Tracking Truth by Weighting Proxies in Liquid Democracy

We study wisdom-of-the-crowd effects in liquid democracy on networks where agents are allowed to apportion parts of their voting weight to different proxies. We show that in this setting---unlike in the standard one where voting weight is delegated in full to only one proxy---it becomes possible to construct delegation structures that optimize the truth-tracking ability of the group. Focusing on group accuracy we contrast this centralized solution with the setting in which agents are free to choose their weighted delegations by greedily trying to maximize their own individual accuracy. While equilibria with weighted delegations may be as bad as with standard delegations, they are never worse and may sometimes be better. To gain further insights into this model we experimentally study quantal response delegation strategies on random networks. We observe that weighted delegations can lead, under specific conditions, to higher group accuracy than simple majority voting.