  Experimental work regularly finds that individual choices are not
deterministically rationalized by well-defined preferences. Nonetheless, recent
work shows that data collected from many individuals can be stochastically
rationalized by a distribution of well-defined preferences. We study the
relationship between deterministic and stochastic rationalizability. We show
that a population can be stochastically rationalized even when half of the
individuals in the population cannot be deterministically rationalized. We also
find the ability to detect individuals who are not deterministically
rationalized from population level data can decrease as the number of
observations increases.
