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