We focus on a simple, one-dimensional collective decision problem (often referred to as the facility location problem) and explore issues of strategyproofness and proportional fairness. We present several characterization results for mechanisms that satisfy strategyproofness and varying levels of proportional fairness. We also characterize one of the mechanisms as the unique equilibrium outcome for any mechanism that satisfies natural fairness and monotonicity properties. Finally, we identify strategyproof and proportionally fair mechanisms that provide the best welfare-optimal approximation among all mechanisms that satisfy the corresponding fairness axiom.

翻译：我们集中关注一个简单、单维的集体决定问题(通常称为设施地点问题),探讨战略防守性和比例公平问题,为符合战略防守性和不同比例公平程度的机制提出若干定性结果,我们还将其中一种机制定性为任何符合自然公平性和单一性特性的机制的独特平衡结果,最后,我们确定战略防守性和比例公平机制,在所有符合相应公平原则的机制中提供最佳福利最佳近似值。