Judgment aggregation: A critical view

The paper gives a brief overview of the theory of aggregation. In theory and practice, one often has to deal with the problem of replacing a large array of homogeneous data with one number or item, which, to the greatest degree, represents this array. Mostly the situation is considered when data is aggregated issue-by-ussue. The main difficulty with this approach is that aggregation often leads to invalid (inconsistent) results. This means that the data to be aggregated, as well as the result of aggregation, must be connected by some specific restrictions. The classic example of this situation is the aggregation of preferences that are assumed to be transitive. Arrow's theorem speaks about the impossibility of maintaining the transitivity requirement under issue of preference aggregation. The culmination of this trend is the work of Nehring and Puppe, in which a complete description of the aggregation rules was obtained that do not lead to unacceptable results. Also, some generalizations related to multivalued questions, subject to aggregation, and the use of multivalued logic (MV-algebras) are discussed.