The distortion of distributed metric social choice

We consider a social choice setting with agents that are partitioned into disjoint groups, and have metric preferences over set of alternatives. Our goal is to choose single alternative aiming optimize various objectives functions the distances between alternatives in space, under constraint this must be made distributed way: The within each group first aggregated representative for group, then these representatives final winner. Deciding winner such way naturally leads loss efficiency, even when complete information about space available. provide series (mostly tight) bounds on distortion mechanisms variations well-known objectives, as (average) total cost maximum cost, also new particularly appropriate not been studied before.