Method of Equal Shares with Bounded Overspending

In participatory budgeting (PB), voters decide through voting which subset of projects to fund within a given budget. Proportionality in the context of PB is crucial to ensure equal treatment of all groups of voters. However, pure proportional rules can sometimes lead to suboptimal outcomes. We introduce the Method of Equal Shares with Bounded Overspending (BOS Equal Shares), a robust variant of Equal Shares that balances proportionality and efficiency. BOS Equal Shares addresses inefficiencies inherent in strict proportionality guarantees yet still provides good proportionality similar to the original Method of Equal Shares. In the course of the analysis, we also discuss a fractional variant of the method which allows for partial funding of projects.