To mark the occasion of my PhD defense. I (Simon Rey) am organising a small workshop on the topic of my PhD thesis the day before the defense in the center of Amsterdam.

## When

On Thursday the 12th of October 2023, from 9:30 to 17:00.

## Where

Room F0.01 at the Bushuis, Kloveniersburgwal 48 (part of the Humanities Labs). The room is on the ground floor, on the left when you enter the building.

## Registration

The workshop is open to everyone (students, colleagues, public audience...) and is free. If you want to attend, please fill in the registration form. This will help us plan everything.

## Programme

Each talk is planned for 30 minutes and 10 minutes of questions.

9:30 | Doors open |
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9:45 - 10:30 | Jan Maly – Game Theoretic Foundations for Multiwinner Voting |

Mutliwinner voting is the process of selecting a committee of fixed size based on the preferences of a group of voters. Recently, there has been much enthusiasm around the idea that fair (i.e., proportional) committees can be achieved through a decentralized, market-based process in which voters are (virtually) given a budget and are allowed to buy candidates they are interested in. In this type of scenario, voters can form coalitions and pool their resources in order to maximize the number of representatives they are able to purchase. In this talk, I will report on an ongoing project that aims to do justice to this intuition by defining budgeting games, a class of normal-form games intended to capture voters coordinating to buy seats in a committee. Remarkably, many solution concepts of these games turn out to correspond to existing rules or fairness notions from the mutliwinner voting literature. As such, budgeting games can be used to rationalize existing rules (e.g., MES) and axioms (e.g., EJR and the core). Additionally, they might help us to discover new and stronger rules or fairness notions. Joint work with Adrian Haret, Sophie Klumper, Simon Rey and Guido Schäfer. | |

10:30 - 10:40 | Markus Utke – Presentation of Visual Tools for Participatory Budgeting |

10:40 - 11:00 | Morning tea |

11:00 - 11:45 | Dominik Peters |

11:45 - 12:30 | Piotr Skowron – Group Fairness in Social Choice |

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 Phragmen 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. | |

12:30 - 14:00 | Lunch |

14:00 - 14:45 | Edith Elkind– An Adaptive and Verifiably Proportional Method for Participatory Budgeting |

Participatory Budgeting (PB) is a form of participatory democracy in which citizens select a set of projects to be implemented, subject to a budget constraint. The Method of Equal Shares (MES) is a simple iterative method for this task which runs in polynomial time and satisfies a demanding proportionality axiom (Extended Justified Representation) in the setting of approval utilities. However, a downside of MES is that it is non-exhaustive: given an MES outcome, it may be possible to expand it by adding new projects without violating the budget constraint. To complete the outcome, the approach currently used in practice is as follows: given an instance with budget b, one searches for a budget b’>= b such that when MES is executed with budget b', it produces a maximal feasible solution for b. The search is greedy, i.e., one has to execute MES from scratch for each value of b'. To avoid redundant computation, we introduce a variant of MES, which we call Adaptive Method of Equal Shares (AMES). Our method is budget-adaptive, in the sense that, given an outcome W for a budget b and a new budget b'>b, it can compute the outcome W' for budget b' by leveraging similarities between W and W'. This eliminates the need to recompute solutions from scratch when increasing virtual budgets. Furthermore, AMES satisfies EJR in a certifiable way: given the output of our method, one can check in time O(n log n+mn) that it provides EJR (here, n is the number of voters and m is the number of projects). We evaluate the potential of AMES on real-world PB data, showing that small increases in budget typically require only minor modifications of the outcome. Based on joint work with Sonja Kraiczy | |

14:45 - 15:30 | Jérôme Lang – Fairness and Efficiency in Railway Network Design |

A geographical entity (a country, a region) wants to build a railway network. It is composed of a set of cities. For the sake of simplicity, we suppose that each inhabitant needs to commute between two cities. Building a line between two cities comes with a cost. A feasible network is a set of lines whose global cost does not exceed a given budget. The travel time along a line between two cities is supposed to be proportional to the distance between them. Given a network, the cost of an inhabitant is the duration, along the shortest path in the network, that they will need to commute. This is a (kind of) participatory budgeting problem. How can we define an optimal network? How can we compute it? How do the actual networks of a few selected countries score according to several criteria? You will learn it when you listen to the talk. Joint work with Florian Sikora, Silas Workman and Sirin Botan. | |

15:30 - 16:00 | Afternoon tea |

16:00 - 17:00 | Panel Discussion (4 panelists, TBA) |

17:00 | Doors close |

## Thesis

If you are curious about the thesis, you can access it here.

## Defence

The PhD defences in the Netherlands are public and open to anyone. If you want to attend it, it will take place on the Friday the 13th of October at 10.00 in the Agnietenkapel.