  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
MC's, broadly being in agreement with predictions in NDLA, as compared to the
often used number of charged tracks observable.
