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Expected Utility Theory and the Tyranny of Catastrophic Risks Dis cus si on Paper No. 10-059 Expected Utility Theory and the Tyranny of Catastrophic Risks Wolfgang Buchholz and Michael Schymura Dis cus si on Paper No. 10-059 Expected Utility Theory and the Tyranny of Catastrophic Risks Wolfgang Buchholz and Michael Schymura First Version: September 01, 2010 This Version: November 09, 2010 Download this ZEW Discussion Paper from our ftp server: ftp://ftp.zew.de/pub/zew-docs/dp/dp10059.pdf Die Dis cus si on Pape rs die nen einer mög lichst schnel len Ver brei tung von neue ren For schungs arbei ten des ZEW. Die Bei trä ge lie gen in allei ni ger Ver ant wor tung der Auto ren und stel len nicht not wen di ger wei se die Mei nung des ZEW dar. Dis cus si on Papers are inten ded to make results of ZEW research prompt ly avai la ble to other eco no mists in order to encou ra ge dis cus si on and sug gesti ons for revi si ons. The aut hors are sole ly respon si ble for the con tents which do not neces sa ri ly repre sent the opi ni on of the ZEW. THE TYRANNY OF CATASTROPHIC RISKS EXECUTIVE SUMMARY Expected Utility (EU) theory is not only applied to individual choices but also to ethical decisions, e.g. in cost-benefit analysis of climate change policy measures that affect 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 un- likely 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 eventu- ally 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 Weitzman´s "dismal theo- rem". In this spirit we will consider the specific 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 out- comes 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 ap- proaches is to give catastrophic risks more attention instead of less such that the TCR might even be aggravated. THE TYRANNY OF CATASTROPHIC RISKS DAS WICHTIGSTE IN KÜRZE Die Erwartungsnutzentheorie (EUT) kann nicht nur für Entscheidungen auf individueller Ebene angewandt werden, sondern auch aggregiert in ethischen Entscheidungssituationen, wie zum Beispiel in Kosten-Nutzen-Analysen bei der Evaluierung klimapolitischer Politik die vor allem zukünftige Generationen be- treffen. In diesem Zusammenhang stellt sich die Frage, inwiefern die EUT mit katastrophalen Ereignissen mit extrem niedriger Wahrscheinlichkeit umgehen kann. In unserer Arbeit zeigen wir die Schwierigkeiten der EUT beim Umgang mit katastrophalen Ereignissen auf. Falls man eine hinreichende Risikoaversion annimmt, tritt eine "Tyrannei der katastrophalen Risken" (TCR) auf. Die Projekte- valuation kann dann von extrem unwahrscheinlichen Ereignissen dominiert wer- den. Falls die angenommene Risikoaversion sehr gering ist, kann es passieren, das solche katastrophalen Ereignisse überhaupt keinen Einfluss auf das Ergeb- nis haben, was aus ethischer Perspektive genauso bedenklich ist. Der Artikel trägt bei zu der Literatur über die Paradoxien der EUT, wie z.B. dem Allais- Paradoxon oder Martin Weitzman´s "dismal theorem". Wir behandeln den spez- ifischen Fall von katastrophalen Ereignissen mit sehr hohen Schäden und sehr geringer Eintrittswahrscheinlichkeit, wie es etwa beim Klimawandel der Fall sein kann. Nach einem einleitenden Teil zeigen wir in heuristischer Art und Weise, dass es aus ethischen Gründen notwendig sein kann, die Zahlungsbereitschaft zur Vermeidung von Extremereignissen nach oben zu begrenzen. Wir formal- isieren dann die sogenannte "Tyrannei der katastrophalen Risiken" (TCR) und zeigen auf, dass das Auftreten der TCR fundamental von der Wahl der zugrunde liegenden Nutzenfunktion abhängt. Wir folgern, dass man eine unrealistisch niedrige Risikoaversion annehmen müsste, um die TCR zu vermeiden. Am Ende bennenen wir die Alternativen zur EUT, die allerdings katastrophale Risiken noch mehr berücksichtigen und so das Problem der TCR noch verschärfen können. EXPECTED UTILITY THEORY AND THE TYRANNY OF CATASTROPHIC RISKS WOLFGANG BUCHHOLZ∗ AND MICHAEL SCHYMURAy FIRST VERSION: SEPTEMBER 01, 2010 THIS VERSION: NOVEMBER 09, 2010 ABSTRACT - Expected Utility theory is not only applied to individual choices but also to eth- ical decisions, e.g. in cost-benefit analysis of climate change policy measures that affect 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 plausi- ble 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. Keywords: Utilitarianism, Expected Utility Theory, Catastrophic Risks JEL-Classification: Q54 ∗University of Regensburg, Universitätsstraße 31, D-93053 Regensburg, Germany; Email: [email protected] yCentre for European Economic Research (ZEW), L7,1, D-68161 Mannheim, Germany; Email: [email protected]. The authors express their thank for helpful comments from John Roemer (Yale University) and Martin Weitzman (Harvard University). Furthermore we thank the Wis- senschaftsgemeinschaft Gottfried Wilhelm Leibniz (WGL) for funding. THE TYRANNY OF CATASTROPHIC RISKS 1 I.I NTRODUCTION XPECTED UTILITY (EU) Theory still provides the standard theoretical tool for E cost-benefit analysis under conditions of risk which, in the context of envi- ronmental economics, is used to assess whether conservation or pollution abate- ment measures with uncertain consequences are economically beneficial or not. For a long time this approach, however, has come under attack. So, in many circumstances, observable behavior of actual people does not conform to the pre- dictions of EU theory. Beginning with Allais (1953) and Ellsberg (1961) it has been shown by a lot of experiments that, regularly, decisions under risk are sub- ject to paradoxes and anomalies such that individuals act not in accordance with the axioms of EU theory. Besides this well-known criticism there is another strand of objections against EU theory which is, in some sense, related to those of behavioral economics but conceptually different. So, in some cases, it is already suggested by theoretical reasoning and thought experiments ("at the desk and not in the lab" ) that in many situations strict application of EU theory would produce results that con- tradict "plausibility", i.e. that do not reflect intuitive expectations and seem hard to accept. A prominent example for this is Rabin (2000) who has first shown by a purely formal argument that moderate risk aversion w.r.t. to small lotteries would, if consistently applied, lead to an immoderate high degree of risk aversion at the large. In a similar vein, standard properties of von Neumann Morgenstern utility functions (as risk aversion as such and decreasing absolute risk aversion in particular) initially were motivated by means of introspection and not by con- ducting experiments in a systematic way (see Arrow (1963)). Even though such considerations refer to behavior of individuals they are also of relevance in another context. So there is long tradition to apply EU theory not only to individual decisions under risk but also to ethical choices concerning the society as a whole (see already Harsanyi (1955))1. This ethical dimension of EU theory is not only of a mere abstract theoretical interest but has much importance for real-life cost-benefit analysis just when, as in the field of climate change policy (see e.g. Stern, 2006 Stern (2006)), the interests of future generations are to be given due attention. In the ethical context plausibility of results obtained through the EU approach can get some new and special meaning since sensibility at the individual level may transform into ethical acceptability at the collective level. So smoothing income across different states of nature which is as an implication of decreasing marginal utility of income, i.e. risk aversion, not only seems to be rational and prudent from a personal viewpoint but, from the standpoint of the 1For a critical assessment of Harsanyi‘s ethical interpretation of EU theory see Roemer (1996) (pp. 147 -152) THE TYRANNY OF CATASTROPHIC RISKS 2 society or an "ethical observer", also serves the purpose to justify a more equal distribution of income and wealth among different individuals or generations. Concerning application of EU theory to ethical decisions a main question is which normative objectives ("values") can be incorporated by this approach. So, in particular, it can be asked whether ethically appealing results can be generated by using specific von Neumann-Morgenstern (vNM) utility functions.
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