Machina and Schmeidler [Econometrica, 60 (1992) 745-780] gave preference co
nditions for probabilistic sophistication, i.e. decision making where uncer
tainty can be expressed in terms of (subjective) probabilities without comm
itment to expected utility maximization; This note shows that simpler and m
ore general results can be obtained by combining results from qualitative p
robability theory with a 'cumulative dominance' axiom. (C) 2000 Elsevier Sc
ience BN. All rights reserved.