Kahneman and Tversky use the expression “failure of invariance” to describe inconsistent (not necessarily incorrect) choices when the same problem appears in different frames. Invariance means that if A is preferred to B and B is preferred to C, then rational people will prefer A to C; this feature is the core of von Neumann and Morgenstern’s approach to utility. Or, in the case above, if 200 lives saved for certain is the rational decision in the first set, saving 200 lives for certain should be the rational decision in the second set as well.
But research suggests otherwise:
The failure of invariance is both pervasive and robust. It is as common among sophisticated respondents as among naive ones. . . . Respondents confronted with their conflicting answers are typically puzzled. Even after rereading the problems, they still wish to be risk averse in the “lives saved” version; they will be risk seeking in the “lives lost” version; and they also wish to obey invariance and give consistent answers to the two versions. . . .
The moral of these results is disturbing. Invariance is normatively essential [what we should do], intuitively compelling, and psychologically unfeasible.
From Against The Gods, Peter Bernstein, discussion about K&T