Distance-Based Aggregation Theory

The problem of aggregating several objects into an object that represents them is a central problem in disciplines as diverse as economics, sociology, political science, statistics and biology (for a survey on aggregation theory in various fields see Day and McMorris [17]). It has been extensively dealt with in the theory of social choice (see Arrow et al. [5]), which analyses the aggregation of individual preferences into a collective preference. In this context, the idea of a consensus is normatively particularly appealing. A natural way to operationalize the consensus among a group of individuals is by means of a distance function that measures the disagreement between them. Thus, in particular, the construction of aggregation rules based on the minimization of distance functions inherits the normative appeal of consensus.

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