We consider a social choice setting with agents that are partitioned into disjoint groups, and have metric preferences over a set of alternatives. Our goal is to choose a single alternative aiming to optimize various objectives that are functions of the distances between agents and alternatives in the metric space, under the constraint that this choice must be made in a distributed way: The preferences of the agents within each group are first aggregated into a representative alternative for the group, and then these group representatives are aggregated into the final winner. Deciding the winner in such a way naturally leads to loss of efficiency, even when complete information about the metric space is available. We provide a series of (mostly tight) bounds on the distortion of distributed mechanisms for variations of well-known objectives, such as the (average) total cost and the maximum cost, and also for new objectives that are particularly appropriate for this distributed setting and have not been studied before.
翻译:我们考虑一种社会选择环境,由被分割成不相连的团体的代理商组成,并且对一套替代物享有基本偏好。我们的目标是选择一种单一的替代物,目的是优化各种目标,这些目标是代理人与替代物在计量空间的距离功能,但这种选择必须以分配方式作出:每个集团内的代理商的偏好首先归为集团的有代表性的替代物,然后将这些集团代表合并为最后的赢家。决定胜者的方式自然会导致效率的丧失,即使有关于计量空间的完整信息。我们提供一系列(最紧凑的)界限,说明如何扭曲分配的机制,以改变众所周知的目标,例如(平均)总成本和最大成本,以及对于特别适合这一分布环境而且以前未曾研究过的新目标。