Can Risk-Benefit Analysis Provide Consistent Policy Evaluations of Projects Involving Loss of Life?

Abstract

Many public projects such as the construction of nuclear reactors, roads and bridges involve risks to life. Risk-benefit analysis assesses the costs and benefits of these projects by an extension of the well-known willingness-to-pay (compensating variation) criterion to these situations (see Mishan (i982) or Jones-Lee (I976)). The approach taken is an ex ante one, looking at people's expected ,utility (or a substitute) before deaths occur rather than a measure of actual (ex post) welfare losses and gains. A good case can be made against these ex ante decision rules (see Broome (I978), Hammond (I983) or Ulph (I982)) but we do not consider it in this paper. Even in the ex ante setting, however, the willingness-to-pay measures used in risk-benefit analysis may not be consistent with individual welfare. These difficulties are surveyed by Arrow (I983). Experimental evidence shows that individuals do not update their subjective probabilities in a way that is consistent with Bayes' theorem -'preference reversal' (willingness to pay is opposite to stated preferences) occurs, and choices depend on the way in which alternatives are described ('framing'). As serious as these problems are, we address, in this paper, the question of the consistency of risk-benefit tests even when individuals are rational and perfectly informed (subjective and objective probabilities coincide) and compensating (or equivalent) variations are summed across individuals to provide a social riskbenefit test. We investigate the conditions under which these tests provide orderings of all the social alternatives, thus avoiding inconsistent social preferences (for example, alternative x preferred to alternative y and y to x, or x preferred to y, y preferred to z, and z preferred to x). We require individual preferences to be consistent in the sense of Hicks and Allais (utility depends on the probability of being alive and on consumption enjoyed while alive) and consider as well the special case of the expected utility hypothesis. We show that, in a simple one-good model (Section I), both compensating and equivalent variations are exact indexes of individual welfare gain or loss. Accepting a project if and only if the sum of compensating variations is positive is equivalent (in this model only) to the (ex ante) potential Pareto improvement criterion for project acceptance. Lemma i argues that the compensating variation (or equivalent variation)