Preserving Consistency for Liquid Knapsack Voting

Liquid Democracy (LD) uses transitive delegations to facilitate joint decision making. In its simplest form, it is used for binary decisions, however its promise holds also for more advanced voting settings. Here we consider LD in the context of Participatory Budgeting (PB), which is a direct democracy approach to budgeting, most usually done in municipal budgeting processes. In particular, we study Knapsack Voting, in which PB voters can approve projects, however the sum of costs of voter-approved projects must respect the global budget limit. We observe inconsistency issues when allowing delegations, as the cost of voter-approved projects may go over the budget limit; we offer ways to overcome such inconsistencies by studying the computational complexity of a related combinatorial problem in which the task is to update as few delegations as possible to arrive—after following all project delegations—to a consistent profile.