Variations on Participatory Budgeting
Simon Rey

Abstract:
The third quarter of the 20th century has seen the rise of the idea of a crisis of democracy, both inside and outside of the academic literature. This crisis is often linked to the observation that confidence and trust in governments and governmental bodies is declining in many countries. There is a—still on-going—debate in the political science literature regarding the optimal level of trust for a well-functioning democratic process, but there is clear consensus that too little trust can endanger it. It is thus not surprising that the past 40 to 50 years have also seen the rise of a wide range of innovative tools developed to deepen and renew the democratic process. One such tool is participatory budgeting (PB), which encompasses a large range of mechanisms that aim to make budgeting decisions in a participatory and collective manner.

This thesis studies PB mechanisms. We view them as ways of obtaining a collective budgeting decision. More specifically, we investigate PB as a voting procedure in which citizens are asked to submit their preferences in order to decide which projects should be funded, subject to a budget constraint. Our investigation has its roots in the literature on computational social choice, the field of research that studies ways of reaching collective decisions from individual preferences. Equipped with the standard toolbox of the computational social choice scientist, we aim at understanding how to aggregate individual opinions into a collective decision in a wide variety of PB contexts.

There exists a myriad of different implementations of PB in real life. This makes  taking a holistic approach to PB particularly challenging. Our investigation is structured along two axes, each defining a part of the thesis, each bringing new aspects of real-world PB processes into the analysis.

The first part of the thesis is dedicated to the so-called standard model of PB, i.e., the most frequently encountered mathematical formalisation of PB processes in the literature. We consider two new perspectives on PB to investigate it.

The study of the standard model in the literature is primarily concerned with the question of how to obtain a fair outcome. However, restrictive hypotheses are usually required, either making unreasonable assumptions about the voters’ behaviours, and/or requiring the voters to provide unrealistic amounts of information. In the first chapter of this part of the thesis, we challenge these approaches and propose a new take on fairness for PB that does not suffer from these drawbacks. We study a large range of new fairness concepts, discuss how they can be enforced, and demonstrate the viability of our new approach.

The standard model captures a large and diverse set of real-life PB processes. However, focusing on fairness restricts the applicability of the formal analysis. Indeed, fairness is not the main objective of all PB processes; some processes are for instance organised to discover what the best alternatives are. Motivated by this observation, the second chapter of this part presents the first study of the standard model from an epistemic perspective. Here, the goal is to uncover some ground truths about the intrinsic qualities of the projects. We investigate the epistemic abilities of many PB rules, and show that most actually do not enjoy any.

In the second part of the thesis, we move to the study of PB models that extend the standard one, in order to capture additional aspects of real-life PB processes.

In the first chapter we investigate multi-constrained PB models. More specifically, we study models of PB in which the budget limit is not the only constraint that determines the feasibility of an outcome. Additional constraints can be used to model statements such as “at least e10 000 have to be allocated to cycling infrastructure”. In this chapter we present a general approach for such extension of the standard model, detailing how to determine budget allocations when the structure of the outcome is more complex.

The second chapter of this part tackles the temporal aspect of PB. Indeed, most PB processes are implemented over the course of several years, one election being ran each year. We incorporate this aspect into the formal analysis, and focus on providing fairness over time. We introduce several notions of temporal fairness and present conditions under which they can be enforced.

Another important aspect of PB processes that had not been incorporated in the analysis before is the fact that projects are not just voted on but also proposed by the citizens. In the last chapter of this part, we extend the standard model by including a preliminary stage in which project proposals are submitted and then shortlisted to form the set of projects that are brought to the vote. We first focus on the first stage, investigating different methods of determining the shortlist, and then move on to the study of the interactions between the two stages.

Overall, this thesis is concerned with procedures to select the projects to be funded in PB scenarios. Throughout our analysis, we aim at incorporating a wider range of actual implementations of PB processes into the formal analysis than had been done before. The end product covers a large diversity of implementations of PB processes, studied from various angles. I hope that this work, at its small scale, can help make better decisions for PB, and by that, improve the democratic process at a larger scale.