  Optimal design theory for nonlinear regression studies local optimality on a
given design space. We identify designs for the Bradley--Terry paired
comparison model with small undirected graphs and prove that every saturated
D-optimal design is represented by a path. We discuss the case of four
alternatives in detail and derive explicit polynomial inequality descriptions
for optimality regions in parameter space. Using these regions, for each point
in parameter space we can prescribe a D-optimal design.
