  We consider a type of pull voting suitable for discrete numeric opinions
which can be compared on a linear scale, for example, 1 ('disagree strongly'),
2 ('disagree'), $\ldots,$ 5 ('agree strongly'). On observing the opinion of a
random neighbour, a vertex changes its opinion incrementally towards the value
of the neighbour's opinion, if different. For opinions drawn from a set
$\{1,2,\ldots,k\}$, the opinion of the vertex would change by $+1$ if the
opinion of the neighbour is larger, or by $-1$, if it is smaller.
  It is not clear how to predict the outcome of this process, but we observe
that the total weight of the system, that is, the sum of the individual
opinions of all vertices, is a martingale. This allows us analyse the outcome
of the process on some classes of dense expanders such as clique graphs $K_n$
and random graphs $ G_{n,p}$ for suitably large $p$. If the average of the
original opinions satisfies $i \le c \le i+1$ for some integer $i$, then the
asymptotic probability that opinion $i$ wins is $i+1-c$, and the probability
that opinion $i+1$ wins is $c-i$. With high probability, the winning opinion
cannot be other than $i$ or $i+1$.
  To contrast this, we show that for a path and opinions $0,1,2$ arranged
initially in non-decreasing order along the path, the outcome is very
different. Any of the opinions can win with constant probability, provided that
each of the two extreme opinions $0$ and $2$ is initially supported by a
constant fraction of vertices.
