Expected Utility Theory and the Tyranny of Catastrophic Risks

Expected Utility (EU) theory is not only applied to individual choices but also to ethical decisions, e.g. in cost-bene t analysis of climate change policy measures that a ect future generations. In this context the crucial question arises whether EU theory is able to deal with "catastrophic risks", i.e. risks of high, but very unlikely losses, in an ethically appealing way. In this paper we show that this is not the case. Rather, if in the framework of EU theory a plausible level of risk aversion is assumed, a "tyranny of catastrophic risk" (TCR)emerges, i.e. project evaluation may be dominated by the catastrophic event even if its probability is negligibly small. With low degrees of risk aversion, however the catastrophic risk eventually has no impact at all when its probability goes to zero which is ethically not acceptable as well. Our work contributes to the literature about the paradoxes of EU theory, like e.g. the Allais paradox or Martin Weitzmans "dismal theorem". In this spirit we will consider the speci c case of catastrophic risks where extremely high losses occur with a very low probability like for example extreme forms of climate change. After introducing the problem we give some heuristic motivation and show, that it can be an ethical imperative that the willingness to pay for avoiding catastrophic risks should be limited. Then we formalize the so-called "Tyranny of Catastrophic Risks"(TCR) and show that it crucially depends on the type of the underlying utility function whether bad but very unlikely outcomes may dominate the results. Furthermore we conclude that one would have to assume an implausibly low degree of risk aversion to exclude TCR. Finally we disucss shortly alternatives to EU theory, but the intention of most of these approaches is to give catastrophic risks more attention instead of less such that the TCR might even be aggravated.

Buchholz, Wolfgang and Michael Schymura (2010), Expected Utility Theory and the Tyranny of Catastrophic Risks, ZEW Discussion Paper No. 10-059, Mannheim.