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Analysis of Boolean Functions by Ryan O'Donnell

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Chapter 2 Basic Concepts and Social Choice

In this chapter we introduce a number of important basic concepts including influences and noise stability. Many of these concepts are nicely motivated using the language of social choice. The chapter is concluded with Kalai’s Fourier-based proof of Arrow’s Theorem.

2.1. Social Choice Functions

In this section we describe some rudiments of the mathematics of social choice, a topic studied by economists, political scientists, mathematicians, and computer scientists. The fundamental question in this area is how best to aggregate the opinions of many agents. Examples where this problem arises include citizens voting in an election, committees deciding on alternatives, and independent computational agents ...

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