PP-2011-04:
Geist, Christian and Endriss, Ulle
(2011)
*Automated Search for Impossibility Theorems in Social Choice Theory: Ranking Sets of Objects.*
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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 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 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: | PP-2011-04 |

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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