Using complexity to protect elections

Abstract

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Voting on Actions with Uncertain Outcomes

“…This paradox is closely related to Arrow's independence of irrelevant alternatives [2]: Arrow postulated that for any reasonable form of preference aggregation the relative collective ranking of two alternatives should only depend on their relative rankings provided by the individuals, and not on any third ("irrelevant") alternative. Our example demonstrates that the Borda rule, when used as an aggregator for preference orders, violates this desideratum: the relative ranking of A and B adopted by the collective does depend on C. Our paradox also has close connections to the topic of election control by means of adding (or deleting) candidates, widely studied in computational social choice [4,9], which in turn relies on violations of Arrow's independence axiom: our example demonstrates how adding candidate C to a Borda election in which B was winning can result in A becoming the new winner.…”

An NTU Cooperative Game Theoretic View of Manipulating Elections

“…4 We use the term (coalitional) manipulation to refer to a situation where a voter (a group of voters) casts votes not according to his (their) true preferences, but rather to obtain some goal. It is one of the best-studied forms of strategic behavior in elections (see the surveys [8,7]). The definition below is taken from the paper of Bachrach, Elkind, and Faliszewski [2], which itself is inspired by the definition of Conitzer, Sandholm, and Lang [5].…”

“…Let P M \Wxc be any profile. For all y, y = x, it holds that s( 7 And so, x will win under P H ∪ P M \Wxc ∪ Q Wxc . Now we prove the "if" part.…”

“…Further, we obtain different flavors of the problem depending on whether the votes are weighted or not, which voting rule is used, etc. Some results on coalitional manipulation can be found in [17,15,14,16]; see also surveys [8,7].…”

“…One of the most influential ideas regarding the computational study of elections, due to Bartholdi, Orlin, Tovey, and Trick [4,3], was to study the computational complexity of computing manipulative votes. The rationale behind it was that if planning a manipulation were computationally hard, then in practice voters would not be able to vote strategically (see the surveys of Faliszewski, Hemaspaandra, and Hemaspaandra [7] and of Faliszewski and Procaccia [8] for a detailed overview of this approach and for two viewpoints regarding its applicability).…”