A structured gamma-ray burst jet could explain the dimness of the prompt emission observed from GRB$,170817$A but the exact form of this structure is still ambiguous. However, with the promise of future joint gravitational wave and gamma-ray burst observations, we shall be able to examine populations of binary neutron star mergers rather than a case-by-case basis. We present an analysis that considers gravitational wave triggered binary neutron star events both with and without short gamma-ray burst counterparts assuming that events without a counterpart were observed off-axis. This allows for Bayes factors to be calculated to compare different jet structure models. We perform model comparison between a Gaussian and power-law apparent jet structure on simulated data to demonstrate that the correct model can be distinguished with a log Bayes factor of $>5$ after less than 100 events. Constraints on the apparent structure jet model parameters are also made. After 25(100) events the angular width of the core of a power-law jet structure can be constrained within a $90%$ credible interval of width $ sim9.1(4.4)^{circ} $, and the outer beaming angle to be within $sim19.9(8.5)^{circ}$. Similarly we show the width of a Gaussian jet structure to be constrained to $sim2.8(1.6)^{circ}$.
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