The Complexity of Manipulating kk-Approval Elections

An important problem in computational social choice theory is the complexity of undesirable behavior among agents, such as control, manipulation, and bribery in election systems. These kinds of voting strategies are often tempting at the individual level but disastrous for the agents as a whole. Creating election systems where the determination of such strategies is difficult is thus an important goal. An interesting set of elections is that of scoring protocols. Previous work in this area has demonstrated the complexity of misuse in cases involving a fixed number of candidates, and of specific election systems on unbounded number of candidates such as Borda. In contrast, we take the first step in generalizing the results of computational complexity of election misuse to cases of infinitely many scoring protocols on an unbounded number of candidates. Interesting families of systems include $k$-approval and $k$-veto elections, in which voters distinguish $k$ candidates from the candidate set. Our main result is to partition the problems of these families based on their complexity. We do so by showing they are polynomial-time computable, NP-hard, or polynomial-time equivalent to another problem of interest. We also demonstrate a surprising connection between manipulation in election systems and some graph theory problems

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

Complexity of Manipulation, Bribery, and Campaign Management in Bucklin and Fallback Voting

A central theme in computational social choice is to study the extent to which voting systems computationally resist manipulative attacks seeking to influence the outcome of elections, such as manipulation (i.e., strategic voting), control, and bribery. Bucklin and fallback voting are among the voting systems with the broadest resistance (i.e., NP-hardness) to control attacks. However, only little is known about their behavior regarding manipulation and bribery attacks. We comprehensively investigate the computational resistance of Bucklin and fallback voting for many of the common manipulation and bribery scenarios; we also complement our discussion by considering several campaign management problems for Bucklin and fallback.Comment: 28 page

Limited Liability and the Known Unknown

Limited liability is a double-edged sword. On the one hand, limited lia-bility may help overcome investors’ risk aversion and facilitate capital formation and economic growth. On the other hand, limited liability is widely believed to contribute to excessive risk-taking and externaliza-tion of losses to the public. The externalization problem can be mitigated imperfectly through existing mechanisms such as regulation, mandatory insurance, and minimum capital requirements. These mechanisms would be more effective if information asymmetries between industry and poli-cymakers were reduced. Private businesses typically have better infor-mation about industry-specific risks than policymakers. A charge for limited liability entities—resembling a corporate income tax but calibrated to risk levels—could have two salutary effects. First, a well-calibrated limited liability tax could help compensate the public fisc for risks and reduce externalization. Second, a limited liability tax could force private industry actors to reveal information to policymakers and regulators, thereby dynamically improving the public response to externalization risk. Charging firms for limited liability at initially similar rates will lead relatively low-risk firms to forgo limited liability, while relatively high-risk firms will pay for limited liability. Policymakers will then be able to focus on the industries whose firms have self-identified as high risk, and thus develop more finely tailored regulatory responses. Because the ben-efits of making the proper election are fully internalized by individual firms, whereas the costs of future regulation or limited liability tax changes will be borne collectively by industries, firms will be unlikely to strategically mislead policymakers in electing limited or unlimited lia-bility. By helping to reveal private information and focus regulators’ at-tention, a limited liability tax could accelerate the pace at which poli-cymakers learn, and therefore, the pace at which regulations improve

Possible Winners in Noisy Elections

We consider the problem of predicting winners in elections, for the case where we are given complete knowledge about all possible candidates, all possible voters (together with their preferences), but where it is uncertain either which candidates exactly register for the election or which voters cast their votes. Under reasonable assumptions, our problems reduce to counting variants of election control problems. We either give polynomial-time algorithms or prove #P-completeness results for counting variants of control by adding/deleting candidates/voters for Plurality, k-Approval, Approval, Condorcet, and Maximin voting rules. We consider both the general case, where voters' preferences are unrestricted, and the case where voters' preferences are single-peaked.Comment: 34 page