Binary Aggregation by Selection of the Most Representative Voter

In a binary aggregation problem, a group of voters each express yes/no choices regarding a number of possibly correlated issues and we are asked to decide on a collective choice that accurately reflects the views of this group. A good collective choice will minimise the distance to each of the individual choices, but using such a distance-based aggregation rule is computationally intractable. Instead, we explore a class of aggregation rules that select the most representative voter in any given situation and return that voter’s choice as the collective out-come. Two such rules, the average-voter rule and the majority-voter rule, are particularly attractive. We analyse their social choice-theoretic properties, their algorithmic efficiency, and the extent to which they are able to approximate the ideal defined by the distance-based rule. We also discuss the relevance of our results for the related framework of preference aggregation.