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 to use the JND approach to derive societal preferences must violate at least one of these three axioms. (shrink)

We examine the impact of Suzumura’s (Economica 43:381–390, 1976) consistency property when applied in the context of collective choice rules that are independent of irrelevant alternatives, neutral, and monotonic. An earlier contribution by Blau and Deb (Econometrica 45:871–879, 1977) establishes the existence of a vetoer if the collective relation is required to be complete and acyclical. The purpose of this paper is to explore the possibilities that result if completeness and acyclicity are dropped and Suzumura consistency is imposed instead. A (...) conceptually similar but logically independent version of the combined axiom that requires the collective decision mechanism to be independent, neutral, and monotonic is employed. In the case of a finite population, we obtain an alternative impossibility theorem if a collective choice rule is assumed to be non-degenerate and a modified no veto requirement is imposed instead of Blau and Deb’s (1977) condition. If the population is countably infinite, the impossibility can be avoided but it resurfaces if our new no veto property is extended to a coalitional variant. (shrink)