Optimising Barcelona's Participatory Budget — Decidim's Knapsack Algorithm Outperforms Rank-and-Select

Barcelona's Decidim platform runs the city's participatory budgeting process: residents submit proposals, a technical review filters them for feasibility, and citizens vote on a shortlist that is funded top-down by vote count ('rank and select') until the budget is exhausted. Researchers at the Artificial Intelligence Research Institute (IIIA-CSIC) and the University of Barcelona argued this method wastes budget on partially-funded slack and under-selects smaller proposals with similar support.

Under the 'Decidim Intel·ligent' project, researchers reformulated proposal selection as a multiple-choice knapsack problem — an integer linear program that maximises total citizen support subject to the budget cap.

The method was tested retrospectively against real vote data from two council-run pilots: Eixample (€500,000 budget, 200 proposals submitted, 22 reaching the final vote, 17 funded, October 2016 to May 2018) and Gràcia (€150,000 budget, 14 finalist proposals).

On the real Eixample results, the optimisation method reached 89.73% of the maximum possible citizen support versus 84.15% for the rank-and-select method actually used; in Gràcia it reached 70% versus 63.86%. Swept across a range of hypothetical budgets, the gap widened further — for example, 91.8% more supported votes and 150% more proposals funded (5 vs 2) for Gràcia at a simulated €60,000 budget, with no increase in total spend.

This is a peer-reviewed, retrospective simulation validated against real historical outcomes, not a live-deployed system. The paper proposes future NLP-based proposal clustering as a next step, and Barcelona's participatory budgeting has continued to run on the standard rank-and-select method since — there is no confirmed evidence the optimisation model has replaced it operationally.