  We present a direct proof of asymptotic consensus in the nonlinear
Hegselmann-Krause model with transmission-type delay, where the communication
weights depend on the particle distance in phase space. Our approach is based
on an explicit estimate of the shrinkage of the group diameter on finite time
intervals and avoids the usage of Lyapunov-type functionals or results from
nonnegative matrix theory. It works for both the original formulation of the
model with communication weights scaled by the number of agents, and the
modification with weights normalized a'la Motsch-Tadmor. We pose only minimal
assumptions on the model parameters. In particular, we only assume global
positivity of the influence function, without imposing any conditions on its
decay rate or monotonicity. Moreover, our result holds for any length of the
delay.
