Further examples of the impact of skewness on the expected utility of a risk-averse agent

Recent literature contains numerous examples where researchers continue to assert that a positive third derivative of the utility function of a risk-averse agent implies a preference for skewness, <italic>ceteris paribus</italic>. The purpose in this letter is to provide some examples pertinent to occupational choice, the gambling literature and experimental work where the assertion is incorrect and an example relevant to experimental work where it is correct.