  This paper presents mathematics relevant to the question whether voting
should be mandatory. Assuming a static distribution of voters' political
beliefs, we model how politicians might adjust their positions to raise their
share of the vote. Various scenarios can be explored using our web-based app
(see text for the link). Abstentions are found to have great impact on the
dynamics of candidates, and in particular to introduce the possibility of
discontinuous jumps in optimal candidate positions. This is a paper intended
for undergraduate students. It is an unusual application of ODEs. We hope that
it might help engage some students who may find it harder to connect with the
more customary applications from the natural sciences.
