  A key aspect for any greedy pursuit algorithm used in compressed sensing is a
good support-set detection method. For distributed compressed sensing, we
consider a setup where many sensors measure sparse signals that are correlated
via the existence of a signals' intersection support-set. This intersection
support-set is called the joint support-set. Estimation of the joint
support-set has a high impact on the performance of a distributed greedy
pursuit algorithm. This estimation can be achieved by exchanging local
support-set estimates followed by a (consensus) voting method. In this paper we
endeavor for a probabilistic analysis of two democratic voting principle that
we call majority and consensus voting. In our analysis, we first model the
input/output relation of a greedy algorithm (executed locally in a sensor) by a
single parameter known as probability of miss. Based on this model, we analyze
the voting principles and prove that the democratic voting principle has a
merit to detect the joint support-set.
