What Are People's Actual Utility Functions in Budget Aggregation?

TL;DR

This study addresses what actual utility functions people use when evaluating budget allocations in participatory budgeting and budget aggregation. It develops a systematic polling method that elicits an individual's ideal budget $\mathbf{p}$ and then tests preferred non-ideal budgets under multiple models, including $U(\mathbf{p},\mathbf{q})$ forms for $\ell_1$, $\ell_2$, and Leontief, as well as single-peaked and peak-linear structures under intertemporal and asymmetry tests. The results show that common distance-based models often fail to explain observed preferences, while single-peaked and peak-linear patterns are prevalent; this motivates asymmetric weighted and potential non-linear utility models. The work introduces an empirical methodology for validating utility-function assumptions underlying budget-aggregation theories and provides directions for designing more robust, realistic mechanisms in participatory budgeting.

Abstract

While participatory budgeting and budget-aggregation mechanisms require assumptions about how voters evaluate non-ideal budget allocations, little empirical evidence exists to validate which utility models accurately capture human preferences. We conducted structured polls with human participants to test whether real people's preferences conform to commonly assumed utility functions such as $\ell_1$, $\ell_2$ and Leontief. Our results suggest that these models may have limited explanatory power for actual behavior: most participants showed inconsistent patterns across different metric comparisons, and standard assumptions of project symmetry and sign symmetry -- core features of common distance-based metrics -- received little empirical support. However, we find encouraging evidence for more fundamental preference structures: a large majority of participants showed consistency with star-shaped preferences, as well as with peak-linear utility functions, where utility changes proportionally with distance from the ideal budget. These findings have important implications for designers of budget aggregation mechanisms. While theoretical results demonstrate impossibility results for standard distance metrics regarding truthfulness, Pareto-efficiency, and proportionality, our evidence suggests alternative modeling approaches may be warranted. More broadly, this work introduces a systematic methodology to empirically test the utility function assumptions that underpin budget aggregation theories, paving the way for more robust and realistic mechanism design.

Figures (5)

• Figure 1: Initial screen where participants enter their ideal budget allocation across education, health, and defense.
• Figure 2: Example of a pairwise comparison question, where participants are asked to choose between two alternative allocations.
• Figure 3: A question where participants are required to rank the three options.
• Figure 4: An example of the automatic budget rescaling feature. (Top) A participant’s initial allocation that does not sum to 100. (Bottom) The allocation after using the "Rescale" button, which automatically adjusts the values to meet the poll's constraints while preserving the user's proportional intent.
• Figure 5: Preference matrix for a participant. Rows correspond to topics, columns correspond to magnitude levels. Each cell is colored to indicate whether the participant preferred a distributed decrease (orange) or a concentrated decrease (blue).