The (Computational) Social Choice Take on Indivisible Participatory Budgeting

Abstract

In this survey, we review the literature investigating participatory budgeting as a social choice problem. Participatory Budgeting (PB) is a democratic tool aiming at making budgeting decisions in a more democratic manner. Specifically, citizens are asked to vote on who to allocate a given amount of money to a set of projects that can potentially be funded. From a social choice perspective, it corresponds then to the problem of aggregating opinions about which projects should be funded, into a budget allocation satisfying a budget constraint. is problem has received substantial a ention in recent years and the literature is growing at a fast pace. In this survey, we present the most important research directions from the literature, each time presenting a large set of representative results. We only focus on the indivisible case, that is, PB problems in which projects can either be fully funded or not at all. e aim of the survey is to present a comprehensive overview of the state of the research on PB. We aim at providing both a general overview of the main research questions that are being investigated, and formal and unified definitions of the most important technical concepts from the literature.Of course a survey is never complete as the state of the research keeps changing. is document is intended to be a living document that gets updated every now and then as the literature grows. If you feel that some papers are not presented correctly, or simply missing, feel free to contact us. We will be more than happy to correct it.⋆ Laruelle (2021) considers that the agents submit weak and complete rankings over the projects, that are then converted into cardinal scores (via positional scoring functions) for the aggregation.

Completing Priceable Committees: Utilitarian and Representation Guarantees for Proportional Multiwinner Voting

“…Finally, we consider completion methods that are relevant for specific applications of multiwinner voting: completion by the maximin support method (Sánchez-Fernández et al 2021), which is relevant for the security of blockchain systems (Cevallos and Stewart 2021), and completion by pertur-bation or by varying the budget, which have been discussed in the participatory budgeting (PB) literature (Rey and Maly 2023). Omitted proofs can be found in the appendix.…”

“…Next, we consider two completion methods that have been suggested in the PB literature (Rey and Maly 2023) for the Method of Equal Shares: "completion by varying the budget" and "completion by perturbation. "…”

“…We note that, due to the non-monotonicity of MES, this method does not necessarily select a superset of the committee selected by MES(Rey and Maly 2023), and is thus not a completion method in the technical sense.…”

Temporal Fairness in Multiwinner Voting

“…Beyond multiwinner voting: Participatory budgeting Throughout the paper, we focused on the setting where the number of candidates to be selected is specified as part of the input. One can also consider a more general setting of participatory budgeting, where candidates (projects) may have distinct costs, and there is a budget, so that the total cost of the selected projects must remain within the budget (Aziz and Shah 2021;Rey and Maly 2023). While some of the work we discussed considers this more expressive setting (Lackner, Maly, and Rey 2021), most of the literature focuses exclusively on the basic multiwinner scenario; it would be interesting to see to what extent the existing positive results carry over to the richer participatory budgeting domain.…”

Opinion Change or Differential Turnout: Austin’s Budget Feedback Exercise and the Police Department

“…A voting method in this context consists on both elicitation (the ballot used to collect opinions from the voter) and aggregation (how an allocation among budget items is determined based on the votes). It would be well beyond the scope of this paper to discuss the different voting methods, but detailed surveys of relevant social choice publications are available in Rey and Maly (2023); Aziz and Shah (2021). The knapsack voting method is most relevant in this paper.…”