A General Approach to Aggregation Problems

There is a new field emerging around issues concerning the aggregation of a collection of individual “judgments” of a group of agents. An individual “judgment” is represented by a set of sentences in some logical language. One looks for a procedure that has as its output a “social” judgment. A key result in this area is List and Pettit’s impossibility result [13]. By generalizing the well-known doctrinal paradox [12], List and Pettit were able to show an “Arrow”-style [1] impossibility theorem: for judgment sets that are subsets of a sufficiently rich collection of sentences there is no “wellbehaved” aggregation procedure. There have been a number of refinements and generalizations of this elegant result [3, 7, 8, 16, 17, 18]. As our starting point we take work of Dietrich and List, which builds on List and Pettit’s result and clarifies the connection between judgment aggregation impossibility results and Arrow’s famous impossibility result. In the setting studied by these authors, an agenda is a collection of sentences in some logical language.1 A judgment set is a subset of the agenda. The impossibility results arise out of assumptions made about 1. the agenda, 2. the possible judgment sets and 3. the aggregation functions. Formal details can be found in [4].