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

by   Christian Geist, et al.

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 agents 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.


page 1

page 2

page 3

page 4


Escaping Arrow's Theorem: The Advantage-Standard Model

There is an extensive literature in social choice theory studying the co...

An approach to generalizing some impossibility theorems in social choice

In social choice theory, voting methods can be classified by invariance ...

Proof Automation in the Theory of Finite Sets and Finite Set Relation Algebra

log ('setlog') is a satisfiability solver for formulas of the theory of ...

Social Choice with Changing Preferences: Representation Theorems and Long-Run Policies

We study group decision making with changing preferences as a Markov Dec...

Consistent ultrafinitist logic

Ultrafinitism postulates that we can only compute on relatively short ob...

Constructive Decision Theory

In most contemporary approaches to decision making, a decision problem i...

The Satisfiability Problem for Boolean Set Theory with a Choice Correspondence

Given a set U of alternatives, a choice (correspondence) on U is a contr...

Please sign up or login with your details

Forgot password? Click here to reset