  Motivated by the analysis of consensus formation in the Deffuant model for
social interaction, we consider the following procedure on a graph $G$.
Initially, there is one unit of tea at a fixed vertex $r \in V(G)$, and all
other vertices have no tea. At any time in the procedure, we can choose a
connected subset of vertices $T$ and equalize the amount of tea among vertices
in $T$. We prove that if $x \in V(G)$ is at distance $d$ from $r$, then $x$
will have at most $\frac{1}{d+1}$ units of tea during any step of the
procedure. This bound is best possible and answers a question of Gantert.
  We also consider arbitrary initial weight distributions. For every finite
graph $G$ and $w \in \mathbb{R}_{\geq 0}^{V(G)}$, we prove that the set of
weight distributions reachable from $w$ is a compact subset of
$\mathbb{R}_{\geq 0}^{V(G)}$.
