# WKRECAI Seminar

## Warsaw–Krakow Seminar on Economics and AI

## About

The seminar is organised by Piotr Faliszewski from AGH University of Science and Technology and by Piotr Skowron and Oskar Skibski from the University of Warsaw. The goal of the seminar is to tighten collaboration between the respective teams interested in computational social choice, social networks analysis, algorithmic game theory, and mechanism design.

We usually meet on the first Thursday of the month at 12:00.

#### Mailing List

The mailing list of the seminar is ai-econ@mimuw.edu.pl. You can subscribe to this list here (the subscription web-page is available from the internal network of the University of Warsaw) or you can send a subscription request to p.skowron@mimuw.edu.pl.

## Talks

*Next meetings: **2024-05-16** – Kraków!**2024-06-06** – Warsaw!* (last seminar of the semester)

2024-04-04: Gleb Polevoy (Paderborn)**Attaining Equilibria Using Control Sets**

Many interactions result in a socially suboptimal equilibrium, or in a non-equilibrium state, from which arriving at the desired equilibrium through simple dynamics can be impossible or take too long. Aiming at the theoretically and practically key problem of guaranteeing a certain equilibrium without altering the game, we persuade, bribe, or coerce a group of participants to make them act in a way that will motivate the rest of the players to act accordingly to the desired equilibrium. Formally, we ask which subset of the players can adopt the goal equilibrium strategies that will make acting according to the desired equilibrium a best response for the other players. We call such a subset a direct control set.

[slides] [example of breaking monotonicity]

We first show when the desired equilibrium having certain direct control sets implies the strength of that equilibrium, and study the hardness of finding lightest direct control sets, even approximately. We then solve important subcases and provide approximation algorithms. Next, we concentrate on potential games and prove that, while finding such a set is \NP-hard, even for a constant-factor approximation, we can still solve the problem approximately or even precisely in relevant special cases. We approximately solve this problem for singleton potential games and treat more closely specific potential games, such as symmetric games and coordination games on graphs.

2024-03-14: Andrzej Kaczmarczyk (AGH)**Selecting the Most Conflicting Pair of Candidates**

We study preference aggregation from a perspective of finding the most conflicting candidates, that is, candidates that imply the largest amount of conflict, as per the preferences. By proposing basic axioms to capture this objective, we observe that none of the prominent multiwinner voting rules meet them. Consequently, we design selection mechanisms 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.

2024-02-01: Tomáš Masařík (University of Warsaw)**A Generalised Theory of Proportionality in Collective Decision Making**

We consider a voting model, where a number of candidates need to be selected subject to certain feasibility constraints. The model generalises committee elections (where there is a single constraint on the number of candidates that need to be selected), various elections with diversity constraints, the model of public decisions (where decisions needs to be taken on a number of independent issues), and the model of collective scheduling. A critical property of voting is that it should be fair—not only to individuals but also to groups of voters with similar opinions on the subject of the vote; in other words, the outcome of an election should proportionally reflect the voters’ preferences. We formulate axioms of proportionality in this general model. Our axioms do not require predefining groups of voters; to the contrary, we ensure that the opinion of every subset of voters whose preferences are cohesive-enough are taken into account to the extent that is proportional to the size of the subset. Our axioms generalise the strongest known satisfiable axioms for the more specific models. We explain how to adapt two prominent committee election rules, Proportional Approval Voting (PAV) and Phragmén Sequential Rule, as well as the concept of stable-priceability to our general model. The two rules satisfy our proportionality axioms if and only if the feasibility constraints are matroids.

2024-01-25: Piotr Faliszewski (AGH University of Science and Technology)**Guide to Experiments in COMSOC**

In this talk I will discuss how numerical experiments on elections were typically performed in computational social choice and what we can learn from it. In particular, we will see what election sizes were considered and what statistical cultures were used etc. Further, we will analyze which choices were reasonable and under what conditions. The talk is based on the “Guide to Experiments” project, which collects experimental election papers from AAAI/IJCAI/AAMAS conferences held since 2010.

2023-12-07: Tomasz Wąs (LAMSADE, Paris)**Fairly Allocating Goods and (Terrible) Chores**

We study the fair allocation of mixtures of indivisible goods and chores under lexicographic preferences—a subdomain of additive preferences. A prominent fairness notion for allocating indivisible items is envy-freeness up to any item (EFX). Yet, its existence and computation has remained a notable open problem. By identifying a class of instances with “terrible chores”, we show that determining the existence of an EFX allocation is NP-complete. This result immediately implies the intractability of EFX under additive preferences. Nonetheless, we propose a natural subclass of lexicographic preferences for which an EFX and Pareto optimal (PO) allocation is guaranteed to exist and can be computed efficiently for any mixed instance. Focusing on two weaker fairness notions, we investigate finding EF1 and PO allocations for special instances with terrible chores, and show that MMS and PO allocations can be computed efficiently for any mixed instance with lexicographic preferences.

[slides]

2023-11-09: Grzegorz Lisowski (AGH University of Science and Technology)**Strategic Cost Selection in Participatory Budgeting**

We study strategic behaviour of project proposers in the context of approval-based participatory budgeting, assuming 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 in such games, for a number of voting rules. While such equilibria might not exist, we provide several positive results for intuitive restrictions of voters’ preferences. Furthermore, we report an experimental study of strategic cost selection on real-life election data.

2023-10-05: Oskar Skibski (University of Warsaw)**Vitality Indices and Game-Theoretic Centralities**

Vitality indices form a natural class of centrality measures that assess the importance of a node based on the impact its removal has on the network. In this talk, we will discuss the connection between vitality indices and game-theoretic centrality measures, which are centrality measures defined based on coalitional game theory. We will also discuss group centrality measures and define a group version of the Shapley value.

2023-06-22: Jarosław Flis (Jagiellonian University)**(PL) Ordynacja Proporcjonalno-Lokalna — ordynacja dla Polski?**

Opracowanie to przedstawia oryginalny projekt ordynacji proporcjonalno-lokalnej (dalej „ordynacji PL”), będący odpowiedzią na postulat wprowadzenia w Polsce ordynacji mieszanej. Proponowany system jest możliwie zbliżony do obecnego, choć jednocześnie wprowadza starannie przemyślane nowe elementy. Nawiązuje zarówno do najlepszych rozwiązań stosowanych w innych krajach, jak też opiera się do dogłębnych studiach nad realiami polskiego życia politycznego. Bierze pod uwagę obecne i możliwe strategie partii, kandydatów oraz wyborców. Wiele jego elementów jest odpowiedzią na obawy, które były podnoszone we wcześniejszych dyskusjach wokół takiej zmiany. Także takie obawy, które wynikają z doświadczeń państw, które dokonywały zmian ordynacji bez głębszych analiz i nie ustrzegły się poważnych błędów. Projekt ten był efektem prac specjalnego zespołu sejmowego, spotykającego się w latach 2021-2022.

2023-05-04: Grzegorz Pierczyński (University of Warsaw)**Market-Based Explanations of Collective Decisions**

We consider approval-based committee elections, in which a size-k subset of available candidates must be selected given approval sets for each voter, indicating the candidates approved by the voter. A number of axioms capturing ideas of fairness and proportionality have been proposed for this framework. We argue that even the strongest of them, such as priceability and the core, only rule out certain undesirable committees, but fail to ensure that the selected committee is fair in all cases. We propose two new solution concepts, stable priceability and balanced stable priceability, and show that they select arguably fair committees. Our solution concepts come with a non-trivial-to-construct but easy-to-understand market-based explanation for why the chosen committee is fair. We show that stable priceability is closely related to the notion of Lindahl equilibrium from economics.

2023-03-02: Sonja Kraiczy (University of Oxford)**Properties of the Mallows Model Depending on the Number of Alternatives: A Warning for an Experimentalist**

The Mallows model is a popular distribution for ranked data. We empirically and theoretically analyze how the properties of rankings sampled from the Mallows model change when increasing the number of alternatives. We find that real-world data behaves differently than the Mallows model, yet is in line with its recent variant proposed by Boehmer et al. [IJCAI ’21]. As part of our study, we issue several warnings about using the model.

2023-02-02: Oskar Skibski (University of Warsaw)**Closeness centrality via the Condorcet principle**

We provide a characterization of closeness centrality in the class of distance-based centralities. To this end, we introduce a natural property, called majority comparison, that states that out of two adjacent nodes the one closer to more nodes is more central. We prove that any distance-based centrality that satisfy this property gives the same ranking in every graph as closeness centrality. The axiom is inspired by the interpretation of the graph as an election in which nodes are both voters and candidates and their preferences are determined by the distances to the other nodes. Given this, majority comparison states that out of two adjacent nodes the one preferred by more nodes should have higher centrality.

2023-01-05: Piotr Faliszewski (AGH University of Science and Technology)**Map of Elections: Diversity, Polarization, and Agreement In Elections (+ some more)**

In this talk I will present the idea of the map of (ordinal) elections and argue what it is good for. First, we will spend considerable amount of time on understanding diversity, polarization, and agreement within elections on the map. Then, we will look at other applications, such as using the map to visualize performance of various algorithms.

2022-12-08: Piotr Skowron (University of Warsaw)**Proportionality in General Social Choice Models**

We consider a model where a number of candidates need to be selected subject to certain feasibility constraints. The model generalises committee elections (where there is a single constraint on the number of candidates that need to be selected), various elections with diversity constraints, the model of public decisions (where there is a set of independent issues, and the constraints say that we need to pick a single decision for each issue) and the model of collective scheduling. The voters express their preferences over the candidates through voting, and the goal is to select the outcome that would be arguable fair. We mainly focus on group fairness understood as proportionality. We formulate axioms of proportionality in this general model. Our axioms are always satisfiable, and generalise the strongest known satisfiable axioms for the more specific models. This is a working paper.

2022-11-03: Łukasz Janeczko (AGH University of Science and Technology)**Ties in Multiwinner Approval Voting**

We investigate ties in multiwinner approval voting both theoretically and experimentally. Specifically, we analyze the computational complexity of 1) determining if there is a tie in a given election for a given rule, and 2) the complexity of counting the number of winning committees. We mainly concentrate on Thiele rules as well as their greedy variants, and Phragmen-like rules (Phragmen and MES). We also conduct some experiments to see a) how often ties occur for different models, and b) how vulnerable to ties are different rules.

2022-10-06: Marcin Dziubiński (University of Warsaw)**Selecting a Winner with Impartial Referees**

We consider a problem of mechanism design without money, where a planner selects a winner among a set of agents with binary types and receives outside signals (like the report of impartial referees). We show that there is a gap between the optimal Dominant Strategy Incentive Compatible (DSIC) mechanism and the optimal Bayesian Incentive Compatible (BIC) mechanism. In the optimal BIC mechanism, the planner can leverage the outside signal to elicit information about agents’ types. BIC mechanisms are lexicographic mechanisms, where the planner first shortlists agents who receive high reports from the referees and then uses agents’ reports to break ties among agents in the shortlist. We compare the “self-evaluation” mechanism with a “peer evaluation” mechanism where agents evaluate other agents, and show that for the same signal precision, the self-evaluation mechanism outperforms the peer evaluation mechanism.

2022-07-06: Stanisław Szufa (AGH University of Science and Technology)**Numerical Experiments in Computational Social Choice**

While many papers in computational social choice are theoretical, the number of experimental works is rapidly growing. During the tutorial, we will focus on experiments related to voting and participatory budgeting. We will discuss most popular statistical culture models (that serve for generating synthetic elections), and real-life elections from several datasources such as, for example, Preflib or Pabulib. Moreover, we will describe Python libraries such as abcvoting (implementations of approval-based multiwinner voting rules) and mapel (tools for generating maps of elections).

2022-06-08: Marcin Waniek (New York University Abu Dhabi)**Social diffusion sources can escape detection**

Influencing (and being influenced by) others through social networks is fundamental to all human societies. Whether this happens through the diffusion of rumors, opinions, or viruses, identifying the diffusion source (i.e., the person that initiated it) is a problem that has attracted much research interest. Nevertheless, existing literature has ignored the possibility that the source might strategically modify the network structure (by rewiring links or introducing fake nodes) to escape detection. Here, without restricting our analysis to any particular diffusion scenario, we close this gap by evaluating two mechanisms that hide the source—one stemming from the source’s actions, the other from the network structure itself. This reveals that sources can easily escape detection, and that removing links is far more effective than introducing fake nodes. Thus, efforts should focus on exposing concealed ties rather than planted.