Probability discounting (or probability weighting) in decision-making is multiplying the value of an outcome by one’s subjective probability that the outcome will occur.2 The broader import of defending probability discounting is to help justify cost-benefit analyses in contexts such as climate change. This chapter, however, addresses only decisions under risk. Decisions can be made under conditions of certainty, risk, and uncertainty.3 Under certainty, the decision-maker knows the outcome of any of his or her decisions.4 Under risk, they know the potential outcomes of any of their decisions, and can assign probabilities to any of those outcomes dependent on particular decisions. Finally, under uncertainty, at least some outcome for at least some decision cannot be assigned a probability. This defence of probability discounting applies only under risk. However, this is not unduly limiting. At a theoretical level, the possibility of probability discounting does not arise under the other conditions. At a practical level, evaluations of climate policy are almost never done under conditions of full certainty, and many are performed under risk. (For an overview of evaluations of climate policy under risk, please see Chapter 3 of this volume.) So addressing probability discounting under risk is widely applicable. The purpose of this chapter is thus to justify the use of probability discounting in contexts of risk – but also cost-benefit analyses more broadly – using a new argument. While such probability discounting is sometimes taken to be objectionable, it is also sometimes taken to be uncontroversial. This chapter addresses both camps. As a representative of the first sceptical camp, I consider an objection by Caney (2008, 2009) in the following section.5 Caney has been particularly influential in the climate debate and argues that, if certain conditions obtain, it is morally impermissible to discount for probability. But his conditions – which are meant to indicate when probability discounting (and cost-benefit analysis) is impermissible – fail, since they overgeneralize. Since climate change is plausibly construed as putting many people’s rights at risk, one question which arises is how to assess the risk of a violation compared to a violation which is certain to occur. Caney’s answer is that, at least under the assumption that certain

conditions (“R1-R4”) obtain, there is no difference in how we ought to assess them: even putting human rights at risk is impermissible. These conditions do not manage to do the work that Caney needs, and, more generally, this type of approach is unworkable; each individual action may increase risks of violation only in very small increments and it is only once these risks are aggregated that initially plausible conditions like Caney’s R1-R4 are satisfied. At least in theory, cost-benefit analyses with probability discounting are sensitive enough on the individual level to compare the small incremental risks and the marginal benefits of individual actions. Among those in the second camp who take probability discounting to be uncontroversial, many refer to the decision-theory literature. However, probability discounting has not received a more catholic defense. Here I offer a defense of probability discounting which does not rely upon decision-theoretic axioms that those outside of decision-theory may not accept. My intention in my positive argument for probability discounting is to address those skeptical of probability discounting with a new normative defence. This defense can be taken as complementary to decision-theoretic defences. The complementarity, for those who are already sympathetic to the decision-theoretic defences of probability discounting, lies in this argument’s reinforcement of this conclusion. This argument involves distinguishing between causal responsibility and moral responsibility, where moral responsibility for an effect can be cashed out in terms of blameworthiness and praiseworthiness and causal responsibility for an effect requires only that that effect is part of a causal chain issuing from one’s act. With this distinction in hand, moral responsibility can be seen as coming in degrees. Given that we can limit our deliberation and consideration to that which we are morally responsible for, and that our moral responsibility for outcomes is limited by our subjective probabilities, it follows that our subjective probabilities can ground probability discounting. The concluding section includes some suggestions about what this means for long-term decision-making. The argument allows us to ground probability discounting in normative terms such as moral responsibility. Evaluations of climate change can be grounded, on this argument, in our moral responsibility which – on the assumption that our subjective probabilities decrease with respect to time – itself decreases with respect to time. This argument also shows that it is permissible for individuals to engage in (mini) cost-benefit analyses with probability discounting.