  Given a consumer data-set, the axioms of revealed preference proffer a binary
test for rational behaviour. A natural (non-binary) measure of the degree of
rationality exhibited by the consumer is the minimum number of data points
whose removal induces a rationalisable data-set.We study the computational
complexity of the resultant consumer rationality problem in this paper. This
problem is, in the worst case, equivalent (in terms of approximation) to the
directed feedback vertex set problem. Our main result is to obtain an exact
threshold on the number of commodities that separates easy cases and hard
cases. Specifically, for two-commodity markets the consumer rationality problem
is polynomial time solvable; we prove this via a reduction to the vertex cover
problem on perfect graphs. For three-commodity markets, however, the problem is
NP-complete; we prove thisusing a reduction from planar 3-SAT that is based
upon oriented-disc drawings.
