The economic theory of individual choice most frequently assumes that individual preferences are weak orders; this implies, among other things, a virtually perfect discriminating power on the part of individual decision makers. R. D. Luce's theory of semiorders generalizes the weak order concept to allow imperfect discrimination when choices are close. This paper examines the demand implications of the semiorder axioms and states conditions on demand that are necessary and sufficient for the revealed ordering to be a semiorder.