We formalize a framework for coordinating the funding of projects and sharing the costs among agents with quasi-linear utility functions and individual budgets. Our model contains the classical discrete participatory budgeting model as a special case, while capturing other well-motivated problems. We propose several important axioms and objectives and study how well they can be simultaneously satisfied. One of our main results is that whereas welfare maximization admits an FPTAS, welfare maximization subject to a well-motivated and very weak participation requirement leads to a strong inapproximability result. We show that this result is bypassed if we consider some natural restricted valuations or when we take an average-case heuristic approach.

翻译：我们正式确定了项目筹资协调框架,在具有准线性公用事业功能和个别预算的代理商之间分担费用。我们的模式将传统的独立参与性预算编制模式作为一个特例,同时抓住其他动机良好的问题。我们提出了一些重要的理论和目标,并研究它们能够同时得到多大的满足。我们的主要成果之一是,虽然福利最大化允许采用FPTAS,但福利最大化需要有一个动机良好和参与能力极弱的要求,导致强烈的不协调结果。我们表明,如果我们考虑一些自然限制的估值,或者我们采取平均个案超额做法,这一结果就会被忽略。