A relativistic jet has been produced in the single well-localised binary neutron star (BNS) merger detected to date in gravitational
waves (GWs), and the local rates of BNS mergers and short gamma-ray bursts are of the same order of magnitude. This suggests that
jet formation is not a rare outcome for BNS mergers, and we show that this intuition can be turned into a quantitative constraint: at
least about one-third of GW-detected BNS mergers and at least about one-fifth of all BNS mergers should produce a successful jet
(90% credible level). Whether a jet is launched depends on the properties of the merger remnant and of the surrounding accretion
disc, which in turn are a function of the progenitor binary masses and equation of state (EoS). The incidence of jets in the population
therefore carries information about the binary component mass distribution and EoS. Under the assumption that a jet can only be
produced by a black hole remnant surrounded by a non-negligible accretion disc, we show how the jet incidence can be used to place
a joint constraint on the space of BNS component mass distributions and EoS. The result points to a broad mass distribution, with
particularly strong support for masses in the 1.3−1.6 M range. The constraints on the EoS are shallow, but we show how they will
tighten as the knowledge on the jet incidence improves. We also discuss how to extend the method to include future BNS mergers,
with possibly uncertain jet associations
