  In~\cite{bgs2013}, exclusion sensitivity and exclusion stability for
symmetric exclusion processes on graphs were defined as a natural analogue of
noise sensitivity and noise stability in this setting. As these concepts were
defined for any sequence of connected graphs, it is natural to study the
monotonicity properties of these definitions with respect to adding edges to
the graphs, and in particular, whether some graphs are more stable or sensitive
than others. The main purpose of this paper is to answer some such question
from~\cite{bgs2013}. The main tool used is included results about the
eigenvectors and eigenvalues of the generator of symmetric exclusion processes
on complete graphs.
