  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 result of this paper is
that, as in the case of preference aggregation, in the case of a subclass of a
natural class of aggregation problems termed `truth-functional agendas', the
set of satisfying aggregation mechanisms does not extend non-trivially when
relaxing the constraints. Our proof techniques involve Boolean Fourier
transform and analysis of voter influences for voting protocols. The question
we raise for Approximate Aggregation can be stated in terms of Property
Testing. For instance, as a corollary from our result we get a generalization
of the classic result for property testing of linearity of Boolean functions.
  An updated version (RePEc:huj:dispap:dp574R) is available at
http://www.ratio.huji.ac.il/dp_files/dp574R.pdf
