The ability to measure the satisfaction of (groups of) voters is a crucial prerequisite for formulating proportionality axioms in approval-based participatory budgeting elections. Two common -- but very different -- ways to measure the satisfaction of a voter consider (i) the number of approved projects and (ii) the total cost of approved projects, respectively. In general, it is difficult to decide which measure of satisfaction best reflects the voters' true utilities. In this paper, we study proportionality axioms with respect to large classes of approval-based satisfaction functions. We establish logical implications among our axioms and related notions from the literature, and we ask whether outcomes can be achieved that are proportional with respect to more than one satisfaction function. We show that this is impossible for the two commonly used satisfaction functions when considering proportionality notions based on extended justified representation, but achievable for a notion based on proportional justified representation. For the latter result, we introduce a strengthening of priceability and show that it is satisfied by several polynomial-time computable rules, including the Method of Equal Shares and Phragmén's sequential rule. 

Proportionality in Approval-Based Participatory Budgeting

We consider a voting scenario in which the resource to be voted upon may consist of both indivisible and divisible goods. This generalizes both the well-studied model of multiwinner voting and the recently introduced model of cake sharing. Under approval votes, we propose two variants of the extended justified representation (EJR) notion from multiwinner voting, a stronger one called EJR for mixed goods (EJR-M) and a weaker one called EJR up to 1 (EJR-1). We extend three multiwinner voting rules to our setting—GreedyEJR, the method of equal shares (MES), and proportional approval voting (PAV)—and show that while all three generalizations satisfy EJR-1, only the first one provides EJR-M. In addition, we derive tight bounds on the proportionality degree implied by EJR-M and EJR-1, and investigate the proportionality degree of our proposed rules.

Approval-Based Voting with Mixed Goods

Selecting a committee that meets diversity and proportionality criteria is a challenging endeavor that has been studied extensively in recent years. This task becomes even more challenging when some of the selected candidates decline the invitation to join the committee. Since the unavailability of one candidate may impact the rest of the selection, inviting all candidates at the same time may lead to a suboptimal committee. Instead, invitations should be sequential and conditional on which candidates invited so far accepted the invitation: the solution to the committee selection problem is a query policy. If invitation queries are binding, they should be safe: one should not query a candidate without being sure that whatever the set of available candidates possible at that stage, her inclusion will not jeopardize committee optimality. Assuming approval-based inputs, we characterize the set of rules for which a safe query exists at every stage. In order to parallelize the invitation process, we investigate the computation of safe parallel queries, and show that it is often hard. We also study the existence of safe parallel queries with respect to proportionality axioms such as extended justified representation.

Multiwinner Voting with Possibly Unavailable Candidates


In the house allocation problem with lower and upper quotas, we are given a set of applicants and a set of projects. Each applicant has a strictly ordered preference list over the projects, while the projects are equipped with a lower and an upper quota. A feasible matching assigns the applicants to the projects in such a way that a project is either matched to no applicant or to a number of applicants between its lower and upper quota. 
In this model we study two classic optimality concepts: Pareto optimality and popularity. We show that finding a popular matching is hard even if the maximum lower quota is 2 and that finding a perfect Pareto optimal matching, verifying Pareto optimality, and verifying popularity are all NP-complete even if the maximum lower quota is 3. We complement the last three negative results by showing that the problems become polynomial-time solvable when the maximum lower quota is 2, thereby answering two open questions of Cechlárová and Fleiner. Finally, we also study the parameterized complexity of all four mentioned problems.

Pareto optimal and popular house allocation with lower and upper quotas


Two actively researched problem settings in matchings under preferences are popular matchings and the three-dimensional stable matching problem with cyclic preferences. In this paper, we apply the optimality notion of the first topic to the input characteristics of the second one. We investigate the connection between stability, popularity, and their strict variants, strong stability and strong popularity in three-dimensional instances with cyclic preferences. Furthermore, we also derive results on the complexity of these problems when the preferences are derived from master lists.

Three-Dimensional Popular Matching with Cyclic Preferences

When selecting multiple candidates based on approval preferences of agents, the proportional representation of agents' opinions is an important and well-studied desideratum. Existing criteria for evaluating the representativeness of outcomes focus on groups of agents and demand that sufficiently large and cohesive groups are "represented" in the sense that candidates approved by some group members are selected. Crucially, these criteria say nothing about the representation of individual agents, even if these agents are members of groups that deserve representation. In this paper, we formalize the concept of individual representation (IR) and explore to which extent, and under which circumstances, it can be achieved. We show that checking whether an IR outcome exists is computationally intractable, and we verify that all common approval-based voting rules may fail to provide IR even in cases where this is possible. We then focus on domain restrictions and establish an interesting contrast between "voter interval" and "candidate interval" preferences. This contrast can also be observed in our experimental results, where we analyze the attainability of IR for realistic preference profiles.

Individual Representation in Approval-Based Committee Voting

In this paper, we study the problem of eliciting preferences of agents in the house allocation model. For this we build on a recently introduced model  and focus on the task of eliciting preferences to find matchings which are necessarily optimal, i.e., optimal under all possible completions of the elicited preferences.  In particular, we investigate the elicitation of necessarily Pareto optimal (NPO) and necessarily rank-maximal (NRM) matchings. Most importantly, we answer an open question and give an online algorithm for eliciting an NRM matching in the next-best query model which is  3/2-competitive, i.e., it takes at most 3/2 as many queries as an optimal algorithm. Besides this, we extend this field of research by introducing two new natural models of elicitation and by studying both the complexity of determining whether a necessarily optimal matching exists in them, and by giving online algorithms for these models.

Online Elicitation of Necessarily Optimal Matchings

GTEP: Fair Division / Social Choice / Voting

poster

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AAAI 2023

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines.

GTEP: Social Choice / Voting 3

Oral Session 1A1-2

technical paper

AAMAS (International Conference on Autonomous Agents and Multiagent Systems) is the largest and most influential conference in the area of agents and multiagent systems. The aim of the conference is to bring together researchers and practitioners in all areas of agent technology and to provide a single, high-profile, internationally renowned forum for research in the theory and practice of autonomous agents and multiagent systems. AAMAS is the flagship conference of the non-profit International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS).

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AAMAS 2022

AAMAS (International Conference on Autonomous Agents and Multiagent Systems) is the largest and most influential conference in the area of agents and multiagent systems. The aim of the conference is to bring together researchers and practitioners in all areas of agent technology and to provide a single, high-profile, internationally renowned forum for research in the theory and practice of autonomous agents and multiagent systems. AAMAS is the flagship conference of the non-profit International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS).

**Session Chair:** Martin Bullinger

Oral Session 1A1-1

Main_Track

The purpose of the AAAI conference is to promote research in artificial intelligence (AI) and scientific exchange among AI researchers, practitioners, scientists, and engineers in affiliated disciplines. 

Jannik Peters

7

3

SHORT BIO