  We introduce a variant of the well-studied sum choice number of graphs, which
we call the interactive sum choice number. In this variant, we request colours
to be added to the vertices' colour-lists one at a time, and so we are able to
make use of information about the colours assigned so far to determine our
future choices. The interactive sum choice number cannot exceed the sum choice
number and we conjecture that, except in the case of complete graphs, the
interactive sum choice number is always strictly smaller than the sum choice
number. In this paper we provide evidence in support of this conjecture,
demonstrating that it holds for a number of graph classes, and indeed that in
many cases the difference between the two quantities grows as a linear function
of the number of vertices.
