1 Knapsack Voting

Recently there has been a rise in attempts to directly engage citizens in policy-making with democratic innovations [Aitamurto et al. 2014; Pateman 2012; Smith 2009]. One of these is participatory budgeting [Cabannes 2004], in which a local government asks residents to vote on proposals for how a certain fraction of their total budget should be spent. Participatory budgeting is now gaining popularity in cities like San Francisco, Vallejo, Chicago and New York [PBP]. This development necessitates the need for a more accurate voting mechanism than the traditional “check-the-box” method used in current ballots and motivates the following question: in a scenario where each voter benefits differently from each proposal, and the benefit from the same proposal varies across voters, how should the preferences of voters be aggregated? We address this question by proposing new voting schemes, and discuss their advantages over existing methods both informally in terms of making users take trade-offs into account, and formally by showing that they are partially strategy-proof. Inspired by the classical Knapsack Problem, we call this class of schemes Knapsack Voting.