSA
2. 2.Department of Philosophy and Religious StudiesUtrecht UniversityUtrechtThe Netherlands