Approximate Judgement Aggregation
Ilan Nehama

TL;DR
This paper investigates how relaxing consistency and independence constraints in judgement aggregation affects the set of mechanisms, finding that for certain problem classes, the set remains essentially unchanged.
Contribution
It extends previous work by analyzing approximate judgement aggregation, showing that relaxing key constraints does not significantly alter the class of mechanisms for certain agendas.
Findings
Relaxation of constraints does not expand the class of mechanisms for truth-functional agendas.
Uses Boolean Fourier analysis and influence measures in the proofs.
Generalizes property testing results for Boolean functions.
Abstract
In this paper we analyze judgement aggregation problems in which a group of agents independently votes on a set of complex propositions that has some interdependency constraint between them(e.g., transitivity when describing preferences). We consider the issue of judgement aggregation from the perspective of approximation. That is, we generalize the previous results by studying approximate judgement aggregation. We relax the main two constraints assumed in the current literature, Consistency and Independence and consider mechanisms that only approximately satisfy these constraints, that is, satisfy them up to a small portion of the inputs. The main question we raise is whether the relaxation of these notions significantly alters the class of satisfying aggregation mechanisms. The recent works for preference aggregation of Kalai, Mossel, and Keller fit into this framework. The main…
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Taxonomy
TopicsGame Theory and Voting Systems · Decision-Making and Behavioral Economics · Game Theory and Applications
