Most people violate expected utility theory’s substitution axiom in identical choice frames

Evidence

Because the same respondents completed both problems 13 and 14, we can examine the number who selected each of the four possible pairs of programs: X and A, X and B, Y and A, Y and B. … The pair most frequently selected is X and B, which corresponds to the modal choices of each problem considered individually. These modal choices pose a problem for the expected utility model. Setting u(0)=0, the preference for X over Y in problem 13 implies that u(20M)>(4/ 5)u(30M), or that u(20M)/u(30M)>4/5. This inequality is inconsistent with that implied by problem 14, because the preference for A over B implies that (1/4)u(20M)<(1/5)u(30M), or that u(20M)/u(30M)<4/5. Note that programs A and B (in problem 14) can be obtained from programs X and Y (in problem 13), respectively, by multiplying the probability of nonnull outcomes by one-fourth. The substitution axiom of expected utility theory says that if X is preferred to Y, then a probability mixture that yields X with probability p and 0 otherwise should be preferred to a mixture that yields Y with probability p and 0 otherwise. If p= 1/4, this axiom implies that X is preferred to Y if and only if A is preferred to B. From the above table it is evident that more than half of our respondents (45 or 88) violated this axiom. — John T. Jost and Jim Sidanius, Political Psychology, 2508

Categorization

• DEFINE: The substitution axiom of expected utility theory is clearly stated and then empirically tested.
• XREF: Connects to Kahneman and Tversky’s framing research and the whole prospect theory literature these problems are lifted from.
• SHARE: Worth sending to anyone who teaches decision theory or behavioral economics — this is the classic Allais-style paradox demonstration.