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Markus Utke

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4 papers

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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.

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IJCAI Conference 2025 Conference Paper

Discrete Budget Aggregation: Truthfulness and Proportionality

Ulrike Schmidt-Kraepelin
Warut Suksompong
Markus Utke

We study a budget aggregation setting where voters express their preferred allocation of a fixed budget over a set of alternatives, and a mechanism aggregates these preferences into a single output allocation. Motivated by scenarios in which the budget is not perfectly divisible, we depart from the prevailing literature by restricting the mechanism to output allocations that assign integral amounts. This seemingly minor deviation has significant implications for the existence of truthful mechanisms. Specifically, when voters can propose fractional allocations, we demonstrate that the Gibbard-Satterthwaite theorem can be extended to our setting. In contrast, when voters are restricted to integral ballots, we identify a class of truthful mechanisms by adapting moving-phantom mechanisms to our context. Finally, we show that while a weak form of proportionality can be achieved alongside truthfulness, stronger proportionality notions derived from approval-based committee voting are incompatible with truthfulness.

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AAMAS Conference 2025 Conference Paper

Pabuviz. org: A Visualisation Platform to Explore Participatory Budgeting Elections

Markus Utke
Simon Rey
Ulle Endriss

We present pabuviz. org, an interactive website that provides indepth visualisation tools to compare the outcomes that would have been returned by a range of different voting rules for participatory budgeting when applied to historical election data. This information can help policy makers with choosing an appropriate voting rule.

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NeurIPS Conference 2023 Conference Paper

Anonymous and Copy-Robust Delegations for Liquid Democracy

Markus Utke
Ulrike Schmidt-Kraepelin

Liquid democracy with ranked delegations is a novel voting scheme that unites the practicability of representative democracy with the idealistic appeal of direct democracy: Every voter decides between casting their vote on a question at hand or delegating their voting weight to some other, trusted agent. Delegations are transitive, and since voters may end up in a delegation cycle, they are encouraged to indicate not only a single delegate, but a set of potential delegates and a ranking among them. Based on the delegation preferences of all voters, a delegation rule selects one representative per voter. Previous work has revealed a trade-off between two properties of delegation rules called anonymity and copy-robustness. To overcome this issue we study two fractional delegation rules: Mixed Borda branching, which generalizes a rule satisfying copy-robustness, and the random walk rule, which satisfies anonymity. Using the Markov chain tree theorem, we show that the two rules are in fact equivalent, and simultaneously satisfy generalized versions of the two properties. Combining the same theorem with Fulkerson's algorithm, we develop a polynomial-time algorithm for computing the outcome of the studied delegation rule. This algorithm is of independent interest, having applications in semi-supervised learning and graph theory.

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