Concave utility curves mathematically imply risk-averse choices.

Evidence

The results showed that the assumptions underlying the classical theory of risky choice are systematically violated in the manner predicted by prospect theory. In particular, our respondents exhibited risk aversion in the domain of gains, risk seeking in the domain of losses, and a greater sensitivity to losses than to gains. — John T. Jost and Jim Sidanius, Political Psychology, 2406 (#complicates, via linked claim)

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 (#complicates, via linked claim)

Categorization

• XREF: connects to: Adding risk to portfolio selection makes the optimization problem nonlinear and mathematically novel. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 211; Loss aversion shapes riskless choice, unlike utility theory’s risk dependence; Risk-averse preference for the known can make travel pointless — Jenny Odell, How to Do Nothing: Resisting the…, 475 (+4 more)

Broader Connections

• People are risk-averse in gains but risk-seeking in losses #complicates (0.90) — John T. Jost and Jim Sidanius, Political Psychology, 2406
• Most people violate expected utility theory’s substitution axiom in identical choice frames #complicates (0.80) — John T. Jost and Jim Sidanius, Political Psychology, 2508