  Cosmological constraints from current and upcoming galaxy cluster surveys are
limited by the accuracy of cluster mass calibration. In particular, optically
identified galaxy clusters are prone to selection effects that can bias the
weak lensing mass calibration. We investigate the selection bias of the stacked
cluster lensing signal associated with optically selected clusters, using
clusters identified by the redMaPPer algorithm in the Buzzard simulations as a
case study. We find that at a given cluster halo mass, the residuals of
redMaPPer richness and weak lensing signal are positively correlated. As a
result, for a given richness selection, the stacked lensing signal is biased
high compared with what we would expect from the underlying halo mass
probability distribution. The cluster lensing selection bias can thus lead to
overestimated mean cluster mass and biased cosmology results. We show that the
lensing selection bias exhibits a strong scale-dependence and is approximately
20 to 60 percent for $\Delta\Sigma$ at large scales. This selection bias
largely originates from spurious member galaxies within +/- 20 to 60 Mpc/h
along the line of sight, highlighting the importance of quantifying projection
effects associated with the broad redshift distribution of member galaxies in
photometric cluster surveys. While our results qualitatively agree with those
in the literature, accurate quantitative modelling of the selection bias is
needed to achieve the goals of cluster lensing cosmology and will require
synthetic catalogues covering a wide range of galaxy-halo connection models.
