  The combined detection of a binary neutron-star merger in both gravitational
waves (GWs) and electromagnetic (EM) radiation spanning the entire spectrum --
GW170817 / AT2017gfo / GRB170817A -- marks a breakthrough in the field of
multi-messenger astronomy. Between the plethora of modeling and observations,
the rich synergy that exists among the available data sets creates a unique
opportunity to constrain the binary parameters, the equation of state of
supranuclear density matter, and the physical processes at work during the
kilonova and gamma-ray burst. We report, for the first time, Bayesian parameter
estimation combining information from GW170817, AT2017gfo, GRB170817 to obtain
truly multi-messenger constraints on the tidal deformability $\tilde{\Lambda}
\in [302,860]$, total binary mass $M \in [2.722,2.751] M_\odot$, the radius of
a $1.4$ solar mass neutron star $R \in [11.3,13.5] \rm km$ (with additional
$0.2\ \rm km$ systematic uncertainty), and an upper bound on the mass ratio of
$q \leq 1.27$, all at 90% confidence. Our joint novel analysis makes use of new
phenomenological descriptions of the dynamical ejecta, debris disk mass, and
remnant black hole properties, all derived from a large suite of numerical
relativity simulations.
