We examine an approval-based model of Liquid Democracy with a budget constraint on voting and delegating costs, aiming to centrally select casting voters ensuring complete representation of the electorate. From a computational complexity perspective, we focus on minimizing overall costs, maintaining short delegation paths, and preventing excessive concentration of voting power. Furthermore, we explore computational aspects of strategic control, specifically, whether external agents can change election components to influence the voting power of certain voters.

Purpose: Multiwinner voting rules typically require full knowledge of voter preferences, which becomes impractical in large-scale or attention-limited settings. This paper investigates how accurately a winning committee can be approximated when voter preferences are elicited using a limited budget of structured queries. Methods: We introduce a query-based framework for multiwinner elections in which voter preferences are elicited through refinement queries over subsets of candidates under a limited budget. We analyse several cost functions that model the cognitive effort needed to answer such queries, propose axiomatic properties for evaluating them, and experimentally evaluate simple query-based committee selection rules across multiple election models. Results: Experimental results show that strategies based on recursively splitting candidate sets provide the best trade-off between elicitation cost and committee accuracy. Across several statistical models, these strategies approximate the outcome of k-Borda elections significantly more efficiently than alternative query types. Conclusion: The results demonstrate that well-designed query strategies can substantially reduce the amount of preference information required while still producing high-quality committee outcomes, suggesting that query-based elicitation is a promising approach for scalable multiwinner decision-making.

My PhD research deals with the use of Liquid Democracy (LD) for social choice scenarios, while considering the scarcity of attention as a driving factor. My aim is to better understand LD: theoretically as well as practically; in particular, by establishing containment in certain computational classes for corresponding combinatorial problems, suggesting methods to improve the use of LD, and understand its adaptation to specific scenarios. Concretely, I consider the use of LD as a solution for the problem of low voter attention in light of the high cognitive effort needed by voters to actively participate in voting processes.

Voting is a crucial methodology for eliciting and combining agents' preferences and information across many applications. Just as there are numerous voting rules exhibiting different properties, we also see many different voting systems. In this paper we investigate how different voting systems perform as a function of the characteristics of the underlying voting population and social network. In particular, we compare direct democracy, liquid democracy, and sortition in a ground truth voting context. Through simulations -- using both real and artificially generated social networks -- we illustrate how voter competency distributions and levels of direct participation affect group accuracy differently in each voting mechanism. Our results can be used to guide the selection of a suitable voting system based on the characteristics of a particular voting setting.

We consider an agent community wishing to decide on several binary issues by means of issue-by-issue majority voting. For each issue and each agent, one of the two options is better than the other. However, some of the agents may be confused about some of the issues, in which case they may vote for the option that is objectively worse for them. A benevolent external party wants to help the agents to make better decisions, i.e., select the majority-preferred option for as many issues as possible. This party may have one of the following tools at its disposal: (1) educating some of the agents, so as to enable them to vote correctly on all issues, (2) appointing a subset of highly competent agents to make decisions on behalf of the entire group, or (3) guiding the agents on how to delegate their votes to other agents, in a way that is consistent with the agents' opinions. For each of these tools, we study the complexity of the decision problem faced by this external party, obtaining both NP-hardness results and fixed-parameter tractability results.