Cost Considerations in Participatory Budgeting: An Empirical Comparison of Knapsack and Approval Ballots

Abstract

This article examines the role of cost considerations in shaping the selection of participatory budgeting projects through an empirical comparison between knapsack and k-approval ballot types. Using data from the 2018–2021 elections in the city of Warsaw (Poland), we analyzed how these two methods – each with a fundamentally different approach to cost – affect individual decision-making and collective outcomes. We find that knapsack voting, with its predefined budget constraint, encourages economically mindful behavior and leads to the funding of a greater number of lower-cost initiatives. In contrast, k-approval voting, which limits the number of projects rather than their costs, results in the selection of relatively fewer but more expensive initiatives. To validate these findings, we conducted an online voting experiment simulating both methods. The results show a consistent bias toward more affordable projects when cost consideration mechanisms are embedded in either the ballot type (knapsack) or the aggregation rule (cost-proportional algorithm). Our findings highlight the importance of voting method design in the participatory budgeting process, provide an empirical contribution to the understanding of how different rules function in practice, and offer crucial insights for guiding future implementations and development.