When there are just $2$ candidates, the majority function possesses all of the mathematical properties that seem desirable in a voting rule (e.g., May’s Theorem and Theorem 32). Unfortunately, as soon as there are $3$ (or more) candidates the problem of social choice becomes much more difficult. For example, suppose we have candidates $a$, [...]

## Recent comments

Matt Franklin: In the proof of Theorem 8.66 (middle of p. 225 in book), the...Matt Franklin: The "Condorcet Jury Theorem" is discussed but not named in t...Matt Franklin: In the first line of the proof of Proposition 8.45 (bottom o...Ryan O'Donnell: Great catch, thanks!Ryan O'Donnell: Thanks! The proofreader should have caught those!Ryan O'Donnell: Thanks -- I think that kind of parenthesis-free notation for...Ryan O'Donnell: Thanks! Unique Games is discussed somewhat in Chapter 7 of ...