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Given a consumer data-set, the axioms of revealed preference proffer a binarytest for rational behaviour. A natural (non-binary) measure of the degree ofrationality exhibited by the consumer is the minimum number of data pointswhose removal induces a rationalisable data-set.We study the computationalcomplexity of the resultant consumer rationality problem in this paper. Thisproblem is, in the worst case, equivalent (in terms of approximation) to thedirected feedback vertex set problem. Our main result is to obtain an exactthreshold on the number of commodities that separates easy cases and hardcases. Specifically, for two-commodity markets the consumer rationality problemis polynomial time solvable; we prove this via a reduction to the vertex coverproblem on perfect graphs. For three-commodity markets, however, the problem isNP-complete; we prove thisusing a reduction from planar 3-SAT that is basedupon oriented-disc drawings.

Testing Consumer Rationality using Perfect Graphs and Oriented Discs