# Truthful Aggregation of Budget Proposals

arXiv: https://arxiv.org/abs/1905.00457 · HTML: https://mlsanity.com/paper/1905.00457/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 May 2019.

## Built on by (most cited first, 10 of 10)

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- [The End Justifies the Mean: A Linear Ranking Rule for Proportional Sequential Decisions](https://mlsanity.com/paper/2605.12717/) (2026)
- [Participatory Budgeting with Donations and Diversity Constraints](https://mlsanity.com/paper/2104.15075/) (2021)
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- [Fraud-Proof Revenue Division on Subscription Platforms](https://mlsanity.com/paper/2511.04465/) (2025)
- [AI of the People, by the People, for the People: A Social Choice Approach to Collective Control of Artificial Intelligence](https://mlsanity.com/paper/2605.16291/) (2026)

## Abstract (arXiv)

We consider a participatory budgeting problem in which each voter submits a proposal for how to divide a single divisible resource (such as money or time) among several possible alternatives (such as public projects or activities) and these proposals must be aggregated into a single aggregate division. Under ℓ1 preferences -- for which a voter's disutility is given by the ℓ1 distance between the aggregate division and the division he or she most prefers -- the social welfare-maximizing mechanism, which minimizes the average ℓ1 distance between the outcome and each voter's proposal, is incentive compatible (Goel et al. 2016). However, it fails to satisfy the natural fairness notion of proportionality, placing too much weight on majority preferences. Leveraging a connection between market prices and the generalized median rules of Moulin (1980), we introduce the independent markets mechanism, which is both incentive compatible and proportional. We unify the social welfare-maximizing mechanism and the independent markets mechanism by defining a broad class of moving phantom mechanisms that includes both. We show that every moving phantom mechanism is incentive compatible. Finally, we characterize the social welfare-maximizing mechanism as the unique Pareto-optimal mechanism in this class, suggesting an inherent tradeoff between Pareto optimality and proportionality.