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Stanisław Szufa

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24 papers

1 author row

AAAI Conference 2026 Conference Paper

Diversity of Structured Domains via k-Kemeny Scores

Piotr Faliszewski
Krzysztof Sornat
Stanisław Szufa
Tomasz Wąs

In the k-Kemeny problem, we are given an ordinal election, i.e., a collection of votes ranking the candidates from best to worst, and we seek the smallest number of swaps of adjacent candidates that ensure that the election has at most k different rankings. We study this problem for a number of structured domains, including the single-peaked, single-crossing, group-separable, and Euclidean ones. We obtain two kinds of results: (1) We show that k-Kemeny remains intractable under most of these domains, even for k=2, and (2) we use k-Kemeny to rank these domains in terms of their diversity.

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AAAI Conference 2026 Conference Paper

Putting Fair Division on the Map

Paula Böhm
Robert Bredereck
Paul Gölz
Andrzej Kaczmarczyk
Stanisław Szufa

The fair division of indivisible goods is not only a subject of theoretical research, but also an important problem in practice, with solutions being offered on several online platforms. Little is known, however, about the characteristics of real-world allocation instances and how they compare to synthetic instances. Using dimensionality reduction, we compute a map of allocation instances: a 2-dimensional embedding such that an instance's location on the map is predictive of the instance's origin and other key instance features. Because the axes of this map closely align with the utility matrix's two largest singular values, we define a second, explicit map, which we theoretically characterize.

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AAAI Conference 2025 Conference Paper

Distances Between Top-Truncated Elections of Different Sizes

Piotr Faliszewski
Jitka Mertlová
Pierre Nunn
Stanisław Szufa
Tomasz Wąs

The map of elections framework is a methodology for visualizing and analyzing election datasets. So far, the framework was restricted to elections that have equal numbers of candidates, equal numbers of voters, and where all the (ordinal) votes rank all the candidates. We extend it to the case of elections of different sizes, where the votes can be top-truncated. We use our results to present a visualization of a large fragment of the Preflib database.

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AIJ Journal 2025 Journal Article

Drawing a map of elections

Stanisław Szufa
Niclas Boehmer
Robert Bredereck
Piotr Faliszewski
Rolf Niedermeier
Piotr Skowron
Arkadii Slinko
Nimrod Talmon

Our main contribution is the introduction of the map of elections framework. A map of elections consists of three main elements: (1) a dataset of elections (i. e. , collections of ordinal votes over given sets of candidates), (2) a way of measuring similarities between these elections, and (3) a representation of the elections in the 2D Euclidean space as points, so that the more similar two elections are, the closer are their points. In our maps, we mostly focus on datasets of synthetic elections, but we also show an example of a map over real-life ones. To measure similarities, we would have preferred to use, e. g. , the isomorphic swap distance, but this is infeasible due to its high computational complexity. Hence, we propose polynomial-time computable positionwise distance and use it instead. Regarding the representations in 2D Euclidean space, we mostly use the Kamada-Kawai algorithm, but we also show two alternatives. We develop the necessary theoretical results to form our maps and argue experimentally that they are accurate and credible. Further, we show how coloring the elections in a map according to various criteria helps in analyzing results of a number of experiments. In particular, we show colorings according to the scores of winning candidates or committees, running times of ILP-based winner determination algorithms, and approximation ratios achieved by particular algorithms.

NeurIPS Conference 2025 Conference Paper

Strategic Cost Selection in Participatory Budgeting

Piotr Faliszewski
Łukasz Janeczko
Andrzej Kaczmarczyk
Grzegorz Lisowski
Piotr Skowron
Stanisław Szufa
Mateusz Szwagierczak

We study strategic behavior of project proposers in the context of approval-based participatory budgeting (PB). In our model we assume that the votes are fixed and known and the proposers want to set as high project prices as possible, provided that their projects get selected and the prices are not below the minimum costs of their delivery. We study the existence of pure Nash equilibria (NE) in such games, focusing on the AV/Cost, Phragmen, and Method of Equal Shares rules. We also provide an experimental study of cost selection on real-life PB election data.

JAIR Journal 2024 Journal Article

A Map of Diverse Synthetic Stable Matching Instances

Niclas Boehmer
Klaus Heeger
Stanisław Szufa

Focusing on Stable Roommates (SR), we contribute to the toolbox for conducting experiments for stable matching problems. We introduce the polynomial-time computable mutual attraction distance to measure the similarity of SR instances, analyze its properties, and use it to create a map of SR instances. This map visualizes 460 synthetic SR instances (each sampled from one of ten different statistical cultures) as follows: Each instance is a point in the plane, and two points are close on the map if the corresponding SR instances are similar with respect to our mutual attraction distance to each other. Subsequently, we conduct several illustrative experiments and depict their results on the map, illustrating the map’s usefulness as a non-aggregate visualization tool, the diversity of our generated dataset, and the need to use instances sampled from different statistical cultures. Lastly, we extend our approach to the bipartite Stable Marriage problem.

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AAMAS Conference 2024 Conference Paper

Discovering Consistent Subelections

Łukasz Janeczko
Jérôme Lang
Grzegorz Lisowski
Stanisław Szufa

We show how hidden interesting subelections can be discovered in ordinal elections. An interesting subelection consists of a reasonably large set of voters and a reasonably large set of candidates such that the former have a consistent opinion about the latter. Consistency may take various forms but we focus on three: Identity (all selected voters rank all selected candidates the same way), antagonism (half of the selected voters rank candidates in some order and the other half in the reverse order), and clones (all selected voters rank all selected candidates contiguously in the original election). We first study the computation of such hidden subelections. Second, we analyze synthetic and real-life data, and find that identifying hidden consistent subelections allows us to uncover some relevant concepts.

IJCAI Conference 2024 Conference Paper

Evaluation of Project Performance in Participatory Budgeting

Niclas Boehmer
Piotr Faliszewski
Łukasz Janeczko
Dominik Peters
Grzegorz Pierczyński
Šimon Schierreich
Piotr Skowron
Stanisław Szufa

We study ways of evaluating the performance of losing projects in participatory budgeting (PB) elections by seeking actions that would make them win. We focus on lowering their costs, obtaining additional approvals, and removing approvals for competing projects: The larger a change is needed, the less successful is the given project. We seek efficient algorithms for computing our measures and we analyze them experimentally, focusing on GreedyAV, Phragmen, and Equal-Shares PB rules.

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IJCAI Conference 2024 Conference Paper

Guide to Numerical Experiments on Elections in Computational Social Choice

Niclas Boehmer
Piotr Faliszewski
Łukasz Janeczko
Andrzej Kaczmarczyk
Grzegorz Lisowski
Grzegorz Pierczyński
Simon Rey
Dariusz Stolicki

We analyze how numerical experiments regarding elections were conducted within computational social choice literature (focusing on papers published in the IJCAI, AAAI, and AAMAS conferences). We analyze the sizes of the studied elections and the methods of generating preference data, thereby making previously hidden standards and practices explicit. In particular, we survey a number of statistical cultures for generating elections and their commonly used parameters.

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IJCAI Conference 2024 Conference Paper

Nonparametric Detection of Gerrymandering in Multiparty Plurality Elections

Dariusz Stolicki
Wojciech Słomczyński
Stanisław Szufa

Partisan gerrymandering, i. e. , manipulation of electoral district boundaries for political advantage, is one of the major challenges to election integrity in modern day democracies. Yet most of the existing methods for detecting partisan gerrymandering are narrowly tailored toward fully contested two-party elections, and fail if there are more parties or if the number of candidates per district varies. We propose a new method, applying nonparametric statistical learning to detect anomalies in the relation between (aggregate) votes and (aggregate) seats. Unlike in most of the existing methods, we propose to learn the standard of fairness in districting from empirical data rather than assume one a priori. Finally, we test the proposed methods against experimental data as well as real-life data from 17 countries employing the plurality (FPTP) system.

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IJCAI Conference 2024 Conference Paper

Selecting the Most Conflicting Pair of Candidates

Théo Delemazure
Łukasz Janeczko
Andrzej Kaczmarczyk
Stanisław Szufa

We study committee elections from a perspective of finding the most conflicting candidates, that is, candidates that imply the largest amount of conflict, as per voter preferences. By proposing basic axioms to capture this objective, we show that none of the prominent multiwinner voting rules meet them. Consequently, we design committee voting rules compliant with our desiderata, introducing conflictual voting rules. A subsequent deepened analysis sheds more light on how they operate. Our investigation identifies various aspects of conflict, for which we come up with relevant axioms and quantitative measures, which may be of independent interest. We support our theoretical study with experiments on both real-life and synthetic data.

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AAMAS Conference 2024 Conference Paper

Single-Winner Voting with Alliances: Avoiding the Spoiler Effect

Grzegorz Pierczyński
Stanisław Szufa

We study the setting of single-winner elections with ordinal preferences where candidates might be members of alliances (which may correspond to e. g. , political parties, factions, or coalitions). However, we do not assume that candidates from the same alliance are necessarily adjacent in voters’ rankings. In such a case, every classical voting rule is vulnerable to the spoiler effect, i. e. , the presence of a candidate may harm his or her alliance. We therefore introduce a new idea of alliance-aware voting rules which extend the classical ones. We show that our approach is superior both to using classical cloneproof voting rules and to running primaries within alliances before the election. We introduce several alliance-aware voting rules and show that they satisfy the most desirable standard properties of their classical counterparts as well as newly introduced axioms for the model with alliances which, e. g. , exclude the possibility of the spoiler effect. Our rules have natural definitions and are simple enough to explain to be used in practice.

AAMAS Conference 2024 Conference Paper

Strategic Cost Selection in Participatory Budgeting

Piotr Faliszewski
Łukasz Janeczko
Andrzej Kaczmarczyk
Grzegorz Lisowski
Piotr Skowron
Stanisław Szufa

We study strategic behavior of project proposers in the context of participatory budgeting. We assume that the votes are fixed and known and the proposers want to set as high project prices as possible, provided that their projects get selected and the prices are not below the minimum costs of their delivery. We study the existence of Nash equilibria in such games. Furthermore, we report an experimental study of the games we propose.

JAIR Journal 2024 Journal Article

The Complexity of Subelection Isomorphism Problems

Piotr Faliszewski
Krzysztof Sornat
Stanisław Szufa

We study extensions of the Election Isomorphism problem, focused on the existence of isomorphic subelections. Specifically, we propose the Subelection Isomorphism and the Maximum Common Subelection problems and study their computational complexity and approximability. Using our problems in experiments, we provide some insights into the nature of several statistical models of elections.

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AAMAS Conference 2023 Conference Paper

A Map of Diverse Synthetic Stable Roommates Instances

Niclas Boehmer
Klaus Heeger
Stanisław Szufa

Focusing on Stable Roommates (SR), we contribute to the toolbox for conducting experiments for stable matching problems. We introduce the polynomial-time computable mutual attraction distance to measure the similarity of SR instances, analyze its properties, and use it to create a map of SR instances. This map visualizes 460 synthetic SR instances (each sampled from one of ten different statistical cultures) as follows: Each instance is a point in the plane, and two points are close on the map if the corresponding SR instances are similar to each other. Subsequently, we conduct several exemplary experiments and depict their results on the map, illustrating the map’s usefulness as a non-aggregate visualization tool, the diversity of our generated dataset, and the need to use instances sampled from different statistical cultures.

IJCAI Conference 2023 Conference Paper

An Experimental Comparison of Multiwinner Voting Rules on Approval Elections

Piotr Faliszewski
Martin Lackner
Krzysztof Sornat
Stanisław Szufa

In this paper, we experimentally compare major approval based multiwinner voting rules. To this end, we define a measure of similarity between two equal sized committees subject to a given election. Using synthetic elections coming from several distributions, we analyze how similar are the committees provided by prominent voting rules. Our results can be visualized as maps of voting rules, which provide a counterpoint to a purely axiomatic classification of voting rules. The strength of our proposed method is its independence from preimposed classifications (such as the satisfaction of concrete axioms), and that it indeed offers a much finer distinction than the current state of axiomatic analysis.

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IJCAI Conference 2023 Conference Paper

Diversity, Agreement, and Polarization in Elections

Piotr Faliszewski
Andrzej Kaczmarczyk
Krzysztof Sornat
Stanisław Szufa
Tomasz Wąs

We consider the notions of agreement, diversity, and polarization in ordinal elections (that is, in elections where voters rank the candidates). While (computational) social choice offers good measures of agreement between the voters, such measures for the other two notions are lacking. We attempt to rectify this issue by designing appropriate measures, providing means of their (approximate) computation, and arguing that they, indeed, capture diversity and polarization well. In particular, we present "maps of preference orders" that highlight relations between the votes in a given election and which help in making arguments about their nature.

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IJCAI Conference 2023 Conference Paper

Participatory Budgeting: Data, Tools and Analysis

Piotr Faliszewski
Jarosław Flis
Dominik Peters
Grzegorz Pierczyński
Piotr Skowron
Dariusz Stolicki
Stanisław Szufa
Nimrod Talmon

We provide a library of participatory budgeting data (Pabulib) and open source tools (Pabutools and Pabustats) for analysing this data. We analyse how the results of participatory budgeting elections would change if a different selection rule was applied. We provide evidence that the outcomes of the Method of Equal Shares would be considerably fairer than those of the Utilitarian Greedy rule that is currently in use. We also show that the division of the projects into districts and/or categories can in many cases be avoided when using proportional rules. We find that this would increase the overall utility of the voters.

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NeurIPS Conference 2022 Conference Paper

Expected Frequency Matrices of Elections: Computation, Geometry, and Preference Learning

Niclas Boehmer
Robert Bredereck
Edith Elkind
Piotr Faliszewski
Stanisław Szufa

We use the "map of elections" approach of Szufa et al. (AAMAS 2020) to analyze several well-known vote distributions. For each of them, we give an explicit formula or an efficient algorithm for computing its frequency matrix, which captures the probability that a given candidate appears in a given position in a sampled vote. We use these matrices to draw the "skeleton map" of distributions, evaluate its robustness, and analyze its properties. We further develop a general and unified framework for learning the distribution of real-world preferences using the frequency matrices of established vote distributions.

IJCAI Conference 2022 Conference Paper

How to Sample Approval Elections?

Stanisław Szufa
Piotr Faliszewski
Łukasz Janeczko
Martin Lackner
Arkadii Slinko
Krzysztof Sornat
Nimrod Talmon

We extend the map-of-elections framework to the case of approval elections. While doing so, we study a number of statistical cultures, including some new ones, and we analyze their properties. We find that approval elections can be understood in terms of the average number of approvals in the votes, and the extent to which the votes are chaotic.

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AAAI Conference 2022 Conference Paper

The Complexity of Subelection Isomorphism Problems

Piotr Faliszewski
Krzysztof Sornat
Stanisław Szufa

We study extensions of the Election Isomorphism problem, focused on the existence of isomorphic subelections. Specifically, we propose the SUBELECTION ISOMORPHISM and the MAXIMUM COMMON SUBELECTION problems and study their computational complexity and approximability. Using our problems in experiments, we provide some insights into the nature of several statistical models of elections.

IJCAI Conference 2022 Conference Paper

Understanding Distance Measures Among Elections

Niclas Boehmer
Piotr Faliszewski
Rolf Niedermeier
Stanisław Szufa
Tomasz Wąs

Motivated by putting empirical work based on (synthetic) election data on a more solid mathematical basis, we analyze six distances among elections, including, e. g. , the challenging-to-compute but very precise swap distance and the distance used to form the so-called map of elections. Among the six, the latter seems to strike the best balance between its computational complexity and expressiveness.

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IJCAI Conference 2021 Conference Paper

Putting a Compass on the Map of Elections

Niclas Boehmer
Robert Bredereck
Piotr Faliszewski
Rolf Niedermeier
Stanisław Szufa

In their AAMAS 2020 paper, Szufa et al. presented a "map of elections" that visualizes a set of 800 elections generated from various statistical cultures. While similar elections are grouped together on this map, there is no obvious interpretation of the elections' positions. We provide such an interpretation by introducing four canonical “extreme” elections, acting as a compass on the map. We use them to analyze both a dataset provided by Szufa et al. and a number of real-life elections. In effect, we find a new parameterization of the Mallows model, based on measuring the expected swap distance from the central preference order, and show that it is useful for capturing real-life scenarios.

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AAAI Conference 2019 Conference Paper

How Similar Are Two Elections?

Piotr Faliszewski
Piotr Skowron
Arkadii Slinko
Stanisław Szufa
Nimrod Talmon

We introduce the ELECTION ISOMORPHISM problem and a family of its approximate variants, which we refer to as d- ISOMORPHISM DISTANCE (d-ID) problems (where d is a metric between preference orders). We show that ELECTION ISOMORPHISM is polynomial-time solvable, and that the d- ISOMORPHISM DISTANCE problems generalize various classic rank-aggregation methods (e. g. , those of Kemeny and Litvak). We establish the complexity of our problems (including their inapproximability) and provide initial experiments regarding the ability to solve them in practice.