Most theoretical definitions about the complexity of manipulating elections focus on the decision problem of recognizing which instances can be successfully manipulated, rather than the search problem of finding the successful manipulative actions. Since the latter is a far more natural goal for manipulators, that definitional focus may be misguided if these two complexities can differ. Our main result is that they probably do differ: If integer factoring is hard, then for election manipulation, election bribery, and some types of election control, there are election systems for which recognizing which instances can be successfully manipulated is in polynomial time but producing the successful manipulations cannot be done in polynomial time. * Also appears as URCS-TR-2012-971. † For each fixed election system E, one can define the election winner problem as follows (see [BTT89b]).Name: E-winner, or the winner problem for E.Given: Election (C, V ) and candidate p ∈ C.Question: Is p a winner of the election (C, V ) under election system E? This is actually, in the way universally accepted in computer science (see [GJ79]), describing a set, i.e., a language. That set is the set of all triples C, V, p such that the answer to the question is "Yes." 3 We now briefly present the key definitions for the three most commonly studied types of manipulative actions: manipulation, bribery, and control. These three types were first studied, respectively, by Bartholdi, Orlin, Tovey, and Trick [BTT89a,BO91], Faliszewski, Hemaspaandra, and Hemaspaandra [FHH09], and Bartholdi, Tovey, and Trick [BTT92], for the "constructive" cases, i.e., where the goal is to make a particular candidate be a winner. 4 The "destructive" cases, where the goal is to ensure that a particular candidate is not a winner, were introduced by Conitzer, Sandholm, and Lang [CSL07] for manipulation, by Faliszewski, Hemaspaandra, and Hemaspaandra for bribery [FHH09], and by Hemaspaandra, Hemaspaandra, and Rothe for control [HHR07].The manipulation problem is defined as follows, and models whether a coalition of strategic voters can make a certain candidate win.Name: E-unweighted coalition manipulation, or the unweighted coalition manipulation problem for E; for short, the manipulation problem for E.Given: Candidate set C, nonmanipulative voter set V 1 (as a set of (name, preferences) ballots with preferences over C), manipulative voter set V 2 (as a set of names of the manipulative voters, none of whose names may belong to V 1 ), and a candidate p ∈ C.Question: Is there some choice of preferences for the manipulative voters such that p is a winner in the election in system E with candidates C and voters V 1 ∪ V 2 ?This again is a decision problem consisting of the set of all inputs yielding the answer "Yes." However, there is a very natural search problem associated with this, which we will call manipulation no one is so strong as to receive the support of 75 percent of the voters, then no one is inducted into the Baseball Hall of Fame that year. Indeed, in thr...

Schulze and ranked-pairs elections have received much attention recently, and the former has quickly become a quite widely used election system. For many cases these systems have been proven resistant to bribery, control, or manipulation, with ranked pairs being particularly praised for being NP-hard for all three of those. Nonetheless, the present paper shows that with respect to the number of candidates, Schulze and ranked-pairs elections are fixed-parameter tractable to bribe, control, and manipulate: we obtain uniform, polynomial-time algorithms whose degree does not depend on the number of candidates. We also provide such algorithms for some weighted variants of these problems.

We study the behavior of Range Voting and Normalized Range Voting with respect to electoral control. Electoral control encompasses attempts from an election chair to alter the structure of an election in order to change the outcome. We show that a voting system resists a case of control by proving that performing that case of control is computationally infeasible. Range Voting is a natural extension of approval voting, and Normalized Range Voting is a simple variant which alters each vote to maximize the potential impact of each voter. We show that Normalized Range Voting has among the largest number of control resistances among natural voting systems.

Schulze voting is a recently introduced voting system enjoying unusual popularity and a high degree of real-world use, with users including the Wikimedia foundation, several branches of the Pirate Party, and MTV. It is a Condorcet voting system that determines the winners of an election using information about paths in a graph representation of the election. We resolve the complexity of many electoral control cases for Schulze voting. We find that it falls short of the best known voting systems in terms of control resistance, demonstrating vulnerabilities of concern to some prospective users of the system.

No abstract