Uncertainty

Georgetown Law Journal

Volumn 99, Issue 4, 2011, Pages 901-959

  Farber, Daniel A ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

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[No Author keywords available]

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EID: 79956151028     PISSN: 00168092     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (392)

1. NICHOLAS STERN, THE ECONOMICS OF CLIMATE CHANGE: THE STERN REVIEW 39 (2007).
2. For a discussion of the debate over the Stern Review, see Daniel H. Cole, The Stern Review and Its Critics: Implications for the Theory and Practice of Benefit-Cost Analysis, 48 NAT. RESOURCES J. 53 (Winter 2008).
3. Cole, supra note 1, at 76.
4. RICHARD BOOKSTABER, A DEMON OF OUR OWN DESIGN: MARKETS, HEDGE FUNDS, AND THE PERILS OF FINANCIAL INNOVATION 241 (2007).
5. A particularly useful discussion of these methods, focusing on the Environmental Protection Agency (EPA), can be found in COMM. ON IMPROVING RISK ANALYSIS APPROACHES USED BY THE U.S. EPA, NAT'L RESEARCH COUNCIL, SCIENCE AND DECISIONS: ADVANCING RISK ASSESSMENT (2009).
6. FRANK KNIGHT, RISK, UNCERTAINTY AND PROFIT (1921). Uncertainty also played a central role in the thought of John Maynard Keynes.
7. See PETER CLARKE, KEYNES: THE RISE, FALL, AND RETURN OF THE 20TH CENTURY'S MOST INFLUENTIAL ECONOMIST 154-57 (2009).
8. See infra sections III.A, III.B.
9. See infra section III.E.
10. Dave Owen, Probabilities, Planning Failures, and Environmental Law, 84 TUL. L. REV. 265, 269 (2009).
11. Quantification of risks is required for cost-benefit analysis, which has been mandated for the past twenty-eight years when the government issues important regulations. Shortly after taking office President Reagan signed Executive Order No. 12,291, 46 Fed. Reg. 13,193 (Feb. 17, 1981), aimed at improving the efficiency of informal rulemaking by executive agencies. Section 2 prohibits issuance of "major" regulations unless, "taking into account the condition of the particular industries affected by regulations [and] the condition of the national economy," the potential benefits to society outweigh potential costs, and net benefits are at a maximum. Id.
12. For recent defenses of cost-benefit analysis, see John D. Graham, Saving Lives Through Administrative Law and Economics, 157 U. PA. L. REV. 395 (2008)
13. W. Kip Viscusi, Monetizing the Benefits of Risk and Environmental Regulation, 33 FORDHAM URB. L.J. 1003 (2006).
14. For a vigorous critique of the way cost-benefit analysis treats environmental and health risks, see Frank Ackerman & Lisa Heinzerling, Pricing the Priceless: Cost-Benefit Analysis of Environmental Protection, 150 U. PA. L. REV. 1553 (2002).
15. See infra text accompanying note 44.
16. See infra text accompanying notes 92-109.
17. See infra text accompanying notes 110-14.
18. See infra text accompanying notes 116-29.
19. See infra text accompanying notes 185-91.
20. See infra text accompanying notes 227-29.
21. As with all decision-making tools, these tools have their costs, and we must always consider whether the benefits of the tools outweigh the decision-making costs. But in most cases the incremental costs will not be high; if we have already determined that a single distribution has fat tails, or that two different models produce different results, the remaining steps in the analysis are often fairly straightforward.
22. An important caveat is in order. The fundamental research discussed in this Article is rapidly developing, and work on practical applications is at an even earlier stage. Thus, the conclusions discussed in this Article-particularly as they bear on issues such as climate change-must be considered preliminary.
23. The models discussed in this Article may also have nonregulatory legal applications. For instance, litigation of major cases may involve uncertainty about results that could affect settlement behavior and litigation strategy in ways relevant to the design of civil procedure rules. Use of ambiguity models in this context might be fruitful.
24. The term "model uncertainty" is sometimes used in this situation, in which we have one or more models of the world but are unsure which one is right. Dealing with model uncertainty is widely acknowledged to be difficult. See COMM. ON IMPROVING RISK ANALYSIS APPROACHES USED BY THE U.S. EPA, supra note 4, at 105-06 ("One of the dimensions of uncertainty that is difficult to capture quantitatively (or even qualitatively) involves model uncertainty."). Even if we know the correct structure for the model, it may be difficult when using complex models to use observations to constrain uncertainties about parameters, although such techniques are now under development.
25. See Trent Russi, Andrew Packard, Ryan Feeley & Michael Frenklach, Sensitivity Analysis of Uncertainty in Model Prediction, 112 J. PHYSICAL CHEMISTRYA 2579, 2579 (2008).
26. See Russi, Packard, Feeley & Frenklach, supra note 19.
27. Some of the complexities are addressed with an eye to practical implementation in MICHAEL V. FRANK, CHOOSING SAFETY: A GUIDE TO USING PROBABILISTIC RISK ASSESSMENT AND DECISION ANALYSIS IN COMPLEX, HIGH-CONSEQUENCE SYSTEMS (2008). A large literature covers the specific problems of determining the level of risk for toxic chemicals, particularly carcinogens, and considerable controversy continues on this subject.
28. See ENVTL. PROT. AGENCY, GUIDELINES FOR CARCINOGEN RISK ASSESSMENT (2005), http://www.epa.gov/raf/publications/pdfs/CANCER-GUIDELINES-FINAL-3-25- 05.PDF
29. ENVTL. PROT. AGENCY, SUPPLEMENTAL GUIDANCE FOR ASSESSING SUSCEPTIBILITY FROM EARLY-LIFE EXPOSURE TO CARCINOGENS (2005), http://www.epa.gov/ttn/atw/ childrens-supplement-final.pdf. Some of the practical difficulties in public health studies are explored in Carole Bass, Solving a Massive Worker Health Puzzle, SCI. AM., Mar. 2008, at 86.
30. A good introduction to probability theory can be found in JOHN HARTE, CONSIDER A CYLINDRICAL COW: MORE ADVENTURES IN ENVIRONMENTAL PROBLEM SOLVING 1-20 (2001).
31. Risk aversion is explained in STEVEN SHAVELL, ECONOMIC ANALYSIS OF LAW 52 (2004).
32. PAUL KRUGMAN & ROBIN WELLS, ECONOMICS 548 (2d ed. 2009).
33. For further discussion of the techniques used by risk analysts, consult DANIEL M. KAMMEN & DAVID M. HASSENZAHL, SHOULD WE RISK IT? EXPLORING ENVIRONMENTAL, HEALTH, AND TECHNOLOGICAL PROBLEM SOLVING (1999)
34. M. GRANGER MORGAN & MAX HENRION, UNCERTAINTY: A GUIDE TO DEALING WITH UNCERTAINTY IN QUANTITATIVE RISK AND POLICY ANALYSIS (1990).
35. For a discussion of the need to keep the uncertainty of parameter estimates and model choice in mind when applying the results of risk analysis, see ADAM M. FINKEL, CONFRONTING UNCERTAINTY IN RISK MANAGEMENT: A GUIDE FOR DECISIONMAKERS (1990).
36. A recent popular book hammers home the point that serious mistakes can follow from attending only to the average rather than the full probability distribution. See SAM L. SAVAGE, THE FLAW OF AVERAGES: WHY WE UNDERESTIMATE RISK IN THE FACE OF UNCERTAINTY (2009). One of Savage's examples, climate change, is particularly relevant for our purposes. Savage asks the reader to consider a hypothetical in which, on average, we expect no sea level rise-perhaps because our best estimate is that climate change will not happen. Id. at 291. However, assume further that we are not certain of this outcome, and the range of possible sea levels forms a bell curve. Id. Savage observes that: "If the sea level ends up below expectations, then damage will be a bit lower than expected, but if sea level is above expectations, damage will be much worse than expected." Id. at 292-93. "Hence," he continues, "the damage associated with the average or expected sea level may be tolerable, but averaged over all the things a scorned and furious Mother Nature might do to us, the damage could be disastrous." Id. at 293. Savage emphasizes, "[F]or this analysis I assumed that the expected temperature would stay the same. Yet the uncertainty alone created great risk."
37. Id. at 294. This argument is presented in more rigorous form in Part III.
38. See, e.g., Private Fuel Storage, L.L.C., 56 N.R.C. 340, 350-51 (2002).
39. San Luis Obispo Mothers for Peace v. Nuclear Regulatory Comm'n, 449 F.3d 1016, 1032 (9th Cir. 2006).
40. Id.
41. Similarly, the Ninth Circuit overturned the Department of Energy's refusal to consider the risk that terrorists might attack a federal biological weapons laboratory. Tri-Valley Cares v. Dep't of Energy, 203 F. App'x 105 (9th Cir. 2006).
42. Amergen Energy Co., No. 50-0219-LR, 2007 WL 595084 (Nuclear Regulatory Comm'n Feb. 26, 2007). Earlier, the agency had said that addressing terrorism was inappropriate because an EIS should only address environmental impacts that will result "with a fair degree of likelihood." Private Fuel Storage, L.L.C., 56 N.R.C. at 347. The agency's position was upheld in New Jersey Department of Environmental Protection v. U.S. Nuclear Regulatory Commission, 561 F.3d 132 (3d Cir. 2009), largely on the ground that relicensing of a plant would not be the "proximate cause" of any harm later resulting from a terrorist attack on the facility. Id. at 140. Legal readers will recall from the first year of law school that proximate cause is a slippery concept.
43. Vt. Yankee Nuclear Power Corp. v. Natural Res. Def. Council, Inc., 435 U.S. 519, 528 (1978).
44. Balt. Gas & Elec. Co. v. Natural Res. Def. Council, Inc., 462 U.S. 87, 93 (1983).
45. Id. at 93-94 (emphasis added).
46. Id. at 94 (citing Licensing and Regulatory Policy and Procedures for Environmental Protection; Uranium Fuel Cycle Impacts from Spent Fuel Reprocessing and Radioactive Waste Management, 44 Fed. Reg. 45,362, 45,368 (Aug. 2, 1979) (codified at 10 C.F.R. pt. 51)). The Commission ultimately determined that any undue optimism in the assumption of appropriate selection and perfect performance of the repository is offset by the cautious assumption, reflected in other parts of the Table, that all radioactive gases in the spent fuel would escape during the initial 6 to 20 year period that the repository remained open, and thus did not significantly reduce the overall conservatism of the S-3 Table. Id. (citation omitted).
47. See infra text accompanying notes 258-60.
48. Balt. Gas & Elec., 462 U.S. at 102.
49. Id. at 102-03. These figures, along with the zero estimate for emissions after permanent disposal, were found in table S-3, published by the Commission.
50. See Environmental Effects of the Uranium Fuel Cycle, 39 Fed. Reg. 14,188, 14,191 (Apr. 22, 1974). Essentially, the Court contended that the table was not misleading as a whole even though the zero emissions number was wrong, because it was balanced by other figures that were deliberately set too high. Balt. Gas & Elec., 462 U.S. at 101-03.
51. Balt. Gas & Elec., 462 U.S. at 103.
52. Richard Stewart describes the current nuclear waste disposal scheme as bankrupt. Richard B. Stewart, U.S. Nuclear Waste Law and Policy: Fixing a Bankrupt System, 17 N.Y.U. ENVTL. L.J. 783, 783 (2008).
53. For another blistering critique of the program from a decade earlier, see James Flynn et al., Redirecting the U.S. High-Level Nuclear Waste Program, 39 ENVIRONMENT 6 (1997).
54. Although the probability may have been nearly zero in the agency's preferred model of the world, we cannot dismiss the risk unless we also know that this particular model is almost certainly correct. For instance, suppose that there are two models available for the storage facility. NRC is eighty percent sure that Model A is correct, but thinks there is a twenty percent chance that Model B is correct. Model A predicts a zero probability of a release. Model B predicts a ten percent probability of a release. The NRC's beliefs under this scenario can be summarized as follows: there is an eighty percent chance that the way the world works is described by Model A and that there is consequently no risk of a release, but a twenty percent chance that the way the world works is described by Model B and that there is consequently a ten percent chance of a release. In this hypothetical situation, the NRC could truthfully say that the best estimate of the probability of a release is zero, and that it is highly confident of that estimate. But taking both models into account, there is actually a twenty percent chance that Model B is right, and then a ten percent chance under Model B that a release would take place. Putting these together means that the probability of a release is ten percent of twenty percent (0.1 × 0.2) or two percent (0.02). Two percent could be quite a significant risk if the costs associated with a release are high. No one would step on a commercial airplane with a two percent (one in fifty) chance of crashing. This example involves known probabilities rather than true uncertainty, but it illustrates a more general point: even if we are highly confident that the true probability of harm is zero, we are not justified in completely discounting the hazard, because if there is any possibility of a higher degree of harm, the expected level of harm is greater than zero. We can discount a hazard entirely only if we are certain that it is zero. Because a probability cannot be less than zero, anything short of complete confidence in a zero level of risk means there is some possibility of harm.
55. See infra text accompanying notes 230-63.
56. 448 U.S. 607, 614-15 (1980) (plurality opinion). The only applicable statutory provision dealing expressly with toxic chemicals in the workplace is section 6(b)(5) of the Occupational Health and Safety Act. See 29 U.S.C. § 655(b)(5) (2006). This provision requires the agency to set a standard for any toxic material "which most adequately assures, to the extent feasible, that no employee will suffer material impairment of health or functional capacity." Another section of the Act, section 3(8), 29 U.S.C. § 652(8) (2006), is also relevant. This section simply defines an occupational safety and health standard as a regulation setting any one of a variety of requirements "reasonably necessary or appropriate to provide safe or healthful employment and places of employment."
57. See, e.g., Howard A. Latin, Good Science, Bad Regulation, and Toxic Risk Assessment, 5 YALE J. ON REG. 89, 91, 144 (1988) (arguing that "uncertainties generally preclude reliable assessments of relevant effects, and there is no scientific consensus on how they should be resolved" and that "[i]n view of the many uncertainties in toxic risk assessment, it is unclear whether risk ranges or point estimates create more of 'a false impression that the bounds of the risks are known with certainty'"). Prior to the Benzene Case, courts were more willing to accept evidence of unquantified risks as sufficient.
58. See John S. Applegate, The Story of Reserve Mining: Managing Scientific Uncertainty in Environmental Regulation, in ENVIRONMENTAL LAW STORIES 43, 70-76
59. (Richard J. Lazarus & Oliver A. Houck eds., 2005) (describing the precautionary approach taken in Reserve Mining Co. v. Envtl. Prot. Agency, 514 F.2d 492 (1975)).
60. For example, in Lead Industries Ass'n v. Environmental Protection Agency, 647 F.2d 1130, 1184 (D.C. Cir. 1980), the D.C. Circuit upheld a primary air quality standard for lead that incorporated an "adequate margin of safety." In setting the margin of safety, the EPA had given no consideration to feasibility or cost. Id. at 1148. Moreover, the evidence of harm was unclear. Id. at 1160. Nevertheless, the court held that feasibility and cost were irrelevant and that the EPA had acted properly in setting the margin of safety. Id. at 1148-49. The court explained Congress's directive to allow a margin of safety "to protect against effects which have not yet been uncovered by research and effects whose medical significance is a matter of disagreement." Id. at 1154.
61. Jonathan Remy Nash, Standing and the Precautionary Principle, 208 COLUM. L. REV. 494, 499 (2008).
62. Id. at 498-99.
63. Id. at 502-03.
64. See DANIEL FARBER, ECO-PRAGMATISM: MAKING SENSIBLE ENVIRONMENTAL DECISIONS IN AN UNCERTAINWORLD 170 (1999).
65. See Jonathan H. Adler, More Sorry than Safe: Assessing the Precautionary Principle and the Proposed International Biosafety Protocol, 35 TEX. INT'L L.J. 173, 195-98 (2000).
66. United Nations Conference on Environment and Development, Rio de Janeiro, Braz., June 3-14, 1992, Rio Declaration on Environment and Development, U.N. Doc. A/CONF.151/26/Rev.1 (Vol. I), Annex I (Aug. 12, 1992).
67. See DAVID HUNTER, JAMES SALZMAN & DURWOOD ZELKE, INTERNATIONAL ENVIRONMENTAL LAW AND POLICY 410 (2d ed. 2002) (discussing these treaties).
68. See id. at 410-11.
69. On the Canadian experience, see Juli Abouchar, The Precautionary Principle in Canada: The First Decade, 32 ENVTL. L. REP. 11407 (2002).
70. See HUNTER, SALZMAN & ZELKE, supra note 50, at 407
71. David G. Owen, Bending Nature, Bending Law, 62 FLA. L. REV. 569, 575 (2010).
72. Food Quality Protection Act of 1996, Pub. L. No. 104-170, 110 Stat. 1489.
73. Id. § 405, 110 Stat., at 1518 (codified as amended at 21 U.S.C. § 346a(b)(2)(C))
74. See Nw. Coal. for Alts. to Pesticides v. U.S. Envtl. Prot. Agency, 544 F.3d 1043, 1051-53 (D.C. Cir. 2008) (reversing the EPA for failing to provide such a justification for downward changes in the magnitude of the safety margin for certain chemicals).
75. See, e.g., Robertson v. Methow Valley Citizens Council, 490 U.S. 332, 350 (1989).
76. For an overview, see Edward A. Fitzgerald, The Rise and Fall of Worst Case Analysis, 18 U. DAYTON L. REV. 1 (1992).
77. 40 C.F.R § 1502.22(b) (1981). If (1) the information relevant to adverse impacts is essential to a reasoned choice among alternatives and is not known and the overall costs of obtaining it are exorbitant or (2) the information relevant to adverse impacts is important to the decision and the means to obtain it are not known ⋯ the agency shall weigh the need for the action against the risk and severity of possible adverse impacts were the action to proceed in the face of uncertainty. If the agency proceeds, it shall include a worst case analysis and an indication of the probability or improbability of its occurrence. Id. (emphasis added).
78. See Vicki O'Meara Masterman, Worst Case Analysis: The Final Chapter?, 19 ENVTL. L. REP. 10026, 10027 & n.14 (1989)
79. (quoting Forty Most Asked Questions Concerning CEQ's National Environmental Policy Act Regulations, 46 Fed. Reg. 18,026, 18,032 (Mar. 23, 1981) (to be codified at 40 C.F.R. pt. 1500-08)).
80. See Charles F. Weiss, Note, Federal Agency Treatment of Uncertainty in Environmental Impact Statements Under the CEQ's Amended NEPA Regulation § 1502.22: Worst Case Analysis or Risk Threshold?, 86 MICH. L. REV. 777, 807-09 (1988)
81. 40 C.F.R. § 1502.22 (2009). The revised regulation applies when an agency completing an EIS has "incomplete information" that is relevant to "reasonably foreseeable significant adverse impacts," including "impacts which have catastrophic consequences, even if their probability of occurrence is low, provided that the analysis of the impacts is supported by credible scientific evidence, is not based on pure conjecture, and is within the rule of reason." Id. If this information is "essential to a reasoned choice among alternatives" and the cost of obtaining it is not "exorbitant," the information must be included. Id. If the information is relevant but cannot be obtained because the cost is too high or the "means to obtain it are not known," the impact statement must include four items: a statement of the information's unavailability; a statement of its relevance to reasonably foreseeable impacts; a summary of the existing scientific evidence relevant to assessing the impacts; and the agency's evaluation of these impacts based on generally accepted scientific methods. Id. This regulation seems reasonable, but it may not put enough pressure on agencies to face up to unpalatable adverse consequences from projects that they may well favor on other grounds.
82. Robertson v. Methow Valley Citizens Council, 490 U.S. 332, 359 (1989).
83. See infra text accompanying notes 126-31.
84. For a recent update on the debate, see Fritz Allhoff, Risk, Precaution, and Emerging Technologies, STUD. IN ETHICS L. & TECH., Aug. 2009, http://www.bepress.com/selt/vol3/iss2/art2. Allhoff suggests that "precaution supplements cost-benefit analysis given uncertainty." Id. at 23.
85. Edward A. Parson, The Big One: A Review of Richard Posner's Catastrophe: Risk and Response, 45 J. ECON. LITERATURE 147, 152 (2007) (book review)
86. (citing RICHARD A. POSNER, CATASTROPHE: RISK AND RESPONSE (2004)).
87. Christopher D. Stone, Is There a Precautionary Principle?, 31 ENVTL. L. REP. 10790, 10791 (2001).
88. Id.
89. Id. at 10792.
90. Nash, supra note 44, at 503 (footnote omitted). Nash calls this "the heartland of the precautionary principle." Id.
91. Id.
92. Id.
93. See Adler, supra note 48, at 195
94. Frank B. Cross, Paradoxical Perils of the Precautionary Principle, 53 WASH. & LEE L. REV. 851, 863-75 (1996) (describing risks created by alternative activities in the face of precautionary government regulation of artificial sweeteners, electric power generation, and pesticides).
95. Cass R. Sunstein, Probability Neglect: Emotions, Worst Cases, and Law, 112 YALE L.J. 61, 93 (2002). The version of precaution discussed in this Article is more forgiving toward technologies with high upside potential and hence seems less vulnerable to this criticism.
96. Id.
97. Id.
98. Id. at 94.
99. Id. at 62-63.
100. Sunstein further elaborated his critique in Cass R. Sunstein, Beyond the Precautionary Principle, 151 U. PA. L. REV. 1003 (2003).
101. See, e.g., Stephen Charest, Bayesian Approaches to the Precautionary Principle, 12 DUKE ENVTL. L. & POL'Y F. 265, 270 (2002) (arguing that "[i]n order to retain its credibility as a legitimate principle of environmental policymaking and not degenerate into an instrument of veiled protectionism," the precautionary principle should be implemented through a Bayesian approach)
102. Christian Gollier, Bruno Jullien & Nicolas Treich, Scientific Progress and Irreversibility: An Economic Interpretation of the 'Precautionary Principle,' 75 J. PUB. ECON. 229 (2000) (proposing an economic interpretation of the precautionary principle)
103. W. David Montgomery & Anne E. Smith, Global Climate Change and the Precautionary Principle, 6 HUM. & ECOLOGICAL RISK ASSESSMENT 399 (2000) (arguing for a Bayesian decision analysis approach to the precautionary principle in the context of global climate change).
104. But see Stone, supra note 65, at 10792, 10799, (arguing that "there appears to be so little content [to the precautionary principle], and so much confusion, that it may be helpful to return to some elementary principles of risk, uncertainty, and law" and "questioning the claim that there is a precautionary principle there").
105. See Stephen Toulmin, The Case for Cosmic Prudence, 56 TENN. L. REV. 29, 35-36 (1998).
106. See David A. Dana, A Behavioral Economic Defense of the Precautionary Principle, 97 NW. U. L. REV. 1315, 1327-28 (2003) (arguing that the principle may "result in the generation of more information" and may "provide advocates of regulation with a discursive tool to increase the amount of information generated and the quality of the analysis of that information").
107. Dana elaborates his position in David A. Dana, The Contextual Rationality of the Precautionary Principle, 35 QUEEN'S L.J. 67 (2009) [hereinafter Dana, Contextual Rationality].
108. See Cass R. Sunstein, The Catastrophic Harm Precautionary Principle, ISSUES LEGAL SCHOLARSHIP, 2007, http://www.bepress.com/ils/iss10/art3.
109. Id. at 28.
110. Id.
111. Id.
112. Id.
113. Id.
114. Id. at 28-29.
115. See generally Jainguao Liu et al., Complexity of Coupled Human and Natural Systems, 317 SCIENCE 1513 (2007) (discussing feedback loops in coupled human and natural systems).
116. 4 ⋯ = 1/(1 - f ) (by the algebra rule for summing geometric series). Lags in the process would complicate the results. Note that this formula applies only for f < 1; if f = 1 or f > 1, the series diverges (or in simpler terms, the sum is infinite).
117. This result is explained in Margaret S. Torn & John Harte, Missing Feedbacks, Asymmetric Uncertainties, and the Underestimation of Future Warming, 33 GEOPHYSICAL RES. LETTERS L10703 (2006).
118. To see why the magnitude of our best estimate of f matters, consider the results of using a best estimate of 3/4 rather than 1/2 for f. Then if the range of uncertainty for f is 5/8 to 7/8, the range of uncertainty in outcomes is 8/3 to 8/1, or 2.66 to 8.0. The uncertainty range in f of 1/4 turns into an uncertainty range in outcomes of 5.33. Note that using the same uncertainty in f but with a best estimate of 1/2, as in the text, leads to an uncertainty in outcome of 0.86. So merely by shifting the best estimate of f while leaving the uncertainty of the estimate of f unchanged, we have amplified the increase in the uncertainty of the outcome by a factor of six.
119. See Gerard H. Roe & Marcia B. Baker, Why Is Climate Sensitivity So Unpredictable?, 318 SCIENCE 629 (2007) (discussing the difficulties in assessing climate sensitivity accurately).
120. See infra text accompanying notes 98-101.
121. This can be seen from the graphs in Eric W. Weisstein, Normal Distribution, WOLFRAM MATHWORLD, http://mathworld.wolfram.com/ NormalDistribution.html (last visited Nov. 6, 2010), which reviews the mathematics of the normal distribution.
122. The term fat tails has recently come into vogue. According to one language expert: "If you want to make an impression at a board meeting or a Congressional hearing these bearish days, make a harrumphing noise and employ the figure of speech now sweeping the economic world: 'But what about the fat tail?'"William Safire, Fat Tail, N.Y. TIMES MAG., Feb. 8, 2009, at 24.
123. For an introduction to power laws, see MANFRED SCHROEDER, FRACTALS, CHAOS, POWER LAWS: MINUTES FROM AN INFINITE PARADISE 103-19 (1991).
124. For a discussion of processes that generate power laws, see Michael Mitzenmacher, A Brief History of Generative Models for Power Law and Lognormal Distributions, 1 INTERNET MATHEMATICS 226 (2004)
125. M.E.J. Newman, Power Laws, Pareto Distributions and Zipf's Law, 46 CONTEMP. PHYSICS 323 (2005).
126. Two other commonly encountered fat-tailed distributions are the Cauchy distribution and the Levy distribution. These distributions behave like power-law distributions in their tails but have different properties for smaller values. The Cauchy distribution, also called the Lorentz distribution, is a continuous distribution describing resonance behavior. See generally Eric W. Weisstein, Cauchy Distribution, WOLFRAM MATHWORLD, http://mathworld.wolfram.com/ CauchyDistribution.html (last visited Nov. 6, 2010). It is symmetric and bell shaped, just like the normal distribution. It is a classical example of a distribution that has no mean (and consequently no variance). As a consequence, the "Law of Large Numbers"-which holds that if a trial is reproduced a large number of times n, then it becomes exceedingly improbable that the average of the outcomes of these n trials will differ significantly from the expected value of one outcome as n grows without limit-does not apply. The Cauchy distribution can be shown to have the distribution of sample means regardless of the sample size. This distribution is just the original Cauchy distribution (sample size one). So the distribution of the sample mean does not "shrink down" as the sample size increases.
127. For a discussion of the Levy distribution, a more advanced treatment is found in SVETLOZAR T. RACHEV, CHRISTIAN MENN & FRANK J. FABOZZI, FAT-TAILED AND SKEWED ASSET RETURN DISTRIBUTIONS: IMPLICATIONS FOR RISK MANAGEMENT, PORTFOLIO SELECTION, AND OPTION PRICING 2, 81-118 (2005).
128. It can be difficult to distinguish power laws from other fat-tailed distributions empirically. See Aaron Clauset, Cosma Rohilla Shalizi & M.E.J. Newman, Power-Law Distributions in Empirical Data (Feb. 2, 2009) (unpublished manuscript), http://arxiv.org/pdf/0706.1062.
129. See RICHARD SOLE & BRIAN GOODWIN, SIGNS OF LIFE: HOW COMPLEXITY PERVADES BIOLOGY 52 (2000) (describing power laws).
130. SIMON A. LEVIN, FRAGILE DOMINION: COMPLEXITY AND THE COMMONS 55 (1999).
131. See SOLE & GOODWIN, supra note 97, at 200-01.
132. Todd M. Scanlon et al., Positive Feedbacks Promote Power-Law Clustering of Kalahari Vegetation, 449 NATURE 209, 209 (2007).
133. See SOLE & GOODWIN, supra note 97, at 205.
134. For further discussion of possible power laws in ecology, see LEVIN, supra note 98, at 55 (discussing whether power laws apply to "catastrophes hitting ecological systems, or extinctions striking taxonomic groups," and stating that this question "represents one of the most intriguing and tantalizing open research problems.").
135. For a compilation of examples of power laws in many different contexts, see Newman, supra note 95, at 327-30.
136. ALBERT-LÁSZLÓ BARABÁSI, LINKED: THE NEW SCIENCE OF NETWORKS 67 (2002).
137. Id. at 67-68.
138. Id. at 68 n.1.
139. This example is given in SCHROEDER, supra note 95, at 157.
140. For a more technical discussion of this phenomenon, see Karl Sigman, Appendix: A Primer on Heavy-Tailed Distributions, 33 QUEUEING SYSS. 261 (1999).
141. Carolyn Kousky & Roger M. Cooke, Climate Change and Risk Management: Challenges for Insurance, Adaptation, and Loss Estimation ii (Res. for the Future, Discussion Paper No. 09-03-REV, 2009), available at http://ssrn.com/ abstract=1346387.
142. See BENOIT B. MANDELBROT, THE FRACTAL GEOMETRY OF NATURE 337-38 (1983).
143. -2. Because of their risk characteristics, fat tails can pose serious problems to insuring risks. See Roger M. Cooke & Carolyn Kousky, Are Catastrophes Insurable?, RESOURCES, Summer 2009, at 18, 20.
144. Martin L. Weitzman, A Review of The Stern Review on the Economics of Climate Change, 45 J. ECON. LITERATURE 703, 723 (2007) (book review).
145. Martin L. Weitzman, On Modeling and Interpreting the Economics of Catastrophic Climate Change, 91 REV. ECON. & STAT. 1, 3 n.4 (2009). Indeed, even determining that data exhibits a fat-tailed distribution such as a power law rather than a thinner tailed distribution such as the lognormal distribution can be difficult. See Newman, supra note 95, at 329-30. The differences can be quite subtle: the same basic model can lead to a power law or a lognormal distribution, depending on whether there is a boundary at an extreme (for example, a requirement that outcomes cannot go below zero).
146. See Mitzenmacher, supra note 95, at 238.
147. For a discussion of the use of lognormal distributions, see Adam M. Finkel, A Simple Formula for Calculating the "Mass Density" of a Lognormally Distributed Characteristic: Applications to Risk Analysis, 10 RISK ANALYSIS 291 (1990).
148. Weitzman, supra note 111, at 9. The distribution that he derives is not a power law but another fat-tailed distribution known for historical reasons as the "Student-t." Id. at 8. This distribution looks like a bell curve "except that the probabilities are somewhat more stretched out, making the tails appear relatively fatter at the expense of a slightly flatter center." Id.
149. One emerging possibility is the use of "real options" analysis, which has only recently been applied to fat-tailed situations such as climate change. See Jon Anda, Alexander Golub & Elena Strukova, Economics of Climate Change Under Uncertainty: Benefits of Flexibility, 37 ENERGY POL'Y 1345, 1354 (2009) (concluding that benefits of early mitigation are increased by uncertainties that could be resolved later).
150. Under some circumstances, we have the advantage of having some information about a distribution, and the question then is how to best select the type of distribution. A technique called "maximum entropy" (MaxEnt) can be helpful in making this choice. MaxEnt selects the distribution
151. Weitzman, supra note 111, at 1.
152. For other legal applications of ambiguity models, see Uzi Segal & Alex Stein, Ambiguity Aversion and the Criminal Process, 81 NOTRE DAME L. REV. 1495 (2006) (identifying and analyzing higher ambiguity aversion of defendants as opposed to prosecutors results in unbalanced plea negotiations)
153. Eric Talley, On Uncertainty, Ambiguity, and Contractual Conditions, 34 DEL. J. CORP. L. 755 (2009) (concluding that ambiguity explains why the possibility of adverse events sometimes results in the use of a conditions clause in a contract rather than a price adjustment)
154. Joshua C. Teitelbaum, A Unilateral Accident Model Under Ambiguity, 36 J. LEGAL STUD. 431 (2007) (arguing that negligence rules may be superior to strict liability under conditions of ambiguity).
155. See Gideon Keren & Leónie E.M. Gerritsen, On the Robustness and Possible Accounts ofAmbiguity Aversion, 103 ACTA PSYCHOLOGICA 149, 149 (1999) ("Ambiguity aversion is one of the most robust phenomena documented in the decision making literature . . . .") The researchers found in one experiment that "ambiguity avoidance is so pervasive that it extends even to situations in which the likelihood of winning in the ambiguity condition is higher than in the risky conditions."
156. Id. at 157.
157. 0 p · 1dp = 1/2 (because one is the probability of a red ball if the urn is red and p is the probability it is red). This is exactly the same as the probability from the half-red, half-blue urn, so there is no reason to favor one over the other. Another way of seeing this more directly is to assume that we have a choice between the following gambles: (1) Betting that the next ball drawn from a half-red, half-blue urn will be red. (2) Betting on a red ball being produced by the following scenario. First, we flip a coin. Second, if the coin comes out heads, we draw a red ball from an all-red urn; if tails, from an all-blue urn. These are just two different mechanisms for producing a fifty-percent probability of red, so with or without risk aversion, a person should be indifferent between them. Thus, risk aversion cannot account for the common preference for the first gamble over the second gamble.
158. Nicholas Barberis & Richard Thaler, A Survey of Behavioral Finance, in HANDBOOK OF THE ECONOMICS OF FINANCE 1053, 1074-75 (George M. Constantinides, Milton Harris & René M. Stulz eds., 2003).
159. Id. at 1075.
160. Id.
161. A good summary can be found in Alessandro Vercelli, Hard Uncertainty and Environmental Policy, in SUSTAINABILITY: DYNAMICS AND UNCERTAINTY 191, 196-205 (Graciela Chichilnsky et al. eds., 1998).
162. Peter Kilbanoff, Massimo Marinacci & Sujoy Mukerji, A Smooth Model of Decision Making Under Ambiguity, 73 ECONOMETRICA 1849, 1849 (2005).
163. Id. at 1869-70.
164. The model has been extended to dynamic-choice situations in which the decision maker receives additional information over time. See Peter Klibanoff, Massimo Marinacci & Sujoy Mukerji, Recursive Smooth Ambiguity Preferences, 144 J. ECON. THEORY 930 (2009).
165. STERN, supra note 1.
166. For discussion of the so-called α-maxmin model in the context of a more general theory, see Paolo Ghirardato, Fabio Maccheroni & Massimo Marinacci, Differentiating Ambiguity and Ambiguity Attitude, 118 J. ECON. THEORY 133, 153-55 (2004) (the crucial result is proposition 19(ii)). α-maxmin can be derived from the assumption that decision makers are indifferent between acts which result in the same range of expected utilities over a set of scenarios.
167. See Paolo Ghirardato, Fabio Maccheroni & Massimo Marinacci, Ambiguity from the Differential Viewpoint 6 (Cal. Inst. of Tech., Social Science Working Paper No. 1130, 2002), available at http://www.hss.caltech.edu/SSPapers/wp1130. pdf. If decision makers care only about the utility associated with outcomes, the assumption seems plausible if we assume that the decision maker has no ability or willingness to evaluate the likelihood of different scenarios, so outcomes across scenarios only reflect the range of possibilities.
168. STERN, supra note 1.
169. A key point in applying these models is identifying the best and worst case scenarios. Use of the models might encourage interest groups to put forward exaggerated scenarios (although this is probably already an incentive for other reasons).
170. Some economists and finance theorists postulate that risk measures should focus solely on adverse outcomes, a concept known as downside risk. See Michael Hanemann et al., Climate Change Impacts to Urban and Agricultural Sectors in California 36-41 (Cal. Climate Change Ctr., Draft Report No. CEC-500-2008-XXX, 2008) (describing theories of downside risk), available at http://calclimate. berkeley.edu/publication/agriculture. The magnitude of α can be considered a measure, in the uncertainty context, of the weight placed on downside outcomes. A low α indicates an aversion to downside uncertainty.
171. If α=1, then α-maxmin becomes ordinary maxmin, in which only the worst case matters. For an axiomatic treatment of maxmin, see Itzhak Gilboa & David Schmeidler, Maxmin Expected Utility With Non-Unique Prior, 18 J. MATHEMATICAL ECON. 141 (1989). The α parameter could be considered a measure of what Keynes called "animal spirits."
172. See CLARKE, supra note 5, at 156. These models are somewhat akin to Dempster-Shafter models of decision making, which use a weighted average of high and low extremes, although the weighting factor (ρ) represents a relative probability rather than ambiguity aversion.
173. See Thomas M. Strat, Decision Analysis Using Belief Functions, in ADVANCES IN THE DEMPSTER-SHAFER THEORY OF EVIDENCE 275, 285, 306 (Ronald R. Yager, Janusz Kacprzyk & Mario Fedrizzi eds., 1994).
174. See Marcello Basili, Alain Chateauneuf & Fulvio Fontini, Precautionary Principle as a Rule of Choice with Optimism on Windfall Gains and Pessimism on Catastrophic Losses, 67 ECOLOGICAL ECON. 485, 486 (2008).
175. Id. at 490.
176. Id.
177. We might be able to narrow the range for α by using empirical evidence showing how individuals approach decision making in situations characterized by ambiguity or through experience over time that might allow officials to develop norms about the appropriate α.
178. See DAVID G. GROVES, NEW METHODS FOR IDENTIFYING ROBUST LONG-TERM WATER RESOURCES MANAGEMENT STRATEGIES FOR CALIFORNIA 12 (2006), available at http://www.rand.org/pubs/rgs-dissertations/2006/RAND-RGSD196.pdf.
179. For an effort to test the usability of this approach for water agencies, see DAVID G. GROVES ET AL., PRESENTING UNCERTAINTY ABOUT CLIMATE CHANGE TO WATERRESOURCE MANAGERS: A SUMMARY OF WORKSHOPS WITH THE INLAND EMPIRE UTILITIES AGENCY 73-74 (2008), available at www.rand.org/pubs/technical-reports/2008/RAND- TR505.pdf.
180. This is a more formalized version of the familiar technique of scenario analysis. For a description of scenario analysis, see JAMES A. DEWAR, ASSUMPTION-BASED PLANNING: A TOOL FOR REDUCING AVOIDABLE SURPRISES 130-42 (2002).
181. See GROVES, supra note 135, at 123-48.
182. See id. at 132-33 (describing the RDM robustness criterion).
183. Id. at 124-25 (describing how the method achieves "robust" policies that are "relatively insensitive to the key uncertainties and different preferences held by decision makers")
184. see also David G. Groves & Robert J. Lempert, A New Analytic Method for Finding Policy-Relevant Scenarios, 17 GLOBAL ENVTL. CHANGE 73, 75 (2007) (stating that "[t]he central idea is to use multiple runs of computer simulation models to identify those scenarios most important to the choices facing decision makers," based on the foundation of RDM).
185. GROVES, supra note 135, at 125.
186. Id.
187. See Michael Margolis & Eric Nævdal, Safe Minimum Standards in Dynamic Resource Problems-Conditions for Living on the Edge of Risk (Res. for the Future, Discussion Paper No. 04-03, 2004), available at www.rff.org/RFF/ Documents/RFF-DP-04-03.pdf. Margolis and Nævdal show that "SMS is optimal policy if managers can put lower bounds on two parameters: the seriousness of the catastrophe and a parameter that determines how the magnitude of risk varies with the state-variable's position in state space."
188. Id. at 3.
189. For further discussion and critique of SMS, see Michael C. Farmer & Alan Randall, The Rationality of a Safe Minimum Standard, 74 LAND ECON. 287, 288 (1998) (arguing in favor of a harder version of SMS where a consensus exists that a resource is a human necessity)
190. J.C. Rolfe, Ulysses Revisited-A Closer Look at the Safe Minimum Standard Rule, 39 AUSTL. J. AGRIC. ECON. 55, 66-68 (1995) (arguing for a softer version in which SMS is understood as merely a switching rule triggering more intensive scrutiny of costs and benefits).
191. See David McInerney & Klaus Keller, Economically Optimal Risk Reduction Strategies in the Face of Uncertain Climate Thresholds, 91 CLIMATIC CHANGE 29, 30 (2007), available at http:// www.springerlink.com/content/ p238w50423462307/.
192. Klaus Keller et al., What Is the Economic Value of Information About Climate Thresholds?, in HUMAN-INDUCED CLIMATE CHANGE: AN INTERDISCIPLINARY ASSESSMENT 343, 349 fig. 28.5 (Michael E. Schlesinger et al. eds., 2007).
193. ROBERT R. M. VERCHICK, FACING CATASTROPHE: ENVIRONMENTAL ACTION FOR A POST-KATRINA WORLD 239-49 (2010).
194. For a recent example of the use of scenario analysis to deal with a situation of high uncertainty, see Gary E. Machlis & Marcia K. McNutt, Scenario-Building for the Deepwater Horizon Oil Spill, 329 SCIENCE 1018 (2010).
195. VERCHICK, supra note 146, at 242-43.
196. Id. at 243.
197. See supra text accompanying notes 92-109.
198. Cole, supra note 1, at 75. Feedback effects, such as methane releases triggered by temperature increases, threaten to accelerate temperature changes.
199. See Katey Walter Anthony, Methane: A Menace Surfaces, SCI. AM., Dec. 2009, at 68.
200. STERN, supra note 1, at 10-11.
201. Id. at 11.
202. Id. at xvi.
203. See Gerald A. Meehl et al., Global Climate Projections, in WORKING GROUP I TO THE FOURTH ASSESSMENT REPORT OF THE INTERGOVERNMENTAL PANEL ON CLIMATE CHANGE, CLIMATE CHANGE 2007: THE PHYSICAL SCIENCE BASIS 747, 800-01 (Susan Solomon et al. eds., 2007), available at http://www.ipcc.ch/pdf/assessment- report/ar4/wg1/ar4-wg1-chapter10.pdf.
204. 2 is disputed, but the most recent study of the historical record suggests that this feedback loop is not terribly strong. See David C. Frank et al., Ensemble Reconstruction Constraints on the Global Carbon Cycle Sensitivity to Climate, 463 NATURE 527 (2010). The authors caution, however, that this estimate is based on preindustrial conditions that may not apply today.
205. Id. at 529.
206. Meehl et al., supra note 154, at 799.
207. Id.
208. See id. ("Most studies do not account for structural uncertainty, and thus probably tend to underestimate the uncertainty. On the other hand, since several largely independent lines of evidence indicate similar most likely values and ranges, climate sensitivity values are likely to be better constrained than those found by methods based on single data sets.").
209. As one climate scientist explains, "While ensemble projections carried out to date give a wide range of responses, they do not sample all possible sources of modelling uncertainty . . . . More generally, the set of available models may share fundamental inadequacies, the effects of which cannot be quantified." Id. at 805.
210. Myles Allen et al., Scientific Challenges in the Attribution of Harm to Human Influence on Climate, 155 U. PA. L. REV. 1353, 1361 (2007).
211. Id. "There is considerable debate over the extent to which currently available models span the range of plausible real-world responses."
212. Id.
213. See id. at 1375.
214. See Meehl et al., supra note 154, at 797. As the IPCC's review of the literature explains: Uncertainty in predictions of anthropogenic climate change arises at all stages of the modelling process . . . . The specification of future emissions of greenhouse gases, aerosols and their precursors is uncertain. It is then necessary to convert these emissions into concentrations of [greenhouse gases], calculate the associated forcing [the direct temperature effect] and predict the response of climate system variables such as surface temperature and precipitation. At each step, uncertainty in the true signal of climate change is introduced both by errors in the representation of Earth system processes in models and by internal climate variability.
215. Id. (citations omitted).
216. Id. at 754.
217. Id.
218. See id.
219. See Myanna Lahsen, Seductive Simulations? Uncertainty Distribution Around Climate Models, 35 SOC. STUD. SCI. 895, 904-08 (2005).
220. For an excellent general treatment of uncertainty in policy analysis, see MORGAN & HENRION, supra note 25. Morgan and Henrion note that in settings "such as nuclear safety analysis"-and one might add climate change here-"where the tails of the distributions are of particular interest," reliance on the mean and variance as a basis for evaluating uncertainty can entail "a serious deficiency."
221. Id. at 213. They prefer Monte Carlo sampling methods.
222. Id. at 215.
223. COUNCIL OF ECON. ADVISORS, ECONOMIC REPORT OF THE PRESIDENT TOGETHER WITH THE ANNUAL REPORT OF THE COUNCIL OF ECONOMIC ADVISORS 242 (2010), available at http://www.gpoaccess.gov/eop/2010/2010-erp.pdf.
224. See Olivier Deschênes & Michael Greenstone, The Economic Impacts of Climate Change: Evidence from Agricultural Output and Random Fluctuations in Weather, 97 AM. ECON. REV. 354, 377, 381 (2007) (finding that the most likely result of climate change on American agricultural profits is an annual increase in profits of roughly 4%, but with California losing 15%). Note, however, that this study excludes possible impacts of increases in extreme events such as storms and droughts.
225. See id. at 380. Extreme local events are a significant factor even in the absence of extreme global temperature changes.
226. For instance, the latest models show indications of more intense hurricanes in the remainder of this century. See Richard A. Kerr, Models Foresee More-Intense Hurricanes in the Greenhouse, 327 SCIENCE 399 (2010).
227. See Wolfram Schlenker, W. Michael Hanemann & Anthony C. Fisher, The Impact of Global Warming on U.S. Agriculture: An Econometric Analysis of Optimal Growing Conditions, 88 REV. ECON. & STAT. 113, 122-24 (2006) (estimating the potential impact on farmland values east of the 100th meridian for a range of warming scenarios and concluding that aggregate losses could be quite severe-with an average impact of up to approximately seventy percent at the end of the century-if fossil fuel use increases).
228. For a good overview of modeling issues, see J.C. Hourcade et al., Estimating the Costs of Mitigating Greenhouse Gases, in WORKING GROUP III TO THE SECOND ASSESSMENT REPORT OF THE INTERGOVERNMENTAL PANEL ON CLIMATE CHANGE, CLIMATE CHANGE 1995: ECONOMIC AND SOCIAL DIMENSIONS OF CLIMATE CHANGE 263, 268 (James P. Bruce et al. eds., 1996) (discussing the "critical determinants likely to influence the overall cost of climate policies and of the main methodologies employed to account for them").
229. Darren Samuelsonn, Climate: Uncertain Economic Models Create Headaches for Senate Panel, GREENWIRE (Oct. 14, 2009), http://www.eenews.net/Greenwire/ 2009/10/14/5.
230. WILLIAM D. NORDHAUS & JOSEPH BOYER, WARMING THE WORLD: ECONOMIC MODELS OF GLOBAL WARMING 86 (2003) (conditioning their model on the need for a "detailed inventory and valuation of climatically sensitive regions for validation").
231. STEPHEN J. DECANIO, ECONOMIC MODELS OF CLIMATE CHANGE: A CRITIQUE 138-39 (2003) (reviewing a study of energy price forecasts made in the 1980s by the U.S. Department of Energy and private organizations that found out of nine forecasts, all but one of the median error rates was over 100%, and four were over 200%).
232. See Alexander I. Shlyakhter et al., Quantifying the Credibility of Energy Projections from Trends in Past Data: The U.S. Energy Sector, 22 ENERGY POL'Y 119, 119 (1994) (finding that often normal distribution fails to model the frequency of extreme outcomes accurately in energy forecasts).
233. See Matthew D. Zinn, Adapting to Climate Change: Environmental Law in a Warmer World, 34 ECOLOGY L.Q. 61, 81-84 (2007) (arguing that adaptation presents great institutional and political difficulties, which may prevent it from being successfully managed to minimize ecological or other impacts).
234. Philippe Tulkens & Henry Tulkens, The White House and the Kyoto Protocol: Double Standards on Uncertainties and Their Consequences 8 (Fondazione Eni Enrico Mattei, Working Paper No. 89, 2006), available at http://ssrn.com/abstract=910811.
235. Weitzman, supra note 111, at 1.
236. Id. A leading critic ofWeitzman concurs that "[m]any people would agree that a 5% chance of a 10° change, or a 1% chance of a 20° change, would be a catastrophic prospect for human societies."
237. William D. Nordhaus, An Analysis of the Dismal Theorem 10 (Cowles Found., Discussion Paper No. 1686, 2009), available at http//ssrn.com/abstracts= 1330454.
238. Weitzman, supra note 111, at 1.
239. Id. at 18. The fat-tail aspect of Weitzman's analysis seems to be crucial. Using a thin-tail analysis while still taking into account possible extreme outcomes, Pindyck finds a case for moderate climate mitigation but nothing more.
240. See Robert S. Pindyck, Uncertain Outcomes and Climate Change Policy 22 (MIT Sloan Sch., Working Paper No. 4742-09, 2009) available at http://ssrn.com/abstract=1448683. Pindyck provides an important caveat: We have no historical or experimental data from which to assess the likelihood of a ΔT [change in temperature] above 5° C, never mind its economic impact, and one could argue á la Weitzman (2009) that we will never have sufficient data because the distributions are fat-tailed, implying a WTP [willingness to pay] of 100% [of consumption] (or at least something much larger than 2%).
241. Id.
242. It is hard to quarrel, however, with Weitzman's statement that "[e]ven just acknowledging more openly the incredible magnitude of the deep structural uncertainties that are involved in climate-change analysis . . . might go a long way toward elevating the level of public discourse concerning what to do about global warming." Weitzman, supra note 111, at 18.
243. See supra text accompanying notes 116-33.
244. See Sunstein, supra note 80.
245. Another attempt to provide a rigorous basis for the precautionary principle can be found in Gollier, Jullien & Treich, supra note 77, at 239 (recommending precaution when "prudence is larger . . . than twice the absolute aversion to risk")
246. see also J. Barkley Rosser, Jr., Complex Ecologic-Economic Dynamics and Environmental Policy, 37 ECOLOGICAL ECON. 23, 32 (2001) (applying, among other theories, the precautionary principle to fishery management and commenting that "the Precautionary Principle is crucial in situations with critical threshold levels or effects").
247. Nordhaus, supra note 180, at 14 (stating that "the discounted value of world consumption is in the order of $1016).
248. STERN, supra note 1, at 187.
249. As Cole, supra note 1, at 62, explains, these numbers are controversial but they are at least illustrative.
250. See Key Development Data and Statistics, THEWORLD BANK, http://econ.worldbank.org/WBSITE/EXTERNAL/DATASTATISTICS/0,,contentMDK: 20535285%A0menuPK:1192694%A0pagePK:64133150%A0piPK:64133175%A0theSitePK:239419, 00.html (last visited Dec. 20, 2010).
251. A caveat is that we could downplay the potential catastrophic possibilities if, as Nordhaus argues, we could learn that catastrophe is impending fast enough to make a sufficiently quick and vigorous global response to head off the possibility. See Nordhaus, supra note 180, at 20. In my view, Nordhaus is excessively optimistic about this last-minute policy response, in part because of the potential for "climate surprises" involving abrupt climate change that might not leave a great deal of time for a response.
252. See JOHN D. COX, CLIMATE CRASH: ABRUPT CLIMATE CHANGE AND WHAT IT MEANS FOR OUR FUTURE 189 (2005) ("The more likely circumstance . . . is that we are not going to predict the future with any degree of confidence-that climate surprises are inevitable."). Nevertheless, the potential for detecting and heading off catastrophic climate change does need to be considered as part of the analysis.
253. As Robert Hahn explains: [I]f one believes that the probability of a catastrophe is high, and the costs of a catastrophe are enormous, there may be a rationale for throwing the "kitchen sink" at the problem. For now, though, we have barely thrown anything at the problem, and the critical question facing politicians is what reasonable next steps in the real world might look like. Robert W. Hahn, Climate Policy: Separating Fact from Fantasy, 33 HARV. ENVTL. L. REV. 557, 577 (2009) (footnote omitted). I believe that a high level of uncertainty, even without knowledge of a high probability, is sufficient to justify strenuous climate mitigation efforts, but Hahn's point about the gap between the required response and the current situation is well taken.
254. For this reason, despite its risks, geoengineering needs to be considered as a fallback measure if mitigation efforts are unsuccessful in limiting climate change to noncatastrophic levels. See Carolyn Kousky, Olga Rostapshova, Michael Toman & Richard Zeckhauser, Responding to Threats of Climate Change Mega-Catastrophes 11-12 (World Bank, Policy Research Working Paper No. 5127, 2009), available at http://go.worldbank.org/OIXDV8KSN0.
255. STERN, supra note 1, at 466.
256. Id. at 483.
257. To get a sense of the potential economic impact, consider the following estimates regarding sea-level rise: a half-meter sea-level rise would place $185 billion of property in jeopardy by 2100, and the cost of protecting all developed areas from a half-meter rise would be $50 to $66 billion. WILLIAM E. EASTERLING III, BRIAN H. HURD & JOEL B. SMITH, COPING WITH GLOBAL CLIMATE CHANGE: THE ROLE OFADAPTATION IN THE UNITED STATES 14 (2004), http://www.pewclimate.org/global-warming-in-depth/all-reports/ adaptation.
258. See STERN, supra note 1, at 466
259. Alejandro E. Comacho, Adapting Governance to Climate Change: Managing Uncertainty Through a Learning Infrastructure, 59 EMORY L.J. 1, 12-15 (2009).
260. See U.S. GOV'T ACCOUNTABILITY OFFICE, GAO-10-113, STRATEGIC FEDERAL PLANNING COULD HELP GOVERNMENT OFFICIALS MAKE MORE INFORMED DECISIONS 36-38 (2009).
261. For an extensive discussion of these uncertainties, see Daniel A. Farber, Modeling Climate Change and Its Impacts: Law, Policy, and Science, 86 TEX. L. REV. 1655, 1656-57 (2008) (discussing the difficulties of making public policy based on computer models that estimate the future effects of climate change).
262. See CAROLYN KOUSKY & ROGER COOKE, RES. FOR THE FUTURE, ISSUE BRIEF 10-12, ADAPTING TO EXTREME EVENTS: MANAGING FAT TAILS (2010), http://www.rff.org/Publications/Pages/PublicationDetails.aspx?PublicationID= 21177.
263. See P.C.D. Milly et al., Stationarity is Dead: Whither Water Management, 319 SCIENCE 573, 573 (2008).
264. U.S. GOV'T ACCOUNTABILITY OFFICE, supra note 195, at 43.
265. Adaptation of water systems includes a variety of responses. See LEVI D. BREKKE ET AL., U.S. GEOLOGICAL SURVEY, U.S. DEP'T OF THE INTERIOR, CIRCULAR 1331, CLIMATE CHANGE AND WATER RESOURCES MANAGEMENT: A FEDERAL PERSPECTIVE 29-31 (2008). Some responses involve management of water systems through use of longer range predictions to guide water reservoir use. Managing water demand is another option, including increased use of market transfer among users or conservation and efficiency improvements. It is also important to evaluate the risks to water infrastructure posed by more severe floods, which may require investment in existing dams and levees. Additional storage capacity (both surface and groundwater) may also be called for.
266. Issues of climate adaptation for water projects are explained in BREKKE ET AL., supra note 200, at 23-27 (advocating the use of scenario planning).
267. Stéphane Hallegatte, Patrice Dumas & Jean-Charles Hourcade, A Note on the Economic Cost of Climate Change and the Rationale to Limit it Below 2°C, at 11 (World Bank, Policy Research Working Paper, No. 5179, 2010).
268. U.S. GOV'T ACCOUNTABILITY OFFICE, supra note 195, at 37.
269. See supra text accompanying notes 135-48.
270. See David G. Groves, Martha Davis, Robert Wilkinson & Robert Lempert, Planning for Climate Change in the Inland Empire: Southern California, WATER RESOURCES IMPACT, July 2008, at 14, 14. Scenario analysis may also help determine what factual issues are critical for deciding between options. This makes it possible to focus climate research on policy-relevant issues. We should not consider the degree of uncertainty to be fixed forever. One role of modeling is to help us identify research priorities that might reduce the range of uncertainties.
271. For a recent discussion that emphasizes the importance of these uncertainties, see Douglas A. Kysar, Ecologic: Nanotechnology, Environmental Assurance Bonding, and Symmetric Humility, 28 UCLA J. ENVTL. L. & POL'Y 201 (2011).
272. For a short overview of the potential regulatory issues, see J. Clarence (Terry) Davies, Nanotechnology and Risk, RESOURCES, Summer 2009, at 10.
273. THE ROYAL SOC'Y & THE ROYALACAD. OF ENG'G, NANOSCIENCE AND NANOTECHNOLOGIES: OPPORTUNITIES AND UNCERTAINTIES 5 (2004).
274. Id. at 9.
275. Id.
276. Id. at 10-12.
277. Id. at 35.
278. Id. at 47. As of 2004, according to the Royal Society, "very few studies have been published on the potential adverse effects that nanoparticles or nanotubes may have on humans, and only one to our knowledge on environmental effects."
279. Id. at 75.
280. Id. at 47.
281. Id. at 74.
282. JOHN F. SARGENT JR., CONG. RESEARCH SERV., RL 34511, NANOTECHNOLOGY: A POLICY PRIMER (2009).
283. Id. at Summary.
284. Id. at 1.
285. Id.
286. Id. at 3-4.
287. Id. at 9.
288. See GEORGIA MILLER & RYE SENJEN, FRIENDS OF THE EARTH, OUT OF THE LABORATORY AND ONTO OUR PLATES 3 (2008).
289. Id. at 5-6.
290. David B. Fischer, Nanotechnology-Scientific and Regulatory Challenges, 19 VILL. ENVTL. L.J. 315, 330 (2008).
291. Dana, Contextual Rationality, supra note 79, at 18-29, argues that the precautionary principle may correct market incentives to avoid investigating possible environmental and health risks.
292. Robin Fretwell Wilson, Nanotechnology: The Challenge of Regulating Known Unknowns, 34 J.L. MED. & ETHICS 704, 710 (2006).
293. Id. at 711.
294. This proposal is made in Albert C. Lin, Size Matters: Regulating Nanotechnology, 31 HARV. ENVTL. L. REV. 349, 396-404 (2007).
295. Kysar, supra note 206, at 208-09, presents an alternative bonding proposal that emphasizes the role played by worst case outcomes in establishing bond amounts.
296. See supra text accompanying notes 126-33.
297. The EPA has embraced such a research program, but if past practice is a guide, it could take a decade or more before the work even begins. This is not acceptable. See Editorial, Nano-Risks: A Big Need for a Little Testing: The EPA Must Act Swiftly to Evaluate the Possible Health Risks of Nanotechnology, SCI. AM., Jan. 2010, at 28.
298. See Diana M. Bowman & Graeme A. Hodge, A Small Matter of Regulation: An International Review of Nanotechnology Regulation, 8 COLUM. SCI. & TECH. L. REV. 1, 36 (2007).
299. An EPA advisory panel is now considering whether to recommend that nanosilver products be treated as new pesticides requiring a new pesticide registration. See Lynn L. Bergeson, FIFRA Scientific Advisory Panel Considers Nanosilver, 39 ENVTL. L. REP. 11143, 11143-44 (2009).
300. LARRY PARKER & MARK HOLT, CONG. RESEARCH SERV., RL 33442, NUCLEAR POWER: OUTLOOK FOR NEW U.S. REACTORS 23 (2007).
301. Beko Reblitz-Richardson, In Brief, D.C. Circuit Rejects EPA's Proposed Standards and Extends Timeline for Yucca Mountain Nuclear Waste Repository, 32 ECOLOGY L.Q. 743, 743 (2005).
302. David P. Ross, Note, Yucca Mountain and Reversing the Irreversible: The Need for Monitored Retrievable Storage in a Permanent Repository, 25 VT. L. REV. 815, 826 (2001).
303. Id. at 829 (citing COMM. ON TECHNICAL BASES FOR YUCCAMOUNTAIN STANDARDS, NAT'L RESEARCH COUNCIL, TECHNICAL BASES FOR YUCCAMOUNTAIN STANDARDS 85, 96 (1995)).
304. Ross, supra note 232, at 838.
305. See 42 U.S.C. § 10133(a) (2006)
306. 42 U.S.C. § 10172(a)(1)-(2) (2006).
307. Some of the major decisions include Nevada v. U.S. Dep't of Energy, 133 F.3d 1201 (9th Cir. 1998)
308. Cnty. of Esmeralda v. U.S. Dep't of Energy, 925 F.2d 1216 (9th Cir. 1991)
309. Nevada v. Watkins, 914 F.2d 1545 (9th Cir. 1990)
310. Nevada v. Herrington, 777 F.2d 529 (9th Cir. 1985)
311. Nevada v. Burford, 708 F. Supp. 289 (D. Nev. 1989).
312. John L. Jurewitz, The Current Outlook for the Nuclear Power Industry in the United States, in INTERNATIONAL PERSPECTIVES OF ENERGY POLICY AND THE ROLE OF NUCLEAR POWER 203, 206-07 (Lutz Mez, Mycle Schneider & Steve Thomas eds., 2009).
313. Matthew L. Wald, Future Dim for Nuclear Waste Repository, N.Y. TIMES, Mar. 6, 2009, at A15.
314. Alexandra Berzon, Yucca Mountain; Energy Department Presses for License as if Nothing's Changed, LAS VEGAS SUN, Apr. 4, 2009, at 1
315. Katherine Ling, Yucca Haunts Admin's Lagging Efforts on Nuclear Waste Study Panel, N.Y. TIMES, Jan. 11, 2010, http://www.nytimes.com/gwire/2010/01/11/ 11greenwire-yucca-haunts-admins-lagging-efforts-on-nuclear-24943.html.
316. Steve Tetreault & Keith Rogers, McCain: Time for Yucca Plan B, LAS VEGAS REV.-J., Apr. 1, 2009, at 1B (quoting John McCain).
317. Jurewitz, supra note 237, at 207.
318. See Ling, supra note 239.
319. Ross, supra note 232, at 815.
320. Id. at 821.
321. Id.
322. Id. at 834.
323. See supra text accompanying notes 31-35.
324. Ross, supra note 232, at 838.
325. It may seem superficially plausible to exclude such remote risks, but some of the unlikely events could have such significant consequences that they are worth considering.
326. Suppose that there are ten different risks, each of which is likely to materialize once in fifty thousand years. We would then expect one of these risks to materialize about once every five thousand years, yet the government would not consider them in the analysis. Thus, excluding all events with a less than 1/10,000 probability does not guarantee the safety of the facility for even ten thousand years.
327. See supra text accompanying notes 102-09.
328. Nuclear Energy Inst., Inc. v. Envtl. Prot. Agency, 373 F.3d 1251, 1273 (D.C. Cir. 2004).
329. As the court explained: With respect to the length of the compliance period, NAS found "no scientific basis for limiting the time period of the individual-risk standard to 10,000 years or any other value." According to the Academy, "compliance assessment is feasible for most physical and geologic aspects of repository performance on the time scale of the long-term stability of the fundamental geologic regime-a time scale that is on the order of 106 [one million] years at Yucca Mountain." NAS also explained that humans may not face peak radiation risks until tens to hundreds of thousands of years after disposal, "or even farther into the future." Id. at 1267 (citations omitted).
330. Id. at 1275 (quoting Public Health and Environmental Radiation Protection Standards for Yucca Mountain, NV, 66 Fed. Reg. 32,074, 32,094 (June 13, 2001) (codified at 40 C.F.R. pt. 197)).
331. The problem of nuclear waste disposal has proved intractable even in France, despite that country's general enthusiasm for nuclear power. See Jon Palfreman, Why the French Like Nuclear Energy, FRONTLINE, http://www.pbs.org/ wgbh/pages/frontline/shows/reaction/readings/french.html (last visited Dec. 21, 2010).
332. Rebecca M. Bratspies, Regulatory Trust, 51 ARIZ. L. REV. 575, 625-26 (2009).
333. Id. at 626.
334. Amanda Leiter, The Perils of a Half-Built Bridge: Risk Perception, Shifting Majorities, and the Nuclear Power Debate, 35 ECOLOGY L.Q. 31, 61 (2008).
335. Id. at 63. Notably, even in France, where the public widely supports nuclear power: "When it came time to develop a waste facility, however, people balked. There were widespread demonstrations and even riots. And the problem has yet to be solved."
336. Id. at 67.
337. Robert H. Socolow & Alexander Glaser, Balancing Risks: Nuclear Energy & Climate Change, DÆDALUS, Fall 2009, at 31, 36 (2009).
338. The case for using nuclear power in this setting is made in Geoffrey Rothwell and Rob Graber, The Role of Nuclear Power in Climate Change Mitigation, in GENERATING ELECTRICITY IN A CARBONCONSTRAINED WORLD 175 (Fereidoon P. Sioshansi ed., 2010). Rothwell and Graber have some concerns about the economics of rapidly ramping up nuclear power but see it as a significant potential component of mitigation strategy: "[N]uclear power is the only central-station, GHG-free alternative that could replace global ever-growing, ever-polluting coal-fired capacity. If utilities and nations are prepared to significantly increase their investment in nuclear power plant construction, nuclear power is capable of making an important contribution to GHG reduction and climate stabilization." Id. at 205.
339. For discussion of the prospects of nuclear power expansion as a response to climate change, see STEWART BRAND, WHOLE EARTH DISCIPLINE: AN ECOPRAGMATIST MANIFESTO 75-76 (2009) (stating that nuclear power is "Green," and that new reactor designs are "even more [green]"); Harold A. Feiveson, A Skeptic's View of Nuclear Energy, DÆDALUS, FALL 2009, at 60, 68 (discussing nuclear energy prospects and expressing "a strong cautionary note to the confident projections of an inevitable nuclear renaissance"); John W. Rowe, Nuclear Power in a Carbon-Constrained World, DÆDALUS, Fall 2009, at 81, 89 (arguing that, considering global warming and projected future energy demands, "[n]uclear power is inescapably part of the answer to addressing climate change").
340. Whether we do so depends largely on whether we apply discounting to harms far in the future. Over long time periods, the results of changes in discount rates are enormous. As Cass Sunstein has explained, "[i]f a human life is valued at $8 million, and if an agency chooses a 10% discount rate, a life saved 100 years from now is worth only $581." Cass R. Sunstein, Cost-Benefit Default Principles, 99 MICH. L. REV. 1651, 1711 (2001). Imagine how little a life saved in 10,000 years is worth on this basis. Discounting is particularly controversial in the multigenerational context. For a review of the debate, see Daniel A. Farber, From Here to Eternity: Environmental Law and Future Generations, 2003 U. ILL. L. REV. 289.
341. RICHARD A. POSNER, A FAILURE OF CAPITALISM: THE CRISIS OF '08 AND THE DESCENT INTO DEPRESSION vii (2009).
342. Id.
343. Id. at 13-14.
344. For more detailed accounts of the crisis, see WILLIAM D. COHAN, A HOUSE OF CARDS: A TALE OF HUBRIS AND WRETCHED EXCESS ON WALL STREET (2009)
345. DAVID WESSEL, IN FED WE TRUST: BEN BERNANKE'S WAR ON THE GREAT PANIC (2009)
346. Steven M. Davidoff & David Zaring, Regulation by Deal: The Government's Response to the Financial Crisis, 61 ADMIN. L. REV. 463, 471-512 (2009).
347. A prophetic analysis can be found in CHARLES R. MORRIS, THE TRILLION DOLLAR MELTDOWN: EASY MONEY, HIGH ROLLERS, AND THE GREAT CREDIT CRASH (2008)
348. While the classic study of similar historical episodes is CHARLES P. KINDLEBERGER, MANIAS, PANICS, AND CRASHES: A HISTORY OF FINANCIAL CRISES (4th ed. 2000).
349. According to Posner: To understand how the difficulty of determining the riskiness of the new financial instruments contributed to the financial crisis, it is helpful to recall a distinction, made long ago by the economist Frank Knight, between two types of risk. One, which he called "risk," is a risk to which a probability can be assigned, and is the kind that insurance companies insure against because they can calculate a premium that will cover the risk. The other, called "uncertainty," is a risk that cannot be quantified. Anyone who insures such a risk is gambling; anyone who rates it (AAA, BB, etc.) is guessing. POSNER, supra note 264, at 60.
350. Id. at 83.
351. Id. at 134.
352. Id. at 248.
353. For a discussion of conventional risk assessment methods, see Eric Talley & JohanWalden, The Supervisory Capital Assessment Program: An Appraisal, in CONG. OVERSIGHT PANEL, JUNE OVERSIGHT REPORT: STRESS TESTING AND SHORING UP BANK CAPITAL annex to §1 (2009), available at http://cop.senate.gov/ documents/cop-060909-report.pdf.
354. See supra text accompanying notes 102-09, 116-21
355. see also JUSTIN FOX, THE MYTH OF THE RATIONALMARKET: A HISTORY OF RISK, REWARD, AND DELUSION ONWALL STREET 134-35 (2009).
356. POSNER, supra note 264, at 62.
357. See Kara M. Westercamp, Note, A Crack in the Façade and the Whole Building Came Tumbling Down: A Critical Examination of the Central Banks' Response to the Subprime Mortgage Loan Crisis and Global Financial Market Turmoil, 18 TRANSNAT'L L. & CONTEMP. PROBS. 197, 215 (2009) ("The subprime market constituted only $600 billion of the $3 trillion mortgage business, yet the spillover has affected hedge funds, private equity, investment banks, commercial paper, and the stock market.").
358. See INT'L MONETARY FUND, GLOBAL FINANCIAL STABILITY REPORT: RESPONDING TO THE FINANCIAL CRISIS AND MEASURING SYSTEMIC RISK (2009). One flaw in this report is that it acknowledges that prior IMF appraisals were too "optimistic,"
359. id. at 6, but it does not probe in detail the analytic weaknesses that led to this misappraisal of the situation.
360. The methodologies include a "network approach," a "co-risk model," a "distress dependence matrix," and a "default intensity model." Id. at 74.
361. Id. at 76.
362. Id. at 90.
363. Id. at 84.
364. Id. at xi.
365. Id. at 98 ("[T]he sharp parallel increase in the economy-wide VaR [value at risk] and the bank-wide VaR suggests a break with the past feedback patterns, indicating that macro-financial linkages are now tighter, potentially complicating the policy response to the financial sector problems.").
366. Id. at 12.
367. Danielle A. Gordon & Daniel M. Kammen, Uncertainty and Overconfidence in Time Series Forecasts: Application to the Standard & Poor's 500 Stock Index, 6 APPLIED FIN. ECON. 189, 193 (1996).
368. See Benoit B. Mandelbrot, A Multifractal Walk Down Wall Street, SCI. AM., Feb. 1999, at 70, 71
369. see also FOX, supra note 272, at 133-34 (describing studies and observations of fat tails and fractals).
370. For a discussion of chaos and complexity theory and possible applications to economics, see J. Barkley Rosser Jr., On the Complexities of Complex Economic Dynamics, 13 J. ECON. PERSP. 169 (1999). The present discussion does not rely on complexity theory except as a heuristic explanation for certain probability distributions; it is the distribution rather than the explanation that is most relevant.
371. Gordon & Kammen, supra note 283, at 193.
372. Barberis & Thaler, supra note 119, at 1075, 1078.
373. See FOX, supra note 272, at 133-35.
374. ROBERT J. SHILLER, THE SUBPRIME SOLUTION: HOW TODAY'S GLOBAL FINANCIAL CRISIS HAPPENED, ANDWHAT TO DO ABOUT IT 101 (2008).
375. See id. at 102, 104.
376. See BOOKSTABER, supra note 3, at 144-45.
377. POSNER, supra note 264, at xii.
378. Id. at 259-60.
379. Id. at 107.
380. INT'L MONETARY FUND, supra note 275, at xxii.
381. For a discussion of reform efforts aimed at the subprime market that triggered the crisis, see SHILLER, supra note 288, at 107-69.
382. See generally HAL S. SCOTT, THE GLOBAL FINANCIAL CRISIS (2009) (reviewing responses to the financial crisis and various reform proposals).
383. See Erik F. Gerding, Code, Crash, and Open Source: The Outsourcing of Financial Regulation to Risk Models and the Global Financial Crisis, 84 WASH. L. REV. 127 (2009). Back testing "involves modelers making several hypothetical jumps back in time, inputting historical data that were available at those respective times, and then comparing the predictions of the model with how losses actually unfolded."
384. Id. at 143.
385. Efforts at stress-testing banks after the financial meltdown are discussed in Talley & Walden, supra note 271.
386. Other applications exist beyond those discussed in this article. For instance, the question of whether to remove a child from a possibly abusive parent involves great uncertainties about the potentially severe harm to the child from remaining with the parent as well as the psychological harm of removing the parent. Counterterrorism is another obvious application, as are measures to prepare for catastrophic events such as Hurricane Katrina.
387. See supra section I.B.3.
388. See supra section II.B.2.
389. See supra section III.C.
390. See supra section III.D.
391. Donald Rumsfeld, Sec'y, Dep't of Def., DoD News Briefing (Feb. 12, 2002) (transcript available at http://www.defense.gov/transcripts/transcript.aspx? transcriptid=2636) ("[A]s we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns-the ones we don't know we don't know. And if one looks throughout the history of our country and other free countries, it is the latter category that tend to be the difficult ones.").
392. See supra text accompanying notes 247-50.