  We study how well void-finding algorithms identify cosmic void regions and
whether we can quantitatively and qualitatively describe their biases by
comparing the voids they find with dynamical information from the underlying
matter distribution. Using the ORIGAMI algorithm to determine the number of
dimensions along which dark matter particles have undergone shell-crossing
(crossing number) in $N$-body simulations from the AbacusSummit simulation
suite, we identify dark matter particles which have undergone no shell crossing
as belonging to voids. We then find voids in the corresponding halo
distribution using two different void-finding algorithms: VoidFinder and V$^2$,
a ZOBOV-based algorithm. The resulting void catalogs are compared to the
distribution of dark matter particles to examine how their crossing numbers
depend on void proximity. While both algorithms' voids have a similar
distribution of crossing numbers near their centers, we find that beyond 0.25
times the effective void radius, voids found by VoidFinder exhibit a stronger
preference for particles with low crossing numbers than those found by V$^2$.
We examine two possible methods of mitigating this difference in efficacy
between the algorithms. While we are able to partially mitigate the
ineffectiveness of V$^2$ by using distance from the void edge as a measure of
centrality, we conclude that VoidFinder more reliably identifies
dynamically-distinct regions of low crossing number.
