On the sensitivity of the value of information to risk aversion in two-action decision problems

This paper discusses the sensitivity of the value of information to the risk aversion in two-action decision problems when the initial wealth is uncertain. We demonstrate that there is no general monotonicity between information value and the Arrow–Pratt risk aversion in this setting. We then show that monotonicity exists in the sense of Rubinstein’s measure of risk aversion when the lottery is independent of the initial wealth. Finally, we show that if the lottery is dependent on the initial wealth, then Ross’s measure of risk aversion is needed to characterize this monotonic relation. Our results explain the shape of the sensitivity analysis curve of the value of information to risk aversion and interpret various measures of risk aversion based on their monotonicity with information value.