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Piotr Faliszewski

Piotr Faliszewski appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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Computer Science and Game TheoryMultiagent SystemsComputational ComplexityArtificial IntelligenceData Structures and Algorithmsecon.THcs.CYDiscrete MathematicsMachine Learning

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Published work

32 published item(s)

preprint2026arXiv

Agreement, Diversity, and Polarization Indices for Approval Elections

An index is a function that given an election outputs a value between 0 and 1, indicating the extent to which this election has a particular feature. We seek indices that capture agreement, diversity, and polarization among voters in approval elections, and that are normalized with respect to saturation. By the latter we mean that if two elections differ by the fraction of candidates approved by an average voter, but otherwise are of similar nature, then they should have similar index values. We propose several indices, analyze their properties, and use them to (a) derive a new map of approval elections, and (b) show similarities and differences between various real-life elections from Pabulib, Preflib and other sources.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

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

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. Finally, we develop a general and unified framework for learning the distribution of real-world preferences using the frequency matrices of established vote distributions.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

A Quantitative and Qualitative Analysis of the Robustness of (Real-World) Election Winners

Contributing to the toolbox for interpreting election results, we evaluate the robustness of election winners to random noise. We compare the robustness of different voting rules and evaluate the robustness of real-world election winners from the Formula 1 World Championship and some variant of political elections. We find many instances of elections that have very non-robust winners and numerous delicate robustness patterns that cannot be identified using classical and simpler approaches.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Robustness of Greedy Approval Rules

We study the robustness of GreedyCC, GreedyPAV, and Phargmen's sequential rule, using the framework introduced by Bredereck et al. for the case of (multiwinner) ordinal elections and adopted to the approval setting by Gawron and Faliszewski. First, we show that for each of our rules and every committee size $k$, there are elections in which adding or removing a certain approval causes the winning committee to completely change (i.e., the winning committee after the operation is disjoint from the one before the operation). Second, we show that the problem of deciding how many approvals need to be added (or removed) from an election to change its outcome is NP-complete for each of our rules. Finally, we experimentally evaluate the robustness of our rules in the presence of random noise.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

The Complexity of Proportionality Degree in Committee Elections

Over the last few years, researchers have put significant effort into understanding of the notion of proportional representation in committee election. In particular, recently they have proposed the notion of proportionality degree. We study the complexity of computing committees with a given proportionality degree and of testing if a given committee provides a particular one. This way, we complement recent studies that mostly focused on the notion of (extended) justified representation. We also study the problems of testing if a cohesive group of a given size exists and of counting such groups.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Using Multiwinner Voting to Search for Movies

We show a prototype of a system that uses multiwinner voting to suggest resources (such as movies) related to a given query set (such as a movie that one enjoys). Depending on the voting rule used, the system can either provide resources very closely related to the query set or a broader spectrum of options. We show how this ability can be interpreted as a way of controlling the diversity of the results. We test our system both on synthetic data and on the real-life collection of movie ratings from the MovieLens dataset. We also present a visual comparison of the search results corresponding to selected diversity levels.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Line-Up Elections: Parallel Voting with Shared Candidate Pool

We introduce the model of line-up elections which captures parallel or sequential single-winner elections with a shared candidate pool. The goal of a line-up election is to find a high-quality assignment of a set of candidates to a set of positions such that each position is filled by exactly one candidate and each candidate fills at most one position. A score for each candidate-position pair is given as part of the input, which expresses the qualification of the candidate to fill the position. We propose several voting rules for line-up elections and analyze them from an axiomatic and an empirical perspective using real-world data from the popular video game FIFA.

0 citations0 reviewsNo code linkedOpen access
preprint2018arXiv

Algorithms for Destructive Shift Bribery

We study the complexity of Destructive Shift Bribery. In this problem, we are given an election with a set of candidates and a set of voters (each ranking the candidates from the best to the worst), a despised candidate $d$, a budget $B$, and prices for shifting $d$ back in the voters' rankings. The goal is to ensure that $d$ is not a winner of the election. We show that this problem is polynomial-time solvable for scoring protocols (encoded in unary), the Bucklin and Simplified Bucklin rules, and the Maximin rule, but is NP-hard for the Copeland rule. This stands in contrast to the results for the constructive setting (known from the literature), for which the problem is polynomial-time solvable for $k$-Approval family of rules, but is NP-hard for the Borda, Copeland, and Maximin rules. We complement the analysis of the Copeland rule showing W-hardness for the parameterization by the budget value, and by the number of affected voters. We prove that the problem is W-hard when parameterized by the number of voters even for unit prices. From the positive perspective we provide an efficient algorithm for solving the problem parameterized by the combined parameter the number of candidates and the maximum bribery price (alternatively the number of different bribery prices).

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Axiomatic Characterization of Committee Scoring Rules

Committee scoring rules form a rich class of aggregators of voters' preferences for the purpose of selecting subsets of objects with desired properties, e.g., a shortlist of candidates for an interview, a representative collective body such as a parliament, or a set of locations for a set of public facilities. In the spirit of celebrated Young's characterization result that axiomatizes single-winner scoring rules, we provide an axiomatic characterization of multiwinner committee scoring rules. We show that committee scoring rules---despite forming a remarkably general class of rules---are characterized by the set of four standard axioms, anonymity, neutrality, consistency and continuity, and by one axiom specific to multiwinner rules which we call committee dominance. In the course of our proof, we develop several new notions and techniques. In particular, we introduce and axiomatically characterize multiwinner decision scoring rules, a class of rules that broadly generalizes the well-known majority relation.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Finding a Collective Set of Items: From Proportional Multirepresentation to Group Recommendation

We consider the following problem: There is a set of items (e.g., movies) and a group of agents (e.g., passengers on a plane); each agent has some intrinsic utility for each of the items. Our goal is to pick a set of $K$ items that maximize the total derived utility of all the agents (i.e., in our example we are to pick $K$ movies that we put on the plane's entertainment system). However, the actual utility that an agent derives from a given item is only a fraction of its intrinsic one, and this fraction depends on how the agent ranks the item among the chosen, available, ones. We provide a formal specification of the model and provide concrete examples and settings where it is applicable. We show that the problem is hard in general, but we show a number of tractability results for its natural special cases.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Multiwinner Analogues of Plurality Rule: Axiomatic and Algorithmic Perspectives

We characterize the class of committee scoring rules that satisfy the fixed-majority criterion. In some sense, the committee scoring rules in this class are multiwinner analogues of the single-winner Plurality rule, which is uniquely characterized as the only single-winner scoring rule that satisfies the simple majority criterion. We define top-$k$-counting committee scoring rules and show that the fixed majority consistent rules are a subclass of the top-$k$-counting rules. We give necessary and sufficient conditions for a top-$k$-counting rule to satisfy the fixed-majority criterion. We find that, for most of the rules in our new class, the complexity of winner determination is high (that is, the problem of computing the winners is NP-hard), but we also show examples of rules with polynomial-time winner determination procedures. For some of the computationally hard rules, we provide either exact FPT algorithms or approximate polynomial-time algorithms.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Prices Matter for the Parameterized Complexity of Shift Bribery

In the Shift Bribery problem, we are given an election (based on preference orders), a preferred candidate $p$, and a budget. The goal is to ensure that $p$ wins by shifting $p$ higher in some voters' preference orders. However, each such shift request comes at a price (depending on the voter and on the extent of the shift) and we must not exceed the given budget. We study the parameterized computational complexity of Shift Bribery with respect to a number of parameters (pertaining to the nature of the solution sought and the size of the election) and several classes of price functions. When we parameterize Shift Bribery by the number of affected voters, then for each of our voting rules (Borda, Maximin, Copeland) the problem is W[2]-hard. If, instead, we parameterize by the number of positions by which $p$ is shifted in total,then the problem is fixed-parameter tractable for Borda and Maximin,and is W[1]-hard for Copeland. If we parameterize by the budget, then the results depend on the price function class. We also show that Shift Bribery tends to be tractable when parameterized by the number of voters, but that the results for the number of candidates are more enigmatic.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Campaign Management under Approval-Driven Voting Rules

Approval-like voting rules, such as Sincere-Strategy Preference-Based Approval voting (SP-AV), the Bucklin rule (an adaptive variant of $k$-Approval voting), and the Fallback rule (an adaptive variant of SP-AV) have many desirable properties: for example, they are easy to understand and encourage the candidates to choose electoral platforms that have a broad appeal. In this paper, we investigate both classic and parameterized computational complexity of electoral campaign management under such rules. We focus on two methods that can be used to promote a given candidate: asking voters to move this candidate upwards in their preference order or asking them to change the number of candidates they approve of. We show that finding an optimal campaign management strategy of the first type is easy for both Bucklin and Fallback. In contrast, the second method is computationally hard even if the degree to which we need to affect the votes is small. Nevertheless, we identify a large class of scenarios that admit fixed-parameter tractable algorithms.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Properties of Multiwinner Voting Rules

The goal of this paper is to propose and study properties of multiwinner voting rules which can be consider as generalisations of single-winner scoring voting rules. We consider SNTV, Bloc, k-Borda, STV, and several variants of Chamberlin--Courant's and Monroe's rules and their approximations. We identify two broad natural classes of multiwinner score-based rules, and show that many of the existing rules can be captured by one or both of these approaches. We then formulate a number of desirable properties of multiwinner rules, and evaluate the rules we consider with respect to these properties.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Cloning in Elections: Finding the Possible Winners

We consider the problem of manipulating elections by cloning candidates. In our model, a manipulator can replace each candidate c by several clones, i.e., new candidates that are so similar to c that each voter simply replaces c in his vote with a block of these new candidates, ranked consecutively. The outcome of the resulting election may then depend on the number of clones as well as on how each voter orders the clones within the block. We formalize what it means for a cloning manipulation to be successful (which turns out to be a surprisingly delicate issue), and, for a number of common voting rules, characterize the preference profiles for which a successful cloning manipulation exists. We also consider the model where there is a cost associated with producing each clone, and study the complexity of finding a minimum-cost cloning manipulation. Finally, we compare cloning with two related problems: the problem of control by adding candidates and the problem of possible (co)winners when new alternatives can join.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Combinatorial Voter Control in Elections

Voter control problems model situations such as an external agent trying to affect the result of an election by adding voters, for example by convincing some voters to vote who would otherwise not attend the election. Traditionally, voters are added one at a time, with the goal of making a distinguished alternative win by adding a minimum number of voters. In this paper, we initiate the study of combinatorial variants of control by adding voters: In our setting, when we choose to add a voter~$v$, we also have to add a whole bundle $κ(v)$ of voters associated with $v$. We study the computational complexity of this problem for two of the most basic voting rules, namely the Plurality rule and the Condorcet rule.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Parameterized Algorithmics for Computational Social Choice: Nine Research Challenges

Computational Social Choice is an interdisciplinary research area involving Economics, Political Science, and Social Science on the one side, and Mathematics and Computer Science (including Artificial Intelligence and Multiagent Systems) on the other side. Typical computational problems studied in this field include the vulnerability of voting procedures against attacks, or preference aggregation in multi-agent systems. Parameterized Algorithmics is a subfield of Theoretical Computer Science seeking to exploit meaningful problem-specific parameters in order to identify tractable special cases of in general computationally hard problems. In this paper, we propose nine of our favorite research challenges concerning the parameterized complexity of problems appearing in this context.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Possible Winners in Noisy Elections

We consider the problem of predicting winners in elections, for the case where we are given complete knowledge about all possible candidates, all possible voters (together with their preferences), but where it is uncertain either which candidates exactly register for the election or which voters cast their votes. Under reasonable assumptions, our problems reduce to counting variants of election control problems. We either give polynomial-time algorithms or prove #P-completeness results for counting variants of control by adding/deleting candidates/voters for Plurality, k-Approval, Approval, Condorcet, and Maximin voting rules. We consider both the general case, where voters' preferences are unrestricted, and the case where voters' preferences are single-peaked.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Achieving Fully Proportional Representation is Easy in Practice

We provide experimental evaluation of a number of known and new algorithms for approximate computation of Monroe's and Chamberlin-Courant's rules. Our experiments, conducted both on real-life preference-aggregation data and on synthetic data, show that even very simple and fast algorithms can in many cases find near-perfect solutions. Our results confirm and complement very recent theoretical analysis of Skowron et al., who have shown good lower bounds on the quality of (some of) the algorithms that we study.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Achieving Fully Proportional Representation: Approximability Results

We study the complexity of (approximate) winner determination under the Monroe and Chamberlin--Courant multiwinner voting rules, which determine the set of representatives by optimizing the total (dis)satisfaction of the voters with their representatives. The total (dis)satisfaction is calculated either as the sum of individual (dis)satisfactions (the utilitarian case) or as the (dis)satisfaction of the worst off voter (the egalitarian case). We provide good approximation algorithms for the satisfaction-based utilitarian versions of the Monroe and Chamberlin--Courant rules, and inapproximability results for the dissatisfaction-based utilitarian versions of them and also for all egalitarian cases. Our algorithms are applicable and particularly appealing when voters submit truncated ballots. We provide experimental evaluation of the algorithms both on real-life preference-aggregation data and on synthetic data. These experiments show that our simple and fast algorithms can in many cases find near-perfect solutions.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Approximating the MaxCover Problem with Bounded Frequencies in FPT Time

We study approximation algorithms for several variants of the MaxCover problem, with the focus on algorithms that run in FPT time. In the MaxCover problem we are given a set N of elements, a family S of subsets of N, and an integer K. The goal is to find up to K sets from S that jointly cover (i.e., include) as many elements as possible. This problem is well-known to be NP-hard and, under standard complexity-theoretic assumptions, the best possible polynomial-time approximation algorithm has approximation ratio (1 - 1/e). We first consider a variant of MaxCover with bounded element frequencies, i.e., a variant where there is a constant p such that each element belongs to at most p sets in S. For this case we show that there is an FPT approximation scheme (i.e., for each B there is a B-approximation algorithm running in FPT time) for the problem of maximizing the number of covered elements, and a randomized FPT approximation scheme for the problem of minimizing the number of elements left uncovered (we take K to be the parameter). Then, for the case where there is a constant p such that each element belongs to at least p sets from S, we show that the standard greedy approximation algorithm achieves approximation ratio exactly (1-e^{-max(pK/|S|, 1)}). We conclude by considering an unrestricted variant of MaxCover, and show approximation algorithms that run in exponential time and combine an exact algorithm with a greedy approximation. Some of our results improve currently known results for MaxVertexCover.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Complexity of Manipulation, Bribery, and Campaign Management in Bucklin and Fallback Voting

A central theme in computational social choice is to study the extent to which voting systems computationally resist manipulative attacks seeking to influence the outcome of elections, such as manipulation (i.e., strategic voting), control, and bribery. Bucklin and fallback voting are among the voting systems with the broadest resistance (i.e., NP-hardness) to control attacks. However, only little is known about their behavior regarding manipulation and bribery attacks. We comprehensively investigate the computational resistance of Bucklin and fallback voting for many of the common manipulation and bribery scenarios; we also complement our discussion by considering several campaign management problems for Bucklin and fallback.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Fully Proportional Representation as Resource Allocation: Approximability Results

We model Monroe's and Chamberlin and Courant's multiwinner voting systems as a certain resource allocation problem. We show that for many restricted variants of this problem, under standard complexity-theoretic assumptions, there are no constant-factor approximation algorithms. Yet, we also show cases where good approximation algorithms exist (briefly put, these variants correspond to optimizing total voter satisfaction under Borda scores, within Monroe's and Chamberlin and Courant's voting systems).

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

The Complexity of Fully Proportional Representation for Single-Crossing Electorates

We study the complexity of winner determination in single-crossing elections under two classic fully proportional representation rules---Chamberlin--Courant's rule and Monroe's rule. Winner determination for these rules is known to be NP-hard for unrestricted preferences. We show that for single-crossing preferences this problem admits a polynomial-time algorithm for Chamberlin--Courant's rule, but remains NP-hard for Monroe's rule. Our algorithm for Chamberlin--Courant's rule can be modified to work for elections with bounded single-crossing width. To circumvent the hardness result for Monroe's rule, we consider single-crossing elections that satisfy an additional constraint, namely, ones where each candidate is ranked first by at least one voter (such elections are called narcissistic). For single-crossing narcissistic elections, we provide an efficient algorithm for the egalitarian version of Monroe's rule.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Weighted Electoral Control

Although manipulation and bribery have been extensively studied under weighted voting, there has been almost no work done on election control under weighted voting. This is unfortunate, since weighted voting appears in many important natural settings. In this paper, we study the complexity of controlling the outcome of weighted elections through adding and deleting voters. We obtain polynomial-time algorithms, NP-completeness results, and for many NP-complete cases, approximation algorithms. In particular, for scoring rules we completely characterize the complexity of weighted voter control. Our work shows that for quite a few important cases, either polynomial-time exact algorithms or polynomial-time approximation algorithms exist.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

The Complexity of Manipulative Attacks in Nearly Single-Peaked Electorates

Many electoral bribery, control, and manipulation problems (which we will refer to in general as "manipulative actions" problems) are NP-hard in the general case. It has recently been noted that many of these problems fall into polynomial time if the electorate is single-peaked (i.e., is polarized along some axis/issue). However, real-world electorates are not truly single-peaked. There are usually some mavericks, and so real-world electorates tend to merely be nearly single-peaked. This paper studies the complexity of manipulative-action algorithms for elections over nearly single-peaked electorates, for various notions of nearness and various election systems. We provide instances where even one maverick jumps the manipulative-action complexity up to $\np$-hardness, but we also provide many instances where a reasonable number of mavericks can be tolerated without increasing the manipulative-action complexity.

0 citations0 reviewsNo code linkedOpen access
preprint2011arXiv

Clone Structures in Voters' Preferences

In elections, a set of candidates ranked consecutively (though possibly in different order) by all voters is called a clone set, and its members are called clones. A clone structure is a family of all clone sets of a given election. In this paper we study properties of clone structures. In particular, we give an axiomatic characterization of clone structures, show their hierarchical structure, and analyze clone structures in single-peaked and single-crossing elections. We give a polynomial-time algorithm that finds a minimal collection of clones that need to be collapsed for an election to become single-peaked, and we show that this problem is NP-hard for single-crossing elections.

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preprint2010arXiv

Approximation Algorithms for Campaign Management

We study electoral campaign management scenarios in which an external party can buy votes, i.e., pay the voters to promote its preferred candidate in their preference rankings. The external party's goal is to make its preferred candidate a winner while paying as little as possible. We describe a 2-approximation algorithm for this problem for a large class of electoral systems known as scoring rules. Our result holds even for weighted voters, and has applications for campaign management in commercial settings. We also give approximation algorithms for our problem for two Condorcet-consistent rules, namely, the Copeland rule and maximin.

0 citations0 reviewsNo code linkedOpen access
preprint2010arXiv

Multimode Control Attacks on Elections

In 1992, Bartholdi, Tovey, and Trick opened the study of control attacks on elections---attempts to improve the election outcome by such actions as adding/deleting candidates or voters. That work has led to many results on how algorithms can be used to find attacks on elections and how complexity-theoretic hardness results can be used as shields against attacks. However, all the work in this line has assumed that the attacker employs just a single type of attack. In this paper, we model and study the case in which the attacker launches a multipronged (i.e., multimode) attack. We do so to more realistically capture the richness of real-life settings. For example, an attacker might simultaneously try to suppress some voters, attract new voters into the election, and introduce a spoiler candidate. Our model provides a unified framework for such varied attacks, and by constructing polynomial-time multiprong attack algorithms we prove that for various election systems even such concerted, flexible attacks can be perfectly planned in deterministic polynomial time.

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preprint2010arXiv

Rationalizations of Condorcet-Consistent Rules via Distances of Hamming Type

The main idea of the {\em distance rationalizability} approach to view the voters' preferences as an imperfect approximation to some kind of consensus is deeply rooted in social choice literature. It allows one to define ("rationalize") voting rules via a consensus class of elections and a distance: a candidate is said to be an election winner if she is ranked first in one of the nearest (with respect to the given distance) consensus elections. It is known that many classic voting rules can be distance rationalized. In this paper, we provide new results on distance rationalizability of several Condorcet-consistent voting rules. In particular, we distance rationalize Young's rule and Maximin rule using distances similar to the Hamming distance. We show that the claim that Young's rule can be rationalized by the Condorcet consensus class and the Hamming distance is incorrect; in fact, these consensus class and distance yield a new rule which has not been studied before. We prove that, similarly to Young's rule, this new rule has a computationally hard winner determination problem.

0 citations0 reviewsNo code linkedOpen access