Realistic Assumptions for Attacks on Elections

We must properly model attacks and the preferences of the electorate for the computational study of attacks on elections to give us insight into the hardness of attacks in practice. Theoretical and empirical analysis are equally important methods to understand election attacks. I discuss my recent work on domain restrictions on partial preferences and on new election attacks. I propose further study into modeling realistic election attacks and the advancement of the current state of empirical analysis of their hardness by using more advanced statistical techniques. Models for Election Attacks In computational social choice we apply techniques from computer science to understand social choice problems such as elections, which are a way to reach a fair decision when presented with the preferences of several agents. However, elections can be vulnerable to voters misrepresenting their preferences (manipulation) or even attacks on the structure of the election itself (control). It is obvious to suggest that we should use election systems where these attacks are not possible. Unfortunately, a crucial negative result, the Gibbard-Sattertwaithe theorem (Gibbard 1973; Satterthwaite 1975), states that every reasonable election system is manipulable. While it is not possible to design an election system that is impossible to manipulate it may be computationally infeasible to determine if a manipulation exists. Bartholdi et al. (1989) introduced the concept of measuring the resistance of elections to manipulation using computational complexity. Since then there has been a focus on determining the worst-case complexity of manipulation and other attacks on different election systems (see, e.g., Faliszewski et al. (2010)) and more recently how hard they are in practice through experimental means (see, e.g., Walsh (2011)). The problems of manipulation and control have been well-studied individually. However, to better model realworld scenarios, other attacks can and have been developed that have aspects of manipulation and control or are logical extensions of them. One extension is to explore multiple attacks happening in the same election, which is more Copyright c © 2015, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. likely in practice than one isolated attack with all other voters and election organizers acting honestly. This was the topic of the paper that I presented at IJCAI-13 (Fitzsimmons, Hemaspaandra, and Hemaspaandra 2013). This paper explored elections where there is both an election chair controlling the election and a subset of voters manipulating the election. The chair and the manipulators may act either collaboratively or competitively and this has interesting effects on the corresponding worst-case complexity. In another paper we explored the complexity of manipulating two-stage elections when the same election system is used at each stage (Fitzsimmons, Hemaspaandra, and Hemaspaandra 2014). The main motivation was that when there are multiple winners in an election it is reasonable to assume that a runoff election would be held among the winners. Like the aforementioned combination of manipulation and control, the aim of this research is to present a model that is likely to occur in real-world situations. Election attacks are not only affected by the structure of the attack, but also the behavior of the voters. One common assumption is that a given electorate satisfies a domain restriction such as single peakedness. The notion of single-peaked preferences introduced by Black (1948) is the most commonly studied domain restriction on voters’ preferences in an election. Single-peaked preferences model the preferences of voters with respect to a polarizing issue where the candidates can be arranged with respect to a one-dimensional axis where the leftmost and rightmost positions of the axis represent the extremes of the issue. When an election has voters with single-peaked preferences the worst-case complexity of the manipulation and control problems often decreases (Faliszewski et al. 2011). In real-world elections voters often have some degree of partial preference and this should be properly considered when determining if a collection of voters satisfies a certain domain restriction. Recently single-peaked preferences were examined for preference profiles of partial votes in an existential model (Lackner 2014). I expanded on this work in a recent technical report (Fitzsimmons 2014) and showed that single-peaked consistency for weak orders in this existential model is in P, solving the main open problem in Lackner (2014). Additionally, I showed that the two other definitions for single-peaked consistency for weak orders are each also in P (Fitzsimmons 2014) and returned to more estabProceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence