Mattei, Nicholas (University of Kentucky) | Goldsmith, Judy (University of Kentucky) | Klapper, Andrew (University of Kentucky)

We study the computational complexity of optimal bribery and manipulation schemes for sports tournaments with uncertain information: cup; challenge or caterpillar; and round robin. Our results carry over to the equivalent voting rules: sequential pair-wise elections, cup, and Copeland, when the set of candidates is exactly the set of voters. This restriction creates new difficulties for most existing algorithms. The complexity of bribery and manipulation are well studied, almost always assuming deterministic information about votes and results. We assume that for candidates i and j the probability that i beats j and the costs of lowering each probability by fixed increments are known to the manipulators. We provide complexity analyses for cup, challenge, and round robin competitions ranging from polynomial time to NP^PP. This shows that the introduction of uncertainty into the reasoning process drastically increases the complexity of bribery problems in some instances.

Mattei, Nicholas Scott (NICTA and University of New South Wales) | Goldsmith, Judy (University of Kentucky) | Klapper, Andrew (University of Kentucky)

We study the computational complexity of optimal bribery and manipulation schemes for sports tournaments with uncertain information: cup; challenge or caterpillar; and round robin. Our results carry over to the equivalent voting rules: sequential pair-wise elections, cup, and Copeland, when the set of candidates is exactly the set of voters. This restriction creates new difficulties for most existing algorithms. The complexity of bribery and manipulation are well studied, almost always assuming deterministic information about votes and results. We assume that for candidates i and j the probability that i beats j and the costs of lowering each probability by fixed increments are known to the manipulators. We provide complexity analyses for cup, challenge, and round robin competitions ranging from polynomial time to np^pp. This shows that the introduction of uncertainty into the reasoning process drastically increases the complexity of bribery problems in some instances.

Narodytska, Nina, Walsh, Toby, Xia, Lirong

Nanson's and Baldwin's voting rules select a winner by successively eliminating candidates with low Borda scores. We show that these rules have a number of desirable computational properties. In particular, with unweighted votes, it is NP-hard to manipulate either rule with one manipulator, whilst with weighted votes, it is NP-hard to manipulate either rule with a small number of candidates and a coalition of manipulators. As only a couple of other voting rules are known to be NP-hard to manipulate with a single manipulator, Nanson's and Baldwin's rules appear to be particularly resistant to manipulation from a theoretical perspective. We also propose a number of approximation methods for manipulating these two rules. Experiments demonstrate that both rules are often difficult to manipulate in practice. These results suggest that elimination style voting rules deserve further study.

Narodytska, Nina (University of New South Wales and NICTA) | Walsh, Toby (University of New South Wales and NICTA) | Xia, Lirong (Duke University)

Nanson's and Baldwin's voting rules selecta winner by successively eliminatingcandidates with low Borda scores. We showthat these rules have a number of desirablecomputational properties. In particular,with unweighted votes, it isNP-hard to manipulate either rule with one manipulator, whilstwith weighted votes, it isNP-hard to manipulate either rule with a small number ofcandidates and a coalition of manipulators.As only a couple of other voting rulesare known to be NP-hard to manipulatewith a single manipulator, Nanson'sand Baldwin's rules appearto be particularly resistant to manipulation from a theoretical perspective.We also propose a number of approximation methodsfor manipulating these two rules.Experiments demonstrate that both rules areoften difficult to manipulate in practice.These results suggest that elimination stylevoting rules deserve further study.

Conitzer, Vincent, Walsh, Toby, Xia, Lirong

We consider manipulation problems when the manipulator only has partial information about the votes of the nonmanipulators. Such partial information is described by an information set, which is the set of profiles of the nonmanipulators that are indistinguishable to the manipulator. Given such an information set, a dominating manipulation is a non-truthful vote that the manipulator can cast which makes the winner at least as preferable (and sometimes more preferable) as the winner when the manipulator votes truthfully. When the manipulator has full information, computing whether or not there exists a dominating manipulation is in P for many common voting rules (by known results). We show that when the manipulator has no information, there is no dominating manipulation for many common voting rules. When the manipulator's information is represented by partial orders and only a small portion of the preferences are unknown, computing a dominating manipulation is NP-hard for many common voting rules. Our results thus throw light on whether we can prevent strategic behavior by limiting information about the votes of other voters.