  We present a proof showing that the weak error of a system of $n$ interacting
stochastic particles approximating the solution of the McKean-Vlasov equation
is $\mathcal O(n^{-1})$. Our proof is based on the Kolmogorov backward equation
for the particle system and bounds on the derivatives of its solution, which we
derive more generally using the variations of the stochastic particle system.
The convergence rate is verified by numerical experiments, which also indicate
that the assumptions made here and in the literature can be relaxed.
