The Complexity of Online Manipulation of Sequential Elections

Most work on manipulation assumes that all preferences are known to the manipulators. However, in many settings elections are open and sequential, and manipulators may know the already cast votes but may not know the future votes. We introduce a framework, in which manipulators can see the past votes but not the future ones, to model online coalitional manipulation of sequential elections, and we show that in this setting manipulation can be extremely complex even for election systems with simple winner problems. Yet we also show that for some of the most important election systems such manipulation is simple in certain settings. This suggests that when using sequential voting, one should pay great attention to the details of the setting in choosing one's voting rule. Among the highlights of our classifications are: We show that, depending on the size of the manipulative coalition, the online manipulation problem can be complete for each level of the polynomial hierarchy or even for PSPACE. We obtain the most dramatic contrast to date between the nonunique-winner and unique-winner models: Online weighted manipulation for plurality is in P in the nonunique-winner model, yet is coNP-hard (constructive case) and NP-hard (destructive case) in the unique-winner model. And we obtain what to the best of our knowledge are the first P^NP[1]-completeness and P^NP-completeness results in the field of computational social choice, in particular proving such completeness for, respectively, the complexity of 3-candidate and 4-candidate (and unlimited-candidate) online weighted coalition manipulation of veto elections.Comment: 24 page

Election-Attack Complexity for More Natural Models

Elections are arguably the best way that a group of agents with preferences over a set of choices can reach a decision. This can include political domains, as well as multiagent systems in artificial-intelligence settings. It is well-known that every reasonable election system is manipulable, but determining whether such a manipulation exists may be computationally infeasible. We build on an exciting line of research that considers the complexity of election-attack problems, which include voters misrepresenting their preferences (manipulation) and attacks on the structure of the election itself (control). We must properly model such attacks and the preferences of the electorate to give us insight into the difficulty of election attacks in natural settings. This includes models for how the voters can state their preferences, their structure, and new models for the election attack itself. We study several different natural models on the structure of the voters. In the computational study of election attacks it is generally assumed that voters strictly rank all of the candidates from most to least preferred. We consider the very natural model where voters are able to cast votes with ties, and the model where they additionally have a single-peaked structure. Specifically, we explore how voters with varying amounts of ties and structure in their preferences affect the computational complexity of different election attacks and the complexity of determining whether a given electorate is single-peaked. For the representation of the voters, we consider how representing the voters succinctly affects the complexity of election attacks and discuss how approaches for the nonsuccinct case can be adapted. Control and manipulation are two of the most commonly studied election-attack problems. We introduce a model of electoral control in the setting where some of the voters act strategically (i.e., are manipulators), and consider both the case where the agent controlling the election and the manipulators share a goal, and the case where they have competing goals. The computational study of election-attack problems allows us to better understand how different election systems compare to one another, and it is important to study these problems for natural settings, as this thesis does

Controlling Candidate-Sequential Elections

All previous work on ``candidate-control'' manipulation of elections has been in the model of full-information, simultaneous voting. This is a problem, since in quite a few real-world settings---from TV singing/dancing talent shows to university faculty-hiring processes---candidates are introduced, and appraised by the voters, in sequence. We provide a natural model for sequential candidate evaluation, a framework for evaluating the computational complexity of controlling the outcome within that framework, and some initial results on the range such complexity can take on. We hope our work will lead to further examination of temporally involved candidate control