  Every halo finding algorithm must make a critical yet relatively arbitrary
choice: it must decide which structures are parent halos, and which structures
are sub-halos of larger halos. We refer to this choice as ${\it percolation}$.
We demonstrate that the choice of percolation impacts the statistical
properties of the resulting halo catalog. Specifically, we modify the
halo-finding algorithm ${\tt ROCKSTAR}$ to construct four different halo
catalogs from the same simulation data, each with identical mass definitions,
but different choice of percolation. The resulting halos exhibit significant
differences in both halo abundance and clustering properties. Differences in
the halo mass function reach $10\%$ for halos of mass $10^{13}\ h^{-1}\ {\rm
M_{\odot}}$, larger than the few percent precision necessary for current
cluster abundance experiments such as the Dark Energy Survey. Comparable
differences are observed in the large-scale clustering bias, while differences
in the halo--matter correlation function reach $40\%$ on translinear scales.
These effects can bias weak-lensing estimates of cluster masses at a level
comparable to the statistical precision of current state-of-the-art
experiments.
