  We show that the set of aggregate choices of a population of rational
decision-makers - random utility models (RUMs) - can be represented by a
population of irrational ones if, and only if, their preferences are
sufficiently uncorrelated. We call this representation: Irrational RUM. We then
show that almost all RUMs can be represented by a population in which at least
some decision-makers are irrational and that under specific conditions their
irrational behavior is unconstrained.
