The Distortion of Public-Spirited Participatory Budgeting
Bibliographic record
Abstract
Participatory budgeting (PB) is an increasingly popular tool for democratically allocating limited budgets to public-good projects. In PB, constituents vote on their preferred projects via ballots, and then an aggregation rule selects a set of projects whose total cost fits within the budget. Recent work studies how to design PB ballots and aggregation rules that yield low-distortion outcomes (informally, outcomes with high social welfare). Existing distortion bounds, however, rely on strong assumptions that restrict voters' latent utilities. We prove that low distortion PB outcomes can be achieved by dropping these assumptions and instead leveraging the established idea that voters can be public-spirited: they may consider others' interests alongside their own when voting. Flanigan, Procaccia, and Wang (2023) prove that in public-spirited single-winner voting (the special case of PB where exactly one project can be funded) with ranking ballots, deterministic aggregation rules can achieve constant distortion. Our first contribution is to extend this analysis to PB; there, we prove that the best distortion permitted by deterministic rules with ranking ballots grows linearly in the number of projects. We find that this impossibility --- a problem in practice, where m is often large --- holds for other known ballots as well. Our second contribution is the design of a new PB ballot format that breaks this linear distortion barrier. This ballot asks voters to rank a predetermined set of entire feasible bundles of projects. We design multiple protocols for implementing these ballots, each striking a different trade-off between the number of bundles voters must rank and the distortion: with m bundles, we get sublinear distortion; with polynomial bundles, we get logarithmic distortion; and with pseudopolynomial bundles, we get constant distortion.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.015 | 0.060 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.009 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".