Conducting Cost Benefit Analysis in Expected Utility Units Using Revealed Social Preferences

Assuming individual preferences satisfy the Von Neumann–Morgenstern axioms for expected utility we show how we can measure an individual’s expected utility of any state using their willingness to accept a gamble over two reference points. The utility function captures the diminishing marginal utility of money with income and risk aversion over gambles. This contrasts with the standard money metric valuations that assume linearity of an individual’s welfare in money. Measuring costs and benefits in expected utility units seems more appropriate than money units for applied welfare economics since it reflects individuals’ preferences more accurately, and can be applied to policies that involve risk. In addition, if social preferences satisfy the Von Neumann–Morgenstern axioms and the Pareto principle, social welfare is the weighted sum of these expected utilities. The weights can be calculated directly for the United States from revealed Government preferences on the allocation of mortality risk. The United States Government values lives equally in calculating the welfare losses from mortality risk and this implies an equal weighting of individual utilities if they are measured using willingness to accept a gamble of a probability of death versus the status quo; we call this life metric expected utility. For projects with small effects on expected utility, we show how to convert existing money metric cost benefit studies into life metric expected utility cost benefit analysis using weights based on how the money value of a statistical life varies with income in the United States. Our approach may be particularly appealing for the conduct of cost-benefit studies mandated by regulation in the United States to inform Government policy. It measures costs and benefits in expected utility units that respect individuals’ preferences over risk and sums these utility gains using the Government’s revealed preferences and implied social welfare function.