The analysis of properties of consequence operators was a particularly active research topic during the 1980s and early 1990s. One possible approach is to start with a model-theoretic semantics and then study the logical consequence relation it induces. In this work, we follow this approach and analyse the consequence operators associated with so-called characterization logics. Roughly speaking, a characterization logic captures—via its own notion of ordinary equivalence—another logic’s notion of strong equivalence. For example, the logic of here-and-there serves as a characterization logic for answer set programs, since strong equivalence in the latter is characterized by ordinary equivalence in the former.

In previous work, we showed that restricting attention to finite knowledge bases—a common assumption in knowledge representation—guarantees the existence and uniqueness of characterization logics. Here, we apply this general existence result to abstract argumentation. We show that the induced consequence operator yields a so-called reverse kernel, a useful construct that has received comparatively little attention in the literature. We also show that, for logics satisfying the intersection property, the consequence operator induced by the characterization logic coincides with the original consequence operator.

A common criticism of liquid democracy within the relevant academic literature is that delegation cycles can occur, seemingly resulting in unused voting power. Yet, practitioners argue that delegation cycles are not only unproblematic but are even formed intentionally by participants. To bring theory closer to reality, we introduce a model that captures this strategic behavior under uncertainty. We study the existence, structure and quality of Nash equilibria, revealing that delegation cycles naturally emerge. To complement these findings, we perform computational experiments using best-response dynamics.

We introduce the Task Allocation with Quotas (Taq) problem, a one-sided allocation model in which agents with limited capacities distribute integer units of effort across tasks subject to lower and upper quota requirements. Each agent approves a subset of tasks, and a feasible allocation assigns effort only to approved tasks while satisfying all constraints. Our results delineate the computational landscape of Taq. We show that deciding whether all tasks can be satisfied is solvable in polynomial time, whereas maximizing the number of satisfied tasks is NP-complete, even when every agent has unit capacity.

Assuming that a feasible allocation exists, we further characterize the complexity of optimizing the number of engaged agents, identifying both polynomial-time solvable and NP-complete cases. Finally, we study settings in which satisfying all tasks requires assigning effort to disapproved tasks. For this setting, we present polynomial-time algorithms for several natural optimization objectives and establish NP-completeness for minimizing the number of agents assigned to disapproved tasks when each agent’s capacity is three, leaving the case of capacity two as an open problem.

A clustering is proportionally fair if no sufficiently large group of agents can jointly form a new cluster that all of them prefer. We study this notion across two settings: centroid clustering, where an agent's loss depends on the distance to the closest center among the selected ones; and non-centroid clustering, where an agent's loss depends on the other members of its cluster, measured either as the maximum or the average distance to them. Prior work focuses on approximate existence guarantees; the complexity of the underlying computational problems is largely open. We study two such problems and their computational complexity: auditing, which asks whether a given clustering satisfies a fairness property, and computing, which asks for a clustering that satisfies it or a report that none exists. We consider three properties: the core, fully justified representation (FJR), and the transferable-utility (TU) core, which we extend from the centroid to the non-centroid clustering.

The complexity picture is mostly hard. In the centroid setting, auditing is in P, but computing a core or TU-core clustering is W[2]-hard wrt. the number of selected centers, strengthening known NP-hardness. In the non-centroid setting, auditing is coNP-complete for all three properties under both loss functions, and under maximum loss already for two clusters; deciding whether a core clustering (maximum loss) or a TU-core clustering (either loss) exists is NP-hard. When restricting to the one-dimensional euclidean space, i.e. agents placed in the numerical line, the core is always non-empty and a clustering can be efficiently found under the maximum loss; under the average loss, the core can be empty. Two cases stay open: existence of a core clustering under average loss, and whether centroid computing is FPT wrt. the number of agents.

Participatory budgeting (PB) increasingly takes place online, and the COMSOC community has responded with a rich toolbox of aggregation rules, from greedy utilitarian methods to rules with proportionality guarantees such as the Method of Equal Shares. These rules are typically evaluated by axiomatic and computational criteria, yet we know little about which of these properties citizens actually value, or what makes an algorithmic outcome legitimate in their eyes. To address this, we worked with political scientists to derive hypotheses and tested them in a conjoint experiment with roughly 1,900 respondents in US metropolitan regions that run PB elections. We ask whether citizens trade off fairness (proportionality and egalitarian guarantees) against simplicity (of the underlying idea and of the calculation), and how this trade-off shapes their preferences over rules and their stated voting intentions.

We introduce a new Participatory Budgeting rule similar to the method of equal shares (MES) that we call dynamic MES. Our results show that dynamic MES preserves the desirable theoretical guarantees of MES, including proportionality and efficiency properties, while showing better performance on real-world datasets from pabulib, especially when considering the rules without completion. However, the enhanced performance comes at the cost of significantly increased computational complexity, which currently limits its practical adoption compared to the original MES algorithm. Additionally, implementation challenges remain unresolved, requiring further development before dynamic MES can serve as a viable alternative in large scale participatory Budgeting instances.