Due to the imperfect ability of individuals to discriminate between sufficiently similar alternatives, individual indifferences may fail to be transitive. I prove two impossibility theorems for social choice under indifference intransitivity, using axioms that are strictly weaker than Strong Pareto and that have been endorsed (sometimes jointly) in prior work on social choice under indifference intransitivity. The key axiom is Consistency, which states that if bundles are held constant for all but one individual, then society’s preferences must align with those of that individual. Theorem 1 combines Consistency with Indifference Agglomeration, which states that society must be indifferent to combined changes in the bundles of two individuals if it is indifferent to the same changes happening to each individual separately. Theorem 2 combines Consistency with Weak Majority Preference, which states that society must prefer whatever the majority prefers if no one has a preference to the contrary. Given that indifference intransitivity is a necessary condition for the just-noticeable difference (JND) approach to interpersonal utility comparisons, a key implication of the theorems is that any attempt use the JND approach to derive societal preferences must violate at least one of these three axioms.