  Gravitational wave measurements of binary neutron star coalescences offer
information about the properties of the extreme matter that comprises the
stars. Despite our expectation that all neutron stars in the Universe obey the
same equation of state, i.e. the properties of the matter that forms them are
universal, current tidal inference analyses treat the two bodies as
independent. We present a method to measure the effect of tidal interactions in
the gravitational wave signal -- and hence constrain the equation of state --
that assumes that the two binary components obey the same equation of state.
Our method makes use of a relation between the tidal deformabilities of the two
stars given the ratio of their masses, a relation that has been shown to only
have a weak dependance on the equation of state. We use this relation to link
the tidal deformabilities of the two stars in a realistic parameter inference
study while simultaneously marginalizing over the error in the relation. This
approach incorporates more physical information into our analysis, thus leading
to a better measurement of tidal effects in gravitational wave signals. Through
simulated signals we estimate that uncertainties in the measured tidal
parameters are reduced by a factor of at least 2 -- and in some cases up to 10
-- depending on the equation of state and mass ratio of the system.
