We show that in studies of light quark- and gluon-initiated jet discrimination, it is important to include the information on softer reconstructed jets (associated jets) around a primary hard jet. This is particularly relevant while adopting a small radius parameter for reconstructing hadronic jets. The probability of having an associated jet as a function of the primary jet transverse momentum ($p_T$) and radius, the minimum associated jet $p_T$ and the association radius is computed upto next-to-double logarithmic accuracy (NDLA), and the predictions are compared with results from Herwig++, Pythia6 and Pythia8 Monte Carlos (MC). We demonstrate the improvement in quark-gluon discrimination on using the associated jet rate variable with the help of a multivariate analysis. The associated jet rates are found to be only mildly sensitive to the choice of parton shower and hadronization algorithms, as well as to the effects of initial state radiation and underlying event. In addition, the number of $k_T$ subjets of an anti-$k_T$ jet is found to be an observable that leads to a rather uniform prediction across different MCs, broadly being in agreement with predictions in NDLA, as compared to the often used number of charged tracks observable.
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