Note: Ordinal Equivalence of Buying and Selling Prices for Information—When is Constant Risk Attitude Entailed?

Hazen and Sounderpandian (1999) claim to have demonstrated that ordinal equivalence of the buying price and the selling price for information entails that the utility function must have constant risk attitude (i.e., be linear or exponential). However, there is no explicit indication of the scope of the ordinal equivalence assumed—is it within any particular decision problem, or within all decision problems sharing the same utility function? Here we explore the difference between these two assumptions, providing counterexamples for the constant risk attitude assertion in the first case, and in the second case a proof that buy-sell ordinal equivalence within all decision problems sharing the same utility forces constant risk attitude. In the first case, the simplest counterexample arises from the assertion that more refined information sources have greater information values.