PP201104: Geist, Christian and Endriss, Ulle (2011) Automated Search for Impossibility Theorems in Social Choice Theory: Ranking Sets of Objects. [Report]

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Abstract
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 manysorted firstorder 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 domain size in propositional logic, which in turn enables us to automatically search for (general) impossibility theorems using a SAT solver. When applied to a space of 20 principles for preference extension familiar from the literature, this method yields a total of 84 impossibility theorems, including both known and nontrivial new results.
Item Type:  Report 

Report Nr:  PP201104 
Series Name:  Prepublication (PP) Series 
Year:  2011 
Uncontrolled Keywords:  computational social choice; automated theorem proving 
Subjects:  Computation 
Depositing User:  Ulle Endriss 
Date Deposited:  12 Oct 2016 14:37 
Last Modified:  12 Oct 2016 14:37 
URI:  https://eprints.illc.uva.nl/id/eprint/408 
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