Jan Maly

AAAI Conference 2026 Conference Paper

City Sampling for Citizens’ Assemblies

• Paul Gölz
• Jan Maly
• Ulrike Schmidt-Kraepelin
• Markus Utke
• Philipp C. Verpoort

In citizens' assemblies, a group of constituents is randomly selected to weigh in on policy issues. We study a two-stage sampling problem faced by practitioners in countries such as Germany, in which constituents' contact information is stored at a municipal level. As a result, practitioners can only select constituents from a bounded number of cities ex post, while ensuring equal selection probability for constituents ex ante. We develop several algorithms for this problem. Although minimizing the number of contacted cities is NP-hard, we provide a pseudo-polynomial time algorithm and an additive 1-approximation, both based on separation oracles for a linear programming formulation. Recognizing that practical objectives go beyond minimizing city count, we further introduce a simple and more interpretable greedy algorithm, which additionally satisfies an ex-post monotonicity property and achieves an additive 2-approximation. Finally, we explore a notion of ex-post proportionality, for which we propose two practical algorithms: an optimal algorithm based on column generation and integer linear programming and a simple heuristic creating particularly transparent distributions. We evaluate these algorithms on data from Germany, and plan to deploy them in cooperation with a leading nonprofit organization in this space.

AAAI Conference 2025 Conference Paper

An Extension-Based Argument-Ranking Semantics: Social Rankings in Abstract Argumentation

• Lars Bengel
• Giovanni Buraglio
• Jan Maly
• Kenneth Skiba

In this paper, we introduce a new family of argument-ranking semantics which can be seen as a refinement of the classification of arguments into skeptically accepted, credulously accepted and rejected. To this end we use so-called social ranking functions which have been developed recently to rank individuals based on their performance in groups. We provide necessary and sufficient conditions for a social ranking function to give rise to an argument-ranking semantics satisfying the desired refinement property.

AAMAS Conference 2024 Conference Paper

Combining Voting and Abstract Argumentation to Understand Online Discussions

• Michael Bernreiter
• Jan Maly
• Oliviero Nardi
• Stefan Woltran

Online discussion platforms are a vital part of the public discourse in a deliberative democracy. However, how to interpret the outcomes of the discussions on these platforms is often unclear. In this paper, we propose a novel and explainable method for selecting a set of most representative, consistent points of view by combining methods from computational social choice and abstract argumentation. Specifically, we model online discussions as abstract argumentation frameworks combined with information regarding which arguments voters approve of. Based on ideas from approval-based multiwinner voting, we introduce several voting rules for selecting a set of preferred extensions that represents voters’ points of view. We compare the proposed methods across several dimensions, theoretically and in numerical simulations, and give clear suggestions on which methods to use depending on the specific situation.

AAMAS Conference 2023 Conference Paper

Fairness in Participatory Budgeting via Equality of Resources

• Jan Maly
• Simon Rey
• Ulle Endriss
• Martin Lackner

We introduce a family of normative principles to assess fairness in the context of participatory budgeting. These principles are based on the fundamental idea that budget allocations should be fair in terms of the resources invested into meeting the wishes of individual voters. This is in contrast to earlier proposals that are based on specific assumptions regarding the satisfaction of voters with a given budget allocation. We analyse these new principles in axiomatic, algorithmic, and experimental terms.

AAMAS Conference 2023 Conference Paper

Free-Riding in Multi-Issue Decisions

• Martin Lackner
• Jan Maly
• Oliviero Nardi

Voting in multi-issue domains allows for compromise outcomes that satisfy all voters to some extent. Such fairness considerations, however, open the possibility of a special form of manipulation: free-riding. By untruthfully opposing a popular opinion in one issue, voters can receive increased consideration in other issues. We study under which conditions this is possible. Additionally, we study free-riding from a computational and experimental point of view. Our results show that free-riding in multi-issue domains is largely unavoidable, but comes at a non-negligible individual risk for voters. Thus, the allure of free-riding is smaller than one could intuitively assume.

AAAI Conference 2023 Conference Paper

Proportional Decisions in Perpetual Voting

• Martin Lackner
• Jan Maly

Perpetual voting is a framework for long-term collective decision making. In this framework, we consider a sequence of subsequent approval-based elections and try to achieve a fair overall outcome. To achieve fairness over time, perpetual voting rules take the history of previous decisions into account and identify voters that were dissatisfied with previous decisions. In this paper, we look at perpetual voting rules from an axiomatic perspective. First, we define two classes of perpetual voting rules that are particularly easy to explain to voters and explore the bounds imposed by this simplicity. Second, we study proportionality in the perpetual setting and identify two rules with strong proportionality guarantees. However, both rules yield different guarantees and we prove them to be incompatible with each other.

AAAI Conference 2023 Conference Paper

Proportionality in Approval-Based Participatory Budgeting

• Markus Brill
• Stefan Forster
• Martin Lackner
• Jan Maly
• Jannik Peters

The ability to measure the satisfaction of (groups of) voters is a crucial prerequisite for formulating proportionality axioms in approval-based participatory budgeting elections. Two common -- but very different -- ways to measure the satisfaction of a voter consider (i) the number of approved projects and (ii) the total cost of approved projects, respectively. In general, it is difficult to decide which measure of satisfaction best reflects the voters' true utilities. In this paper, we study proportionality axioms with respect to large classes of approval-based satisfaction functions. We establish logical implications among our axioms and related notions from the literature, and we ask whether outcomes can be achieved that are proportional with respect to more than one satisfaction function. We show that this is impossible for the two commonly used satisfaction functions when considering proportionality notions based on extended justified representation, but achievable for a notion based on proportional justified representation. For the latter result, we introduce a strengthening of priceability and show that it is satisfied by several polynomial-time computable rules, including the Method of Equal Shares and Phragmén's sequential rule.

AIJ Journal 2022 Journal Article

Choice logics and their computational properties

• Michael Bernreiter
• Jan Maly
• Stefan Woltran

AAAI Conference 2022 Conference Paper

Participatory Budgeting with Donations and Diversity Constraints

• Jiehua Chen
• Martin Lackner
• Jan Maly

Participatory budgeting (PB) is a democratic process where citizens jointly decide on how to allocate public funds to indivisible projects. In this work, we focus on PB processes where citizens may provide additional money to projects they want to see funded. We introduce a formal framework for this kind of PB with donations. Our framework also allows for diversity constraints, meaning that each project belongs to one or more types, and there are lower and upper bounds on the number of projects of the same type that can be funded. We propose three general classes of methods for aggregating the citizens’ preferences in the presence of donations and analyze their axiomatic properties. Furthermore, we investigate the computational complexity of determining the outcome of a PB process with donations and of finding a citizen’s optimal donation strategy.

JAIR Journal 2022 Journal Article

Ranking Sets of Objects: The Complexity of Avoiding Impossibility Results

• Jan Maly

The problem of lifting a preference order on a set of objects to a preference order on a family of subsets of this set is a fundamental problem with a wide variety of applications in AI. The process is often guided by axioms postulating properties the lifted order should have. Well-known impossibility results by Kannai and Peleg and by Barbera and Pattanaik tell us that some desirable axioms – namely dominance and (strict) independence – are not jointly satisfiable for any linear order on the objects if all non-empty sets of objects are to be ordered. On the other hand, if not all non-empty sets of objects are to be ordered, the axioms are jointly satisfiable for all linear orders on the objects for some families of sets. Such families are very important for applications as they allow for the use of lifted orders, for example, in combinatorial voting. In this paper, we determine the computational complexity of recognizing such families. We show that it is \Pi_2^p-complete to decide for a given family of subsets whether dominance and independence or dominance and strict independence are jointly satisfiable for all linear orders on the objects if the lifted order needs to be total. Furthermore, we show that the problem remains coNP-complete if the lifted order can be incomplete. Additionally, we show that the complexity of these problems can increase exponentially if the family of sets is not given explicitly but via a succinct domain restriction. Finally, we show that it is NP-complete to decide for a family of subsets whether dominance and independence or dominance and strict independence are jointly satisfiable for at least one linear order on the objects.

AAMAS Conference 2021 Conference Paper

Approval-Based Shortlisting

• Martin Lackner
• Jan Maly

Shortlisting is the task of reducing a long list of alternatives to a (smaller) set of best or most suitable alternatives from which a final winner will be chosen. Shortlisting is often used in the nomination process of awards or in recommender systems to display featured objects. In this paper, we analyze shortlisting methods that are based on approval data, a common type of preferences. Furthermore, we assume that the size of the shortlist, i. e. , the number of best or most suitable alternatives, is not fixed but determined by the shortlisting method. We axiomatically analyze established and new shortlisting methods and complement this analysis with an experimental evaluation based on imperfect quality estimates. Our results lead to recommendations which shortlisting methods to use, depending on the desired properties.

IJCAI Conference 2021 Conference Paper

Choice Logics and Their Computational Properties

• Michael Bernreiter
• Jan Maly
• Stefan Woltran

Qualitative Choice Logic (QCL) and Conjunctive Choice Logic (CCL) are formalisms for preference handling, with especially QCL being well established in the field of AI. So far, analyses of these logics need to be done on a case-by-case basis, albeit they share several common features. This calls for a more general choice logic framework, with QCL and CCL as well as some of their derivatives being particular instantiations. We provide such a framework, which allows us, on the one hand, to easily define new choice logics and, on the other hand, to examine properties of different choice logics in a uniform setting. In particular, we investigate strong equivalence, a core concept in non-classical logics for understanding formula simplification, and computational complexity. Our analysis also yields new results for QCL and CCL. For example, we show that the main reasoning task regarding preferred models is ϴ₂P-complete for QCL and CCL, while being Δ₂P-complete for a newly introduced choice logic.

IJCAI Conference 2021 Conference Paper

Fairness in Long-Term Participatory Budgeting

• Martin Lackner
• Jan Maly
• Simon Rey

Participatory Budgeting (PB) processes are usually designed to span several years, with referenda for new budget allocations taking place regularly. This paper presents a first formal framework for long-term PB, based on a sequence of budgeting problems as main input. We introduce a theory of fairness for this setting, focusing on three main concepts that apply to types (groups) of voters: (i) achieving equal welfare for all types, (ii) minimizing inequality of welfare (as measured by the Gini coefficient), and (iii) achieving equal welfare in the long run. We investigate under which conditions these criteria can be satisfied, and analyze the computational complexity of verifying whether they hold.

AAMAS Conference 2021 Conference Paper

Fairness in Long-Term Participatory Budgeting

• Martin Lackner
• Jan Maly
• Simon Rey

Participatory Budgeting processes are usually designed to span several years, with referenda for new budget allocations taking place regularly. This paper presents the first formalization of long-term PB. We introduce a theory of fairness for this setting, investigate under which conditions our fairness criteria can be satisfied, and analyze the computational complexity of verifying them.

AAAI Conference 2021 Conference Paper

Ranking Sets of Defeasible Elements in Preferential Approaches to Structured Argumentation: Postulates, Relations, and Characterizations

• Jan Maly
• Johannes P. Wallner

Preferences play a key role in computational argumentation in AI, as they reflect various notions of argument strength vital for the representation of argumentation. Within central formal approaches to structured argumentation, preferential approaches are applied by lifting preferences over defeasible elements to rankings over sets of defeasible elements, in order to be able to compare the relative strength of two arguments and their respective defeasible constituents. To overcome the current gap in the scientific landscape, we give in this paper a general study of the critical component of lifting operators in structured argumentation. We survey existing lifting operators scattered in the literature of argumentation theory, social choice, and utility theory, and show fundamental relations and properties of these operators. Extending existing works from argumentation and social choice, we propose a list of postulates for lifting operations, and give a complete picture of (non-)satisfaction for the considered operators. Based on our postulates, we present impossibility results, stating for which sets of postulates there is no hope of satisfaction, and for two main lifting operators presented in structured argumentation, Elitist and Democratic, we give a full characterization in terms of our postulates.

AAAI Conference 2020 Conference Paper

Lifting Preferences over Alternatives to Preferences over Sets of Alternatives: The Complexity of Recognizing Desirable Families of Sets

• Jan Maly

The problem of lifting a preference order on a set of objects to a preference order on a family of subsets of this set is a fundamental problem with a wide variety of applications in AI. The process is often guided by axioms postulating properties the lifted order should have. Well-known impossibility results by Kannai and Peleg and by Barberà and Pattanaik tell us that some desirable axioms – namely dominance and (strict) independence – are not jointly satisfiable for any linear order on the objects if all non-empty sets of objects are to be ordered. On the other hand, if not all non-empty sets of objects are to be ordered, the axioms are jointly satisfiable for all linear orders on the objects for some families of sets. Such families are very important for applications as they allow for the use of lifted orders, for example, in combinatorial voting. In this paper, we determine the computational complexity of recognizing such families. We show that it is Πp 2-complete to decide for a given family of subsets whether dominance and independence or dominance and strict independence are jointly satisfiable for all linear orders on the objects if the lifted order needs to be total. Furthermore, we show that the problem remains coNP-complete if the lifted order can be incomplete. Additionally, we show that the complexity of these problem can increase exponentially if the family of sets is not given explicitly but via a succinct domain restriction.

JAIR Journal 2019 Journal Article

Preference Orders on Families of Sets - When Can Impossibility Results Be Avoided?

• Jan Maly
• Miroslaw Truszczyński
• Stefan Woltran

Lifting a preference order on elements of some universe to a preference order on subsets of this universe is often guided by postulated properties the lifted order should have. Well-known impossibility results pose severe limits on when such liftings exist if all non-empty subsets of the universe are to be ordered. The extent to which these negative results carry over to other families of sets is not known. In this paper, we consider families of sets that induce connected subgraphs in graphs. For such families, common in applications, we study whether lifted orders satisfying the well-studied axioms of dominance and (strict) independence exist for every or, in another setting, for some underlying order on elements (strong and weak orderability). We characterize families that are strongly and weakly orderable under dominance and strict independence, and obtain a tight bound on the class of families that are strongly orderable under dominance and independence.

IJCAI Conference 2018 Conference Paper

Preference Orders on Families of Sets - When Can Impossibility Results Be Avoided?

• Jan Maly
• Miroslaw Truszczynski
• Stefan Woltran

Lifting a preference order on elements of some universe to a preference order on subsets of this universe is often guided by postulated properties the lifted order should have. Well-known impossibility results pose severe limits on when such liftings exist if all non-empty subsets of the universe are to be ordered. The extent to which these negative results carry over to other families of sets is not known. In this paper, we consider families of sets that induce connected subgraphs in graphs. For such families, common in applications, we study whether lifted orders satisfying the well-studied axioms of dominance and (strict) independence exist for every or, in another setting, only for some underlying order on elements (strong and weak orderability). We characterize families that are strongly and weakly orderable under dominance and strict independence, and obtain a tight bound on the class of families that are strongly orderable under dominance and independence.