Introduction to the Theory of Voting

Introduction to Computational Social Choice

“…First, it may be interpreted as demonstrating a lack of fairness of the plurality rule: even though a majority of voters believes A to be inferior to one of the other options (namely B), A still wins. This and other fairness properties of voting rules are reviewed in Chapter 2 (Zwicker, 2016). Second, Pliny's anecdote is an instance of what nowadays is called election control by deleting candidates.…”

“…Even if option C had not been removed, the supporters of C could have manipulated the election by pretending that they support B rather than C, thereby ensuring a preferred outcome, namely B rather than A. Manipulation is discussed in depth in Chapters 2 (Zwicker, 2016) and 6 (Conitzer and Walsh, 2016).…”

“…The technique we have used to prove it is also used in Chapter 2 (Zwicker, 2016) on voting theory and in Chapter 17 (Endriss, 2016) on judgment aggregation. These chapters also discuss possible approaches for dealing with such impossibilities by weakening our requirements somewhat.…”

Barriers to Manipulation in Voting

“…We could declare any vote that is not single-peaked invalid, but this just comes down to forcing voters to manipulate. For more discussion of single-peaked preferences, see Chapter 2 (Zwicker, 2015).…”

Matching under Preferences

“…See also Chapter 2 (Zwicker, 2015). Abraham et al (2007b) derived a neat characterisation of popular matchings, leading to an O(m) algorithm to check whether a given matching M in I is popular.…”