Abstract: In its ideal form, arbitrariness review is an instrument for promoting “deliberative democracy” – a system that combines reason-giving with political accountability. Under arbitrariness review in its current form, courts tend to embrace the “hard look doctrine,” which has a procedural component, requiring agencies to offer detailed justifications, and also a substantive component, in which courts assess the reasonableness of the agencies’ choices on the merits. These are serious constraints on the executive branch, and they also reduce the risk of large-scale instability in government, in which scientific and economic judgments are overridden by political considerations. With respect to regulatory policy, it is not enough to say that “elections have consequences.” For climate change in particular, the “social cost of carbon,” or more broadly the “social cost of greenhouse gases,” is sometimes described as “the most important number you’ve never heard of.” A key reason is that within the executive branch, the stringency of regulation of greenhouse gases emissions often depends on that number. Another reason is that the social cost of carbon can and should play a role in determining the content of other kinds of initiatives, such as a carbon tax. In the United States, the relevant numbers were challenged in court under the administrations of Barack Obama (where they were upheld) and Donald Trump (where they were struck down). The litigation raises fundamental questions about the role of science, economics, and politics in judicial review of agency action, and about the relationship between courts and the administrative state. With respect to the social cost of carbon: (1) A decision to use the global number, as opposed to the domestic number, would be straightforward to defend against an arbitrariness challenge; a decision to use the domestic number, as opposed to the global number, would be difficult to defend against an arbitrariness challenge. (2) A decision to use a low discount rate, such as two percent, would be straightforward to defend against an arbitrariness challenge; a decision to use a high discount rate, such as seven percent, would be exceedingly difficult to defend against an arbitrariness challenge. (3) A wide range of decisions – involving, for example, climate sensitivity and the damage function -- raise difficult questions in science and economics; they should be straightforward to defend against an arbitrariness challenge, but only if they follow from a reasoned justification. (4) Approaches that take account of equity – including “prioritarianism” – should be defensible against an arbitrariness challenge, as should be a refusal to adopt such approaches, but here again, a reasoned justification is required. (5) A decision to “back out” a social cost of carbon, from some specific target, would be challenging to defend against an arbitrariness challenge. A general lesson, with broader implications, is that judicial review of the social cost of carbon should (and likely will) involve a procedural hard look, not a substantive hard look. A procedural hard look is important to defend against failures of both deliberation and democracy; a substantive hard look would strain judicial capacities.