  We investigate halo mass selection properties of red-sequence cluster finders
using galaxy populations of the Millennium Simulation (MS). A clear red
sequence exists for MS galaxies in massive halos at redshifts z < 1, and we use
this knowledge to inform a cluster-finding algorithm applied to 500 Mpc/h
projections of the simulated volume. At low redshift (z=0.4), we find that 90%
of the clusters found have galaxy membership dominated by a single, real-space
halo, and that 10% are blended systems for which no single halo contributes a
majority of a cluster's membership. At z=1, the fraction of blends increases to
22%, as weaker redshift evolution in observed color extends the comoving length
probed by a fixed range of color. Other factors contributing to the increased
blending at high-z include broadening of the red sequence and confusion from a
larger number of intermediate mass halos hosting bright red galaxies of
magnitude similar to those in higher mass halos. Our method produces catalogs
of cluster candidates whose halo mass selection function, p(M|\Ngal,z), is
characterized by a bimodal log-normal model with a dominant component that
reproduces well the real-space distribution, and a redshift-dependent tail that
is broader and displaced by a factor ~2 lower in mass. We discuss implications
for X-ray properties of optically selected clusters and offer ideas for
improving both mock catalogs and cluster-finding in future surveys.
