Parameterized Algorithmics for Computational Social Choice: Nine Research Challenges

Computational Social Choice is an interdisciplinary research area involving Economics, Political Science, and Social Science on the one side, and Mathematics and Computer Science (including Artificial Intelligence and Multiagent Systems) on the other side. Typical computational problems studied in this field include the vulnerability of voting procedures against attacks, or preference aggregation in multi-agent systems. Parameterized Algorithmics is a subfield of Theoretical Computer Science seeking to exploit meaningful problem-specific parameters in order to identify tractable special cases of in general computationally hard problems. In this paper, we propose nine of our favorite research challenges concerning the parameterized complexity of problems appearing in this context

Bribery Can Get Harder in Structured Multiwinner Approval Election

We study the complexity of constructive bribery in the context of structured multiwinner approval elections. Given such an election, we ask whether a certain candidate can join the winning committee by adding, deleting, or swapping approvals, where each such action comes at a cost and we are limited by a budget. We assume our elections to either have the candidate interval or the voter interval property, and we require the property to hold also after the bribery. While structured elections usually make manipulative attacks significantly easier, our work also shows examples of the opposite behavior. We conclude by presenting preliminary insights regarding the destructive variant of our problem.Comment: 23 pages, 1 figure, 1 table, published in the Proceedings of AAMAS-2

Campaign Management under Approval-Driven Voting Rules

Approval-like voting rules, such as Sincere-Strategy Preference-Based Approval voting (SP-AV), the Bucklin rule (an adaptive variant of $k$-Approval voting), and the Fallback rule (an adaptive variant of SP-AV) have many desirable properties: for example, they are easy to understand and encourage the candidates to choose electoral platforms that have a broad appeal. In this paper, we investigate both classic and parameterized computational complexity of electoral campaign management under such rules. We focus on two methods that can be used to promote a given candidate: asking voters to move this candidate upwards in their preference order or asking them to change the number of candidates they approve of. We show that finding an optimal campaign management strategy of the first type is easy for both Bucklin and Fallback. In contrast, the second method is computationally hard even if the degree to which we need to affect the votes is small. Nevertheless, we identify a large class of scenarios that admit fixed-parameter tractable algorithms.Comment: 34 pages, 1 figur

Defending Elections Against Malicious Spread of Misinformation

The integrity of democratic elections depends on voters' access to accurate information. However, modern media environments, which are dominated by social media, provide malicious actors with unprecedented ability to manipulate elections via misinformation, such as fake news. We study a zero-sum game between an attacker, who attempts to subvert an election by propagating a fake new story or other misinformation over a set of advertising channels, and a defender who attempts to limit the attacker's impact. Computing an equilibrium in this game is challenging as even the pure strategy sets of players are exponential. Nevertheless, we give provable polynomial-time approximation algorithms for computing the defender's minimax optimal strategy across a range of settings, encompassing different population structures as well as models of the information available to each player. Experimental results confirm that our algorithms provide near-optimal defender strategies and showcase variations in the difficulty of defending elections depending on the resources and knowledge available to the defender.Comment: Full version of paper accepted to AAAI 201

Resolving the Complexity of Some Fundamental Problems in Computational Social Choice

This thesis is in the area called computational social choice which is an intersection area of algorithms and social choice theory.Comment: Ph.D. Thesi