Normalized Range Voting Broadly Resists Control

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

Manipulation and Control Complexity of Schulze Voting

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

Range voting is resistant to control

Social choice theory is concerned with developing and evaluating voting systems, both for the use of political and organizational elections and for use as decision making process for multiagent systems. Particularly in the context of multiagent systems, computational resistance to various types of control has become a desired property of a voting system. Though manipulative actions may always be possible, strong computational barriers to efficient control can give us sufficient confidence in the integrity of an election. Range Voting is a natural extension of approval voting that is resistant to a large number of cases of control. In particular, the variant Normalized Range Voting has among the largest number of control resistances among natural voting systems

Schulze and Ranked-Pairs Voting are Fixed-Parameter Tractable to Bribe, Manipulate, and Control

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

Attacking and defending popular election systems

Thesis (Ph. D.)--University of Rochester. Dept. of Computer Science, 2013.The thesis of this dissertation is that complexity and algorithms, used appropriately, are important factors in assessing the value and uses of election systems. The chapter on search versus decision points out the importance of that “appropriately”; it proves that unless integer factoring is easy, the standard definitions of manipulability do not capture what they were designed to capture. Other chapters use complexity and algorithms to analyze the complexity of various types of manipulative attacks on elections, as a way of understanding how computationally vulnerable election systems are. Among the contributions of those chapters are: showing that a type of range voting is the most control-attack resistant among all currently analyzed natural election systems; exploring for the first time the detailed control complexity of Schulze elections; and exploring the parameterized complexity of manipulative actions in Schulze and ranked-pairs elections. Such results will better allow choosers of election methods to match the protections of the systems they choose with the types of attack that are of greatest concern

Search versus Decision for Election Manipulation Problems

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

Search versus Decision for Election Manipulation Problems

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