  The recent discovery of planets orbiting main sequence binaries will provide
crucial constraints for theories of binary and planet formation. The formation
pathway for these planets is complicated by uncertainties in the formation
mechanism of the host stars. In this paper, we compare the dynamical states of
single and binary star planetary systems. Specifically, we pose two questions:
(1) What does it mean for a circumbinary system to be dynamically packed? (2)
How many systems are required to differentiate between a population of packed
or sparse planets? We determine when circumbinary systems become dynamically
unstable as a function of the separation between the host-stars and the inner
planet, and the first and second planets. We show that these represent unique
stability constraints compared to single-star systems. We find that although
the existing Kepler data is insufficient to distinguish between a population of
packed or sparse circumbinary systems, a more thorough study of circumbinary
TTVs combined with an order of magnitude increase in the number of systems may
prove conclusive. Future space missions such as TESS provide the best
opportunity for increasing the sample size.
