Lottery acquisition versus information acquisition: Prices and preference reversals

Suppose you must choose between two pieces of information A and B. In the absence of cost, you would prefer to obtain A rather than B, and in fact would be willing to take more risk to obtain A than B. Nevertheless, you would pay more money for B than for A. Are your preferences consistent with expected utility? The answer is yes; they may very well be. We give an example to illustrate how this may happen, and relate this reversal phenomenon to the well-known discrepancy between buying and selling prices for lotteries. Along the way, we demonstrate that even though selling an information source is strictly analogous to selling a lottery, buying an information source is not strictly analogous to buying a lottery. However, for any collection of lotteries there is a decision problem with corresponding information sources, each source having both buying price and selling price equal to the buying and selling prices of the corresponding lottery. The existence of preference reversals for mode of information acquisition dispels any notion that the relative value of competing information acquisitions should not depend on the nature of the acquisition. Among expected utility maximizers, only those with constant risk attitude avoid these reversals.