Automated Search for Impossibility Theorems in Social Choice Theory: Ranking Sets of Objects

We present a method for using standard techniques from satisfiability checking to automatically verify and discover theorems in an area of economic theory known as ranking sets of objects. The key question in this area, which has important applications in social choice theory and decision making under uncertainty, is how to extend an agent’s preferences over a number of objects to a preference relation over nonempty sets of such objects. Certain combinations of seemingly natural principles for this kind of preference extension can result in logical inconsistencies, which has led to a number of important impossibility theorems. We first prove a general result that shows that for a wide range of such principles, characterised by their syntactic form when expressed in a many-sorted first-order logic, any impossibility exhibited at a fixed (small) domain size will necessarily extend to the general case. We then show how to formulate candidates for impossibility theorems at a fixed ...

• Type: Journal
• Year: 2011
• Where: JAIR
• Authors: C. Geist, Ulrich Endriss
• Keywords: Domain Size, Impossibility Theorems, JAIR 2011, Preference Extension