arXiv subjects

Grzegorz Lisowski

Publications and source records attributed to Grzegorz Lisowski.

15 recordsLinked to original sources

arXiv2026

Representation in Peer Selection: A Liquid Democracy Perspective

We study the peer selection problem in which a group of peers must select a fixed-size committee from among themselves. To this end, we introduce a class of approval-based preference profiles, inspired by delegation graphs in liquid democracy and the transitivity of trust therein, which we call ``liquid profiles''. Under this new domain restriction, each voter designates a single trusted agent and, in turn, approves all those trusted by that individual. After establishing relationships to standard restricted preference profiles and examining computational properties of liquid profiles, we focus on understanding how novel and established proportionality axioms behave in this domain and how they relate to one another. Then, we study their satisfaction under various voting rules, including new ones that are directly inspired by the structure of liquid profiles. Our findings reveal that particularly strong proportionality guarantees are attainable in this new domain, showing promise for applications to real-world peer selection problems via transitive delegations.

cs.GT↗

arXiv2026

Cycles in Liquid Democracy: A Game-Theoretic Justification

A common criticism of liquid democracy within the relevant academic literature is that delegation cycles can occur, seemingly resulting in unused voting power. Yet, practitioners argue that delegation cycles are not only unproblematic but are even formed intentionally by participants. To bring theory closer to reality, we introduce a model that captures this strategic behavior under uncertainty. We study the existence, structure and quality of Nash equilibria, revealing that delegation cycles naturally emerge. To complement these findings, we perform computational experiments using best-response dynamics.

cs.GT↗

arXiv2026

The Team Order Problem: Maximizing the Probability of Matching Being Large Enough

We consider a matching problem, which is meaningful in team competitions, as well as in information theory, recommender systems, and assignment problems. In the competitions which we study, each competitor in a team order plays a match with the corresponding opposing player. The team that wins more matches wins. We consider a problem where the input is the graph of probabilities that a team 1 player can win against the team 2 player, and the output is the optimal ordering of team 1 players given the fixed ordering of team 2. Our central result is a polynomial-time approximation scheme (PTAS) to compute a matching whose winning probability is at most epsilon less than the winning probability of the optimal matching. We also provide tractability results for several special cases of the problem, as well as an analytical bound on how far the winning probability of a maximum weight matching of the underlying graph is from the best achievable winning probability.

cs.GT↗

arXiv2025

Computing Equilibrium Nominations in Presidential Elections

We study strategic candidate nomination by parties in elections decided by Plurality voting. Each party selects a nominee before the election, and the winner is chosen from the nominated candidates based on the voters' preferences. We introduce a new restriction on these preferences, which we call party-aligned single-peakedness: all voters agree on a common ordering of the parties along an ideological axis, but may differ in their perceptions of the positions of individual candidates within each party. The preferences of each voter are single-peaked with respect to their own axis over the candidates, which is consistent with the global ordering of the parties. We present a polynomial-time algorithm for recognizing whether a preference profile satisfies party-aligned single-peakedness. In this domain, we give polynomial-time algorithms for deciding whether a given party can become the winner under some (or all) nominations, and whether this can occur in some pure Nash equilibrium. We also prove a tight result about the guaranteed existence of pure strategy Nash equilibria for elections with up to three parties for single-peaked and party-aligned single-peaked preference profiles.

cs.GT↗

arXiv2025

Identifying Imperfect Clones in Elections

A perfect clone in an ordinal election (i.e., an election where the voters rank the candidates in a strict linear order) is a set of candidates that each voter ranks consecutively. We consider different relaxations of this notion: independent or subelection clones are sets of candidates that only some of the voters recognize as a perfect clone, whereas approximate clones are sets of candidates such that every voter ranks their members close to each other, but not necessarily consecutively. We establish the complexity of identifying such imperfect clones, and of partitioning the candidates into families of imperfect clones. We also study the parameterized complexity of these problems with respect to a set of natural parameters such as the number of voters, the size or the number of imperfect clones we are searching for, or their level of imperfection.

cs.GT↗

arXiv2025

Project Submission Games in Participatory Budgeting

We introduce the framework of project submission games, capturing the behavior of project proposers in participatory budgeting (and multiwinner elections). Here, each proposer submits a subset of project proposals, aiming at maximizing the total cost of those that get funded. We focus on finding conditions under which pure Nash equilibria (NE) exist in our games, and on the complexity of checking whether they exist. We also seek algorithms for computing best responses for the proposers

cs.GT↗

arXiv2025

Two-Sided Manipulation Games in Stable Matching Markets

The Deferred Acceptance (DA) algorithm is an elegant procedure for finding a stable matching in two-sided matching markets. It ensures that no pair of agents prefers each other to their matched partners. In this work, we initiate the study of two-sided manipulations in matching markets as non-cooperative games. We introduce the accomplice manipulation game, where a man misreports to help a specific woman obtain a better partner, whenever possible. We provide a polynomial time algorithm for finding a pure strategy Nash equilibrium (NE) and show that our algorithm always yields a stable matching - although not every Nash equilibrium corresponds to a stable matching. Additionally, we show how our analytical techniques for the accomplice manipulation game can be applied to other manipulation games in matching markets, such as one-for-many and the standard self-manipulation games. We complement our theoretical findings with empirical evaluations of different properties of the resulting NE, such as the welfare of the agents.

cs.GT↗

arXiv2025

The Cost Perspective of Liquid Democracy: Feasibility and Control

We examine an approval-based model of Liquid Democracy with a budget constraint on voting and delegating costs, aiming to centrally select casting voters ensuring complete representation of the electorate. From a computational complexity perspective, we focus on minimizing overall costs, maintaining short delegation paths, and preventing excessive concentration of voting power. Furthermore, we explore computational aspects of strategic control, specifically, whether external agents can change election components to influence the voting power of certain voters.

cs.GT↗

arXiv2024

Strategic Cost Selection in Participatory Budgeting

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, Phragmén, and Method of Equal Shares rules. Furthermore, we report an experimental study of strategic cost selection on real-life PB election data.

cs.GT↗

arXiv2024

Discovering Consistent Subelections

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.

cs.GT↗

arXiv2024

Neighborhood Stability in Assignments on Graphs

We study the problem of assigning agents to the vertices of a graph such that no pair of neighbors can benefit from swapping assignments -- a property we term neighborhood stability. We further assume that agents' utilities are based solely on their preferences over the assignees of adjacent vertices and that those preferences are binary. Having shown that even this very restricted setting does not guarantee neighborhood stable assignments, we focus on special cases that provide such guarantees. We show that when the graph is a cycle or a path, a neighborhood stable assignment always exists for any preference profile. Furthermore, we give a general condition under which neighborhood stable assignments always exist. For each of these results, we give a polynomial-time algorithm to compute a neighborhood stable assignment.

cs.GT↗

arXiv2024

Guide to Numerical Experiments on Elections in Computational Social Choice

We analyze how numerical experiments regarding elections were conducted within the 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 used for 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.

cs.GT↗

arXiv2022

On the Complexity of Majority Illusion in Social Networks

Majority illusion occurs in a social network when the majority of the network nodes belong to a certain type but each node's neighbours mostly belong to a different type, therefore creating the wrong perception, i.e., the illusion, that the majority type is different from the actual one. From a system engineering point of view, we want to devise algorithms to detect and, crucially, correct this undesirable phenomenon. In this paper we initiate the computational study of majority illusion in social networks, providing complexity results for its occurrence and avoidance. Namely, we show that identifying whether a network can be labelled such that majority illusion is present, as well as the problem of removing an illusion by adding or deleting edges of the network, are NP-complete problems.

cs.MA↗

arXiv2020

Convergence of Opinion Diffusion is PSPACE-complete

We analyse opinion diffusion in social networks, where a finite set of individuals is connected in a directed graph and each simultaneously changes their opinion to that of the majority of their influencers. We study the algorithmic properties of the fixed-point behaviour of such networks, showing that the problem of establishing whether individuals converge to stable opinions is PSPACE-complete.

cs.MA↗

arXiv2019

Aggregation in Value-Based Argumentation Frameworks

Value-based argumentation enhances a classical abstract argumentation graph - in which arguments are modelled as nodes connected by directed arrows called attacks - with labels on arguments, called values, and an ordering on values, called audience, to provide a more fine-grained justification of the attack relation. With more than one agent facing such an argumentation problem, agents may differ in their ranking of values. When needing to reach a collective view, such agents face a dilemma between two equally justifiable approaches: aggregating their views at the level of values, or aggregating their attack relations, remaining therefore at the level of the graphs. We explore the strenghts and limitations of both approaches, employing techniques from preference aggregation and graph aggregation, and propose a third possibility aggregating rankings extracted from given attack relations.

cs.MA↗