Martin Lackner

Paul Anton Bachmann, Niclas Boehmer, Lukas Daniel Klausner et al.

With the growing adoption of AI systems, reasoning about how society can exert control over AI becomes an increasingly urgent problem. Existing work on democratic control largely focuses on macro-level governance. In contrast, we propose a new approach grounded in social choice theory, which we term collective control of artificial intelligence. We argue that collective input can and should be incorporated at multiple points across the ML development pipeline, from data collection through objective design to alignment. We further demonstrate that social choice provides a well-suited modelling language for the treatment of collective input across all stages and that its axiomatic methodology yields principled criteria for evaluating various control mechanisms. Overall, our conceptual contribution provides a mathematically grounded framework to implement and analyse collective control of AI systems.

Anton Baychkov, Martin Lackner, Jan Maly et al.

Recently, in the social choice literature, much attention has been given to the question of avoiding underrepresentation in approval-based multi-winner voting. In this paper, we explore the largely overlooked complementary question of avoiding overrepresentation. This has not been explored systematically, despite being a desirable property with concrete applications. Intuitively, overrepresentation happens when a group determines a disproportionately large part of the committee, thereby exceeding the group's quota. We formulate a strong and appealing axiom for avoiding overrepresentation, called justifiable upper quota (JUQ). We introduce a generalization of Thiele rules, composite Thiele rules, and characterize the unique rule in this class satisfying our axiom. This rule, Adams-AV, which naturally extends Adams' apportionment method, has not been studied before. Additionally, we introduce a polynomial-time rule that satisfies JUQ. Furthermore, we introduce justified near quota, an axiom that balances avoiding under- and overrepresentation. It characterizes the unique Thiele rule extending the Sainte-Laguë apportionment method. Finally, we analyze the compatibility of our axioms with established proportionality notions such as EJR+.

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. This paper focuses on PB processes where citizens may give 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.

Martin Lackner, Piotr Skowron

To choose a suitable multiwinner voting rule is a hard and ambiguous task. Depending on the context, it varies widely what constitutes the choice of an ``optimal'' subset of alternatives. In this paper, we provide a quantitative analysis of multiwinner voting rules using methods from the theory of approximation algorithms---we estimate how well multiwinner rules approximate two extreme objectives: a representation criterion defined via the Approval Chamberlin--Courant rule and a utilitarian criterion defined via Multiwinner Approval Voting. With both theoretical and experimental methods, we classify multiwinner rules in terms of their quantitative alignment with these two opposing objectives. Our results provide fundamental information about the nature of multiwinner rules and, in particular, about the necessary tradeoffs when choosing such a rule.

Piotr Skowron, Martin Lackner, Markus Brill et al.

In this paper we extend the principle of proportional representation to rankings. We consider the setting where alternatives need to be ranked based on approval preferences. In this setting, proportional representation requires that cohesive groups of voters are represented proportionally in each initial segment of the ranking. Proportional rankings are desirable in situations where initial segments of different lengths may be relevant, e.g., hiring decisions (if it is unclear how many positions are to be filled), the presentation of competing proposals on a liquid democracy platform (if it is unclear how many proposals participants are taking into consideration), or recommender systems (if a ranking has to accommodate different user types). We study the proportional representation provided by several ranking methods and prove theoretical guarantees. Furthermore, we experimentally evaluate these methods and present preliminary evidence as to which methods are most suitable for producing proportional rankings.