  The first detection of a binary neutron star merger, GW170817, and an
associated short gamma-ray burst confirmed that neutron star mergers are
responsible for at least some of these bursts. The prompt gamma ray emission
from these events is thought to be highly relativistically beamed. We present a
method for inferring limits on the extent of this beaming by comparing the
number of short gamma-ray bursts observed electromagnetically to the number of
neutron star binary mergers detected in gravitational waves. We demonstrate
that an observing run comparable to the expected Advanced LIGO 2016--2017 run
would be capable of placing limits on the beaming angle of approximately
$\theta \in (2.88^\circ,14.15^\circ)$, given one binary neutron star detection.
We anticipate that after a year of observations with Advanced LIGO at design
sensitivity in 2020 these constraints would improve to $\theta \in
(8.10^\circ,14.95^\circ)$.
