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Christian Hatschka

Publications and source records attributed to Christian Hatschka.

8 recordsLinked to original sources
arXiv2026

Multi-Winner Voting Games in TU and NTU: When is the Core Always Non-Empty?

Multi-winner approval voting selects a size-$k$ committee that aggregates voters' approval preferences over a set of alternatives. A central question is coalitional stability: No coalition should be able to pick a committee -- of size at most its proportional share -- under which every coalition member has strictly more approved alternatives. This notion, introduced by Aziz et al. (2017) as core-stable committees, is naturally interpreted as a core notion with non-transferable utility. We introduce multi-winner voting games, a cooperative-game framework that unifies prior work and supports a systematic study of two utility-transfer models across different voting rules. Players are voters. Each coalition has a proportional seat cap and may only propose admissible committees up to that size. Fixing a multi-winner rule, each admissible committee induces a utility vector for the members of the coalition. In the transferable utility (TU) model, a coalition may redistribute the total utility of an admissible committee among its members. In the non-transferable utility (NTU) model, a coalition may only use utility vectors that are realized directly by some admissible committee. The core consists of utility vectors feasible for the grand coalition that are not blocked by any coalition. A coalition is blocking if it can propose an admissible committee that makes all its members strictly better off, directly in NTU and after redistribution in TU. When instantiated with the standard PAV/approval utility, the NTU-core is equivalent to the core-stable committee concept studied in prior work. To our knowledge, the TU-core for multi-winner voting has not been previously studied. We analyze core existence and computation for four prominent rules: Approval Voting (AV), Satisfaction Approval Voting (SAV), Chamberlin--Courant (CC), Proportional Approval Voting (PAV).

cs.GT↗
arXiv2025

How Hard is it to Explain Preferences Using Few Boolean Attributes?

We study the computational complexity of explaining preference data through Boolean attribute models (BAMs), motivated by extensive research involving attribute models and their promise in understanding preference structure and enabling more efficient decision-making processes. In a BAM, each alternative has a subset of Boolean attributes, each voter cares about a subset of attributes, and voters prefer alternatives with more of their desired attributes. In the BAM problem, we are given a preference profile and a number k, and want to know whether there is a Boolean k-attribute model explaining the profile. We establish a complexity dichotomy for the number of attributes k: BAM is linear-time solvable for $k \le 2$ but NP-complete for $k \ge 3$. The problem remains hard even when preference orders have length two. On the positive side, BAM becomes fixed-parameter tractable when parameterized by the number of alternatives m. For the special case of two voters, we provide a linear-time algorithm. We also analyze variants where partial information is given: When voter preferences over attributes are known (BAM WITH CARES) or when alternative attributes are specified (BAM WITH HAS), we show that for most parameters BAM WITH CARES is more difficult whereas BAM WITH HAS is more tractable except for being NP-hard even for one voter.

cs.MA↗
arXiv2025

Partitioned Combinatorial Optimization Games

We propose a class of cooperative games, called d Partitioned Compbinatorial Optimization Games (PCOGs). The input of PCOG consists of a set of agents and a combinatorial structure (typically a graph) with a fixed optimization goal on this structure (e.g., finding a minimum dominating set on a graph) such that the structure is divided among the agents. The value of each coalition of agents is derived from the optimal solution for the part of the structure possessed by the coalition. We study two fundamental questions related to the core: Core Stability Verification and Core Stability Existence. We analyze the algorithmic complexity of both questions for four classic graph optimization tasks: minimum vertex cover, minimum dominating set, minimum spanning tree, and maximum matching.

cs.GT↗
arXiv2025

Multi-Organizational Scheduling: Individual Rationality, Optimality, and Complexity

We investigate multi-organizational scheduling problems, building upon the framework introduced by Pascual et al.[2009]. In this setting, multiple organizations each own a set of identical machines and sequential jobs with distinct processing times. The challenge lies in optimally assigning jobs across organizations' machines to minimize the overall makespan while ensuring no organization's performance deteriorates. To formalize this fairness constraint, we introduce individual rationality, a game-theoretic concept that guarantees each organization benefits from participation. Our analysis reveals that finding an individually rational schedule with minimum makespan is $Θ_2^{\text{P}}$-hard, placing it in a complexity class strictly harder than both NP and coNP. We further extend the model by considering an alternative objective: minimizing the sum of job completion times, both within individual organizations and across the entire system. The corresponding decision variant proves to be NP-complete. Through comprehensive parameterized complexity analysis of both problems, we provide new insights into these computationally challenging multi-organizational scheduling scenarios.

cs.GT↗
arXiv2023

Deontic Paradoxes in ASP with Weak Constraints

The rise of powerful AI technology for a range of applications that are sensitive to legal, social, and ethical norms demands decision-making support in presence of norms and regulations. Normative reasoning is the realm of deontic logics, that are challenged by well-known benchmark problems (deontic paradoxes), and lack efficient computational tools. In this paper, we use Answer Set Programming (ASP) for addressing these shortcomings and showcase how to encode and resolve several well-known deontic paradoxes utilizing weak constraints. By abstracting and generalizing this encoding, we present a methodology for translating normative systems in ASP with weak constraints. This methodology is applied to "ethical" versions of Pac-man, where we obtain a comparable performance with related works, but ethically preferable results.

cs.LO↗
arXiv2023

Efficient Algorithms for Monroe and CC Rules in Multi-Winner Elections with (Nearly) Structured Preferences

We investigate winner determination for two popular proportional representation systems: the Monroe and Chamberlin-Courant (abbrv. CC) systems. Our study focuses on (nearly) single-peaked resp. single-crossing preferences. We show that for single-crossing approval preferences, winner determination of the Monroe rule is polynomial, and for both rules, winner determination mostly admits FPT algorithms with respect to the number of voters to delete to obtain single-peaked or single-crossing preferences. Our results answer some complexity questions from the literature [18, 28, 21].

cs.MA↗
arXiv2022

Edge-Cut Width: An Algorithmically Driven Analogue of Treewidth Based on Edge Cuts

Decompositional parameters such as treewidth are commonly used to obtain fixed-parameter algorithms for NP-hard graph problems. For problems that are W[1]-hard parameterized by treewidth, a natural alternative would be to use a suitable analogue of treewidth that is based on edge cuts instead of vertex separators. While tree-cut width has been coined as such an analogue of treewidth for edge cuts, its algorithmic applications have often led to disappointing results: out of twelve problems where one would hope for fixed-parameter tractability parameterized by an edge-cut based analogue to treewidth, eight were shown to be W[1]-hard parameterized by tree-cut width. As our main contribution, we develop an edge-cut based analogue to treewidth called edge-cut width. Edge-cut width is, intuitively, based on measuring the density of cycles passing through a spanning tree of the graph. Its benefits include not only a comparatively simple definition, but mainly that it has interesting algorithmic properties: it can be computed by a fixed-parameter algorithm, and it yields fixed-parameter algorithms for all the aforementioned problems where tree-cut width failed to do so.

cs.DS↗