Filters in abstract aggregation with infinite sequences of signals

Abstract

This study proposes a general framework for aggregation problems, in which agents’ signals given in an infinite sequence are aggregated. Notably, no restriction is imposed on the set of signals; hence, this framework is applicable to any type of attributes, including preferences, ballots, pieces of information, or judgments. The result can include the empty set that corresponds to the silence of the aggregation rule. Our main focus is to analyze the process by which the structure of the family of decisive coalitions forms a filter or an ultrafilter. In our framework, a coalition is regarded as decisive if a signal is socially approved as long as every agent in the coalition picks the signal up unanimously. First, we show that the family of decisive coalitions forms a filter under a certain axiom representing a stability condition. Next, in the case where the set of signals is finite, we provide axiomatic characterizations of the class of agreement-based rules associated with filters or ultrafilters: a signal is approved if and only if it is a unanimous agreement of some coalition in a specified filter or ultrafilter. Our axiomatic results demonstrate the robustness and stability of such rules.