Epistemic Selection of Costly Alternatives: The Case of Participatory Budgeting
Simon Rey, Ulle Endriss
TL;DR
This paper casts PB rule design through an epistemic lens, asking whether common PB rules can be viewed as maximum likelihood estimators under plausible noise models for an objectively best funded set of projects $π^*$. It systematically analyzes a broad spectrum of rules, showing that the greedy, Sequential Phragmén, and MES rules fail the weak reinforcement condition and hence cannot be MLEs in general, including unit-cost PB. It then focuses on additive argmax rules based on Nash and utilitarian welfare, establishing that while many Nash variants satisfy weak reinforcement, they typically do not admit an MLE interpretation except under restricted, normalised variants and specific noise models; conversely, some normalised Nash variants do become MLEs under tailored noise models, while utilitarian rules largely resist MLE interpretation except in narrow unit-cost exhaustive cases. The findings reveal a tension between epistemic guarantees and standard normative properties (like exhaustiveness) and point to future work on alternative epistemic criteria, robustness to noise, and scenario-specific conditions that could reconcile truth-tracking with practical PB design.
Abstract
We initiate the study of voting rules for participatory budgeting using the so-called epistemic approach, where one interprets votes as noisy reflections of some ground truth regarding the objectively best set of projects to fund. Using this approach, we first show that both the most studied rules in the literature and the most widely used rule in practice cannot be justified on epistemic grounds: they cannot be interpreted as maximum likelihood estimators, whatever assumptions we make about the accuracy of voters. Focusing then on welfare-maximising rules, we obtain both positive and negative results regarding epistemic guarantees.