i How to Be Rational: How to Think and Act Rationally David Robert March 2, 2020 ii © Copyright by David Robert, 2020. All rights reserved iii About this book In this book, I will address the question of how to think and act rationally. For example, should one be skeptical of climate change? And should one invest in life-extension medical research? Chapter 2 of this book is an updated version of a previously published paper (David Robert, "Expected Comparative Utility Theory: A New Theory of Rational Choice," The Philosophical Forum 49, no. 1 (2018): 19–37, https://doi.org/10.1111/phil.12178.) Thanks to Douglas Lackey and several anonymous reviewers for very helpful comments on that paper. I dedicate this book to my Aunt Patricia Moffa, who has always been an inspiration to me. Love you Pat. Please contact me at jeandavidrobert@hotmail.com with any comments on the book manuscript. iv Table of Contents Introduction Chapter 1: How to Acquire Rational Belief Attitudes Chapter 2: How to Make Rational Choices 2.1 Introduction 2.2 Preliminaries 2.3 The CU Principle 2.4 ECU Theory 2.5 The Failure of EU Theory 2.6 ECU Theory and the Problem of Act Versions Chapter 3: Should You Be Skeptical of Climate Change Chapter 4: Should You Invest in Life-Extension Medical Research? Bibliography 1 Introduction It has always appalled me that really bright scientists almost all work in the most competitive fields, the ones in which they are making the least difference. In other words, if they were hit by a truck, the same discovery would be made by somebody else about 10 minutes later. -Aubrey de Grey To make rational choices involves choosing courses of action that best serve one's ends. As a good example, one's chances of having a positive impact on the world are significantly greater if one focuses one's efforts on solving the world's biggest, most urgent problems than if one focuses one's efforts on solving comparatively small, non-urgent problems that will not ultimately matter in the long run if the biggest, most urgent problems are left unsolved. Therefore, if one's goal is to make a difference in the world, then it is simply not rational to focus one's efforts on solving comparatively small, non-urgent problems. It is true that functioning societies do need people working on comparatively small dayto-day problems. But a shortage of people working on comparatively small day-to-day problems is itself a big urgent problem and so, something that one would need to factor into any rational decision about where to apply one's efforts. Moreover, it does not require an exceptionally intelligent person to survey the literature on the various problems that we may be facing and to arrive at a correct assessment of what problems are the biggest and most urgent and what problems are comparatively small and nonurgent. To adopt rational belief attitudes is to adopt belief attitudes (i.e., to believe, to disbelieve or to withhold belief) that best serve one's epistemic ends, namely those of acquiring true beliefs and avoiding false beliefs. So, provided that one's methodology for acquiring rational belief attitudes is robust, then there is surely a reasonably approachable threshold of analysis and synthesis beyond which more sophisticated analysis and synthesis will not likely yield a more correct assessment of what problems are the biggest and most urgent and what problems are comparatively small and non-urgent. We face today an unprecedented number of big urgent problems. With those problems in mind, in this book, I will supply readers with a robust methodology for acquiring rational belief attitudes and making rational decisions. Readers will then be better equipped to identify and solve the world's biggest, most pressing problems.1 1 See also Bill Gates and Melinda Gates, "Annual Letters From Bill & Melinda Gates," Bill & Melinda Gates Foundation, accessed August 10, 2018, https://www.gatesfoundation.org/Who-We-Are/Resources-andMedia/Annual-Letters-List; William MacAskill, Doing Good Better: How Effective Altruism Can Help You Make a Difference (New York: Avery, 2015), http://www.effectivealtruism.org/doing-good-better; Peter Singer, The Life You Can Save: How to Do Your Part to End World Poverty (New York: Random House Trade Paperbacks, 2010), https://www.thelifeyoucansave.org/about-us/book; Peter Singer, The Most Good You Can Do: How Effective Altruism is Changing Ideas about Living Ethically (Yale University Press, 2015), https://www.thelifeyoucansave.org/blog/id/170/the-most-good-you-can-do; Benjamin J. Todd, 80,000 Hours: Find a 2 This book is divided into 4 chapters. In Chapters 1 and 2, I will address the question of (1) how to acquire rational belief attitudes and (2) how to make rational choices. Building on Chapters 1 and 2, I will then answer two of the most pressing questions of our time: (3) Should one be skeptical of climate change? (4) Should one invest in life-extension medical research? Chapter 1: How to Acquire Rational Belief Attitudes How should a layperson think (or form belief attitudes) about any given statement? Is it enough to research reliable sources and use logical, unbiased thinking? In this chapter, I will argue that it is not and that a layperson should instead defer to the majority testimony of experts on that statement, if there are any experts on that statement. For any statement (or proposition), p, there are three possible belief attitudes (or doxastic attitudes, in technical jargon) toward p: to believe p (which is consistent with having a range of degrees of confidence in p), to disbelieve p (to believe that p is false), and to withhold belief about p (to withhold belief about whether p is true or false). Doxastic attitudes may not be directly voluntary, but they can be informed by guiding principles that are sufficiently prima facie plausible or evidenced.2 Consider the following prima facie plausible principle: Unless there are overriding moral objections, one should form epistemically rational doxastic attitudes-that is, doxastic attitudes that best serve one's epistemic ends, namely those of acquiring true beliefs and avoiding false beliefs to some respective extent. Generally, when choosing between different courses of action, with a view to achieving one's ends, false beliefs are undesirable more so than true beliefs are desirable. One error or miscalculation is often enough to undermine such a decision. Nevertheless, true beliefs are still obviously essential to choosing the best courses of action in pursuit of one's goals. Therefore, one should aim to maximize one's subjective chances of holding a favorable ratio of true beliefs to false beliefs,3 rather than the highest absolute number of true beliefs or the lowest absolute number of false beliefs. It follows that unless there are overriding moral objections, one should acquire epistemically rational doxastic attitudes-that is, doxastic attitudes that maximize one's subjective chances of holding a favorable ratio of true beliefs to false beliefs. fulfilling career that does good (CreateSpace Independent Publishing Platform, 2016), https://80000hours.org/book/. (See also https://80000hours.org/career-guide/.) 2 Rico Vitz, "Doxastic Voluntarism," In The Internet Encyclopedia of Philosophy, accessed June 3, 2018, https://www.iep.utm.edu/doxa-vol/. 3 William Alston, "Concepts of epistemic justification," The Monist 68, no. 1 (1985): 57–89, https://doi.org/10.5840/monist198568116. 3 Now, avoiding fallacies,4 mitigating one's cognitive biases,5 and relying on trustworthy sources of information6 are the most commonly talked about ways of promoting truth-conducive thinking (or, in other words, acquiring epistemically rational doxastic attitudes). But for any given proposition, unless one is an expert on that proposition, there are ways of thinking about that proposition that are considerably more truth-conducive (or epistemically rational) but rarely if ever discussed outside of specialist academic circles-namely, following the rules of epistemic rationality that govern how laypeople should learn from the testimony of experts. There are cases of credentialed experts defending fringe claims in reliable sources, such as academic journals, without apparently committing any logical fallacies and without showing any overt signs of bias.7 This is to be expected in the sciences and in philosophy, where progress often requires that individual scientists and philosophers challenge mainstream or even consensus views. Laypeople who have learned how to discern logical fallacies, cognitive biases, as well as reputable and disreputable sources of information will be poorly equipped to rationally assess the statements made by those credentialed experts unless and until these laypeople are made acutely aware of the rules of epistemic rationality that govern how they should learn from the testimony of experts-that is, how they should adjust their own doxastic attitudes in light of what doxastic attitudes experts hold. These rules of epistemic rationality can be summarised as follows: For any proposition, p, unless and until you become an expert on p, you are rationally required to hold whatever doxastic attitude is the majority doxastic attitude toward p among experts on p, unless there are not any experts on p or there is no majority doxastic attitude toward p among experts on p, in which cases you are rationally required to withhold belief about p as long as you are not yourself an expert on p. This can be distilled down to the following rule: For any proposition, p, a layperson with respect to p is rationally required to believe p if and only if p is believed by the majority of experts on p.8 Of course, there is, in principle, nothing stopping a layperson from becoming an 4 Gary N. Curtis, The Fallacy Files, accessed July 21, 2018, http://www.fallacyfiles.org/; Bradley Dowden, "Fallacies," In The Internet Encyclopedia of Philosophy, accessed June 4, 2018, https://www.iep.utm.edu/fallacy/. 5 David Dunning, "We are all confident idiots," Pacific Standard 7, no. 6 (November/December 2014): 46–54, https://psmag.com/social-justice/confident-idiots-92793. 6 "Is My Source Credible?," Library, University of Maryland University College, accessed June 4, 2018, https://sites.umuc.edu/library/libhow/credibility.cfm. 7 See for example Judith Curry, "Reasoning about climate uncertainty," Climatic Change 108 (2011): 723–732, https://doi.org/10.1007/s10584-011-0180-z. See also Michael D. Lemonick, "Climate heretic: Judith Curry turns on her colleagues," Nature, November 1, 2010, https://doi.org/10.1038/news.2010.577. 8 There are exceptions to the rule. See Bernd Lahno, "Challenging the majority rule in matters of truth," Erasmus Journal for Philosophy and Economics 7, no. 2 (Autumn 2014): 54–72, https://doi.org/10.23941/ejpe.v7i2.167. See also David Coady, What to Believe Now: Applying Epistemology to Contemporary Issues (Chichester: WileyBlackwell, 2012); Alvin Goldman, "Experts: Which Ones Should You Trust?," Philosophy and Phenomenological Research 63, no. 1 (2001): 85–110, https://doi.org/10.1111/j.1933-1592.2001.tb00093.x; and Michael Huemer, "Is 4 expert on p. In that case, there are several alternative belief-forming methodologies available to him or her in the published literature.9 Anyone can be an expert on any given proposition, regardless of their academic or professional credentials, provided that they have studied or researched sufficiently thoroughly and impartially the evidence that bears on that proposition.10 The key word here is "sufficiently". Given the Dunning–Kruger effect (i.e., "difficulties in recognizing one's own incompetence lead to inflated self-assessments"11), those who lack the academic or professional credentials of credentialed experts should exercise caution in self-identifying as experts, and others should also exercise caution in identifying them as experts. In the case of philosophical propositions, and especially ethical and religious propositions, it is arguable whether there are any genuine experts on those propositions.12 Chapter 2: How to Make Rational Choices 2.1 Introduction Unless there are overriding moral objections, one should make rational choices. Standard rational choice theory, otherwise known as Expected Utility (EU) Theory, counsels agents to rank their choice options (from least to most choiceworthy) according to their EU. The EU of an option is a probability‐weighted sum of each of its possible utilities. EU Theory has been the dominant normative model of rational choice since the late 17th century,13 and in more recent years Critical Thinking Epistemically Responsible?," Metaphilosophy 36, no. 4 (July 2005): 522–31, https://doi.org/10.1111/j.1467-9973.2005.00388.x. 9 Jonathan Matheson, "Disagreement and Epistemic Peers," Oxford Handbooks Online, February 2015, http://dx.doi.org/10.1093/oxfordhb/9780199935314.013.13. 10 Michel Croce, "On What it Takes to be an Expert," The Philosophical Quarterly 69, no. 274 (January 2019): 1– 21, https://doi.org/10.1093/pq/pqy044. 11 Justin Kruger and David Dunning, "Unskilled and unaware of it: How difficulties in recognizing one's own incompetence lead to inflated self-assessments," Journal of Personality and Social Psychology 77, no. 6 (1999): 1121–34, http://dx.doi.org/10.1037/0022-3514.77.6.1121. 12 See Helen De Cruz, Religious Disagreement (Cambridge: Cambridge University Press, 2018); Bryan Frances, "Philosophical Expertise," In The Routledge Handbook of Applied Epistemology (Routledge Handbooks in Philosophy), edited by David Coady and James Chase (Routledge, 2018), https://doi.org/10.4324/9781315679099; Jonathan Matheson, Scott McElreath, and Nathan Nobis, "Moral Experts, Deference & Disagreement," In Moral Expertise: New Essays from Theoretical and Clinical Bioethics, edited by Jamie Carlin Watson and Laura K. Guidry-Grimes, 87–106 (Springer, 2018), https://doi.org/10.1007/978-3-319-92759-6_5. 13 Antoine Arnauld and Pierre Nicole, The Art of Thinking; Port‐Royal Logic. Translated, with an introduction by James Dickoff and Patricia James, and a foreword by Charles W. Hendel (Indianapolis: Bobbs‐Merrill, 1964 [1662]). 5 (1920s–), has received foundational support from both economists and philosophers.14 In this chapter, I will argue for a new normative alternative to EU Theory, namely Expected Comparative Utility (ECU) Theory. ECU Theory aims to improve upon rational choice models based on regret minimization.15 These models are founded on the idea that rational decision‐ makers strive to minimize regret-the disappointment that occurs when they fail to choose the available option they most prefer (i.e., the available option which carries the greatest utility). Regret minimization models grew out of the seminal work done in the 1950s by economist Leonard Savage and mathematician John Milnor.16 Later, in the 1970s, psychologists Daniel Kahneman and Amos Tversky demonstrated deviations between EU‐maximizing choices and people's actual choices, and proposed an alternative (descriptive) decision theory, Prospect Theory, which introduced for the first time the notion of a reference point (a benchmark of sorts)-that is, an outcome that partitions the set of possible decision outcomes into perceived gains and losses.17 Like Prospect Theory, but unlike EU Theory, the basic regret minimization choice model makes use of a benchmark (or zero point of choiceworthiness). According to this model, for any choice option, a, and for any state of the world, G, the extent of a's "regret," in G, is the extent to which a, in G, falls short of whichever available option carries the greatest utility in G, and the degree of choiceworthiness of a, in G, is the degree to which the choice of a minimizes that "regret." Thus, the degree of choiceworthiness of a, in G, is the difference in utility, in G, between a and whichever available option carries the greatest utility in G (i.e., the benchmark). Understood in this way, maximizing expected choiceworthiness (where "expected 14 Frank P. Ramsey, "Truth and Probability," The Foundations of Mathematics and other Logical Essays, ed. Richard B. Braithwaite (London: Routledge and Kegan Paul, 1931) 156–84; John Von Neumann and Oskar Morgenstern, Theory of Games and Economic Behavior (Princeton UP, 1944); Leonard Savage, The Foundations of Statistics (Wiley, 1954); Ethan Bolker, "Functions Resembling Quotients of Measures," Transactions of the American Mathematical Society 2 (1966): 292–312, https://doi.org/10.1090/S0002-9947-1966-0197671-9; Richard Jeffrey, The Logic of Decision, 2nd ed. (Chicago: U of Chicago P, 1983). According to Martin Peterson, today, nearly all decision theorists accept EU Theory (see Martin Peterson, An Introduction to Decision Theory (Cambridge University Press, 2017), p. 66). As such, as long as that is the case, laypeople with respect to decision theory will be rationally required to accept EU Theory. 15 See Ronald R. Yager, "Generalized Regret Based Decision Making," Engineering Applications of Artificial Intelligence 65 (2017): 400–05, https://doi.org/10.1016/j.engappai.2017.08.001. 16 Leonard Savage, "The theory of statistical decision," Journal of the American Statistical Association 46 (1951) 55–67; John Willard Milnor, "Games Against Nature," Decision Processes, ed. R. M. Thrall, C. H. Coombs and R. L. Davis (New York: Wiley, 1954). For a later normative theory which takes into account anticipated regret, i.e., Regret Theory, see David E. Bell, "Regret in Decision Making Under Uncertainty," Operations Research 30 (1982): 961–81, https://doi.org/10.1287/opre.30.5.961; Peter C. Fishburn, "Nontransitive Measurable Utility," Journal of Mathematical Psychology 26 (1982): 31–67, https://doi.org/10.1016/0022-2496(82)90034-7; Graham Loomes and Robert Sugden, "Regret Theory: An Alternative Theory of Rational Choice Under Uncertainty," Economic Journal 92 (1982): 805–24, https://doi.org/10.2307/2232669. 17 Daniel Kahneman and Amos Tversky, "Prospect Theory: An Analysis of Decision under Risk," Econometrica 47 (1979): 263–92, https://doi.org/10.2307/1914185; idem, "The Psychology of Preferences," Scientific American 246 (1982): 160–73, https://doi.org/10.1038/scientificamerican0182-160. 6 choiceworthiness" is a probability-weighted sum of an option's choiceworthiness values) always coincides with maximizing EU. ECU Theory also makes use of a benchmark, one that is importantly different from that employed in the regret minimization choice model: for any choice option, a, and for any state of the world, G, the degree of choiceworthiness of a, in G, is the difference in utility, in G, between a and whichever alternative to a carries the greatest utility in G (i.e., the benchmark). This difference in utility is what I will call the comparative utility (CU) of a. Roughly speaking, ECU Theory counsels agents to rank their options (in terms of how choiceworthy they are) according to their ECU. For any choice option, a, the ECU of a is a probability‐weighted sum of the comparative utilities of a across the various possible states of the world. In this chapter, I will show that in a number of ordinary decision cases, ECU Theory gives different verdicts from those of EU Theory and that EU Theory therefore fails as a normative theory of rational choice. 2.2 Preliminaries From start to finish, this chapter is predicated upon two basic assumptions: First assumption: For any agent, S, and for any choice option, a, for S, a's utility is a cardinal indicator of (S's) preference and is derived from S's preferences as in standard decision theory, that is, via a representation theorem. This requires that S's preferences obey a series of axioms of rational preference, one of which (i.e., the independence axiom) entails the Independence of irrelevant alternatives (IIA) (for preferences): if an option, a, is preferred over some alternative option, b, then introducing a third option, c, in the choice situation will not change the preference ordering between a and b. For the present purposes, rational preference is defined, by stipulation, as satisfying the IIA. Second assumption: Let a decision under certainty be a choice situation where an agent is subjectively certain about which state the world is in (and assigns probability 1 to that state being actual), and let a decision under uncertainty be a choice situation where an agent is not subjectively certain about which state the world is in, but where she can nevertheless assign subjective probabilities to the different possible states. (States of the world, or states, are defined here as possible, mutually exclusive states of affairs.) For any agent, S, faced with any decision under certainty and for any option, a, for S, a is choiceworthy for S (or [i.e.] it is rational for S to choose a) if and only if a maximizes utility, over the space of all alternatives, in the state of the world to which S assigns probability 1. I will refer to this as the Utility Maximization (UM) Principle. The UM Principle defines a binary measure of choiceworthiness for decisions under certainty (i.e., whether an option is choiceworthy tout court or unchoiceworthy tout court). Now, in addition to a binary measure, we also require a graded measure of choiceworthiness. For any number of alternative choice options, a, b, c, d, and e, we want to say that a (utility: 100) is more choiceworthy than b (utility: 5) even if a is not choiceworthy tout court (i.e., a does not maximize utility). We also want to say that the extent to which a is more choiceworthy than b is greater than the extent to which c (utility: 10) is more choiceworthy than 7 b. In order to say that a is more choiceworthy than b (and to what extent), we cannot rely on a binary measure of choiceworthiness. Whether (and to what extent) a is more choiceworthy than b, and by implication, whether (and to what extent) any option is more choiceworthy than any other within a set of alternatives is necessarily a function of how choiceworthy each of the two options is within the set of alternatives (and not necessarily a function of one being choiceworthy tout court and the other unchoiceworthy tout court). To ask how choiceworthy an option is is to ask how desirable or worthy of being chosen that option is, (more or less18) how imperative it is to choose that option. Such a question is well‐formed and meaningful. In order to answer the question, we require a graded (quantitative) measure of how choiceworthy options are. In this chapter, I will develop such a measure.19 In particular, I will show that utility and EU, as well as measures of regret minimization are inadequate as measures of choiceworthiness. I will argue that from the fact that we need a graded (quantitative) measure of choiceworthiness, it follows that we need a new normative theory of rational choice, namely ECU Theory. The remainder of this chapter is divided into 4 sections. Section 2.3 will develop a graded choiceworthiness measure for decisions under certainty (i.e., CU). On the basis of this measure, Section 2.4 will explicate and argue for ECU Theory. In light of ECU Theory, Section 2.5 will assess the cogency of EU Theory. Finally, in light of the so-called "Problem of act versions," Section 2.6 will define choice options as exhaustive sets of joint intentional acts. 2.3 The CU Principle It is generally accepted that for any agent, S, faced with any decision under certainty and for any number of alternative options, a, b, c, d, and e, available to S, the extent to which a is more choiceworthy than b, for S, is the extent to which S (rationally) prefers a to b, or equivalently the extent to which S (rationally) prefers a to b more than S (rationally) prefers b to a. However, intuitively, that is a mistake. Even though we are comparing a to b, we want to see how a and b measure up to the very best alternative options on offer, in the following way: the extent to which a is more choiceworthy than b, for S, is the extent to which S (rationally) prefers a to the 18 Let a and b denote two mutually exclusive and jointly exhaustive choice options. a is more choiceworthy than b if and only if choosing a is more imperative than choosing b, and a is just as choiceworthy as b if and only if choosing a is just as imperative as choosing b. However, if a is just as choiceworthy as b, then both a and b are choiceworthy, whereas if choosing a is just as imperative as choosing b, then neither choosing a nor choosing b is imperative. 19 "Choiceworthiness," as I understand it in this chapter, expresses the degree to which a choice is rational. "Choiceworthiness" should therefore be distinguished from the moral notion of "rightness," which arguably cannot be measured on a graded scale. See Thomas Hurka, "More Seriously Wrong, More Importantly Right," Journal of the American Philosophical Association 5 (2019): 41–58, https://doi.org/10.1017/apa.2018.41; Neil Sinhababu, "Scalar Consequentialism the Right Way," Philosophical Studies 175 (2018): 3131–44, https://doi.org/10.1007/s11098-017-0998-y; Kristian Olsen, "Subjective Rightness and Minimizing Expected Objective Wrongness," Pacific Philosophical Quarterly 99 (2018): 417–41. https://doi.org/10.1111/papq.12188. 8 most preferred alternative to a (either b, c, d, or e) more than S (rationally) prefers b to the most preferred alternative to b (either a, c, d, or e), or so I will argue in what follows. The present section is devoted to explicating a graded, quantitative choiceworthiness measure for decisions under certainty. Let us begin with a short argument for such a measure. For any agent, S, faced with any decision under certainty and for any option, a, for S, a is choiceworthy for S, by definition, if and only if a is worthy of being chosen by S over whichever alternative to a carries the greatest utility. It follows that the extent to which a is choiceworthy for S is the extent to which a is worthy of being chosen by S over whichever alternative to a carries the greatest utility. But the extent to which a is worthy of being chosen by S over whichever alternative to a carries the greatest utility is the difference in utility between a and whichever alternative to a carries the greatest utility. Therefore, the extent to which a is choiceworthy for S (or [i.e.] the measure of how choiceworthy a is for S) is the difference in utility between a and whichever alternative to a carries the greatest utility (henceforth, the CU Principle). Let us now consider a longer argument. The simplest attempt at defining a quantitative choiceworthiness measure for decisions under certainty is as follows: for any agent, S, faced with any decision under certainty and for any option, a, for S, a measure of the choiceworthiness of a for S is the utility of a (or [i.e.] the measure of the utility of a) (in the state of the world to which S assigns probability 1). I will refer to this as the Utility Principle. The UM Principle is true if (but not only if) the Utility Principle is true. If the Utility Principle were true, then EU Theory would be vindicated, since measures of choiceworthiness would be interchangeable with measures of (rational) preference (for further elaboration, see Section 2.5). The Utility Principle is, however, untenable. First, measures of quantities, for example, 20°C for temperature, are meaningful (and only meaningful) relative to a given zero point and unit of measurement. (Let us call this the Measurement Principle.) In the case of temperature, the measure (e.g., 20°C) is defined in relation to the zero point and unit of measurement (i.e., the measure itself presupposes a given temperature unit and zero point of temperature). That is not the case for utility. In accordance with the Measurement Principle, the measure of a's utility (e.g., 20 units of utility [or utiles]) is meaningful (and only meaningful) relative to a given utility unit and zero point of utility. However, the measure (e.g., 20 units of utility) is not defined in relation to the unit and zero point (i.e., the utility measure itself does not presuppose a given utility unit and zero point of utility).20 These values must be explicitly specified. Hence, the Utility Principle is at best underspecified. Second, even relative to an explicitly given utility unit and zero point of utility, the measure of the choiceworthiness of a for S is not necessarily its utility. In accordance with the Measurement Principle, for any given decision situation (under certainty) and for any specified 20 "The zero point and the unit in an expected utility representation are arbitrary; utility values become meaningful only once they have been fixed." (Mark Colyvan and Alan Hájek, "Making Ado Without Expectations," Mind 125 (2016): 834, https://doi.org/10.1093/mind/fzv160). 9 utility unit and zero point of utility (for that situation), the measure of the choiceworthiness of any available option is its utility value if and only if it is possible to ascertain how choiceworthy any available option is (in that situation) by solely considering its utility value in relation to that specified utility unit and zero point of utility. In practical terms, what this means is that, for any given decision setup (i.e., any decision situation combined with any explicit specification of a utility unit and zero point of utility), the measure of the choiceworthiness of any available option is its utility value if and only if (1) any available option is choiceworthy just in case its utility value is equal to or greater than zero (and not choiceworthy otherwise) and (2) the degree of choiceworthiness of any available option is its utility value. Now, it is straightforward to come up with decision situations where it is possible to select a specific zero point of utility (and a specific utility unit) such that it is not the case that any available option is choiceworthy (in that situation) if and only if its utility value is equal to or greater than zero. Per the UM Principle, there are possible decision setups where an option has a positive utility value and is nevertheless unchoiceworthy, namely setups where that option does not maximize utility over the space of all available alternatives, and there are possible decision setups where an option has a negative utility value and is nevertheless choiceworthy, namely setups where that option does maximize utility over the space of all available alternatives. Therefore, per the Measurement Principle, there are possible decision setups such that it is not the case that the measure of the choiceworthiness of any available option (in that setup) is its utility value. In light of the preceding considerations and in accord with the Measurement Principle, it is necessarily the case that for any agent, S, faced with any decision situation under certainty and for any option, a, for S, the measure of the choiceworthiness of a for S depends on a unit of measurement of choiceworthiness as well as a zero point of choiceworthiness (or a benchmark) in the following way: the measure of the choiceworthiness of a for S (relative to any explicitly given utility unit and zero point of utility) is the difference in utility between a and some benchmark for a, such that (1) a is choiceworthy for S if and only if the difference in utility between a and the benchmark for a is equal to or greater than zero (and not choiceworthy otherwise), and (2) the degree of choiceworthiness of a for S is the difference in utility between a and the benchmark for a. In other words, the measure of the choiceworthiness of a for S is the degree to which a is worthy of being chosen over the benchmark for a. The benchmark for a can be, for example, some option in the set of available options, such as the status quo,21 or some average of the utilities of the available options. Choiceworthiness is thus a relative concept.22 As 21 Jacob M. Nebel, "Status Quo Bias, Rationality, and Conservatism about Value," Ethics 125 (2015): 449–76. https://doi.org/10.1086/678482. 22 Ralph Wedgwood ("Must Rational Intentions Maximize Utility?" Philosophical Explorations 20 (2017): 1–20, https://doi.org/10.1080/13869795.2017.1356352) relies on considerations of incommensurability to argue for the same idea: "the choiceworthiness of options is relative to choice situations". Larry S. Temkin (Rethinking the Good: Moral Ideals and the Nature of Practical Reasoning (Oxford UP, 2012), https://doi.org/10.1093/acprof:oso/9780199759446.001.0001) also addresses this idea: what he calls the "Essentially Comparative View." 10 will become clear in what follows, the concept of choiceworthiness itself presupposes a given benchmark (or zero point of choiceworthiness). If there are any alternatives to a which carry a greater utility than does a, then the benchmark for a is whichever alternative to a carries the greatest utility. Indeed, if there are any alternatives to a with a greater utility than a, then, in accordance with the UM Principle, a is not choiceworthy for S. But if a is not choiceworthy for S, then how choiceworthy a is for S is simply how a compares to whichever alternative is choiceworthy for S (or, per the UM Principle, whichever alternative to a carries the greatest utility).23 This is consistent with the basic "regret minimization" rational choice model introduced in Section 2.1. If there are not any alternatives to a which carry a greater utility than does a, then, according to the regret minimization model, the benchmark for a is a. Against this model, I will now argue that if there are not any alternatives to a which carry a greater utility than does a, then the benchmark for a still has to be whichever alternative to a carries the greatest utility.24 Let us consider two decision situations (or setups): 1 and 2. In each situation, S is faced with the same three options: a, b, and c. What's more, in each situation, S assigns probability 1 to a given state of the world (and not the same state for both situations). If that state of the world is realized, then S assigns the following utilities to the set of options: 1: a (100), b (−10,000), c (−10,000) 2: a (100), b (99), c (99) Per the UM Principle, a is choiceworthy for S in both situations 1 and 2. a is also more choiceworthy for S in 1 than in 2-that is to say, it is more imperative for S to choose a if she is in situation 1 than if she is in situation 2. In 2, S misses out on only 1 utile by not choosing a, but instead choosing the best alternative to a (i.e., b or c), whereas in 1, S misses out on 10,100 utiles by not choosing a, but instead choosing the best alternative to a (i.e., b or c). Another way of putting it is that a is more choiceworthy in 1 than in 2 because a is more worthy of being chosen over the best alternative to a in 1 than in 2. Let me now briefly introduce Ralph Wedgwood's Benchmark Theory (BT).25 The basic idea of BT is to rank choice options (in terms of how choiceworthy they are) according to their expected comparative value, where the comparative value of an option is its value (broadly 23 See the discussion of the notion of "shortfall from optimality" in Ralph Wedgwood, "Choosing Rationally and Choosing Correctly," Weakness of Will and Practical Irrationality, ed. Sarah Stroud and Christine Tappolet (Oxford UP, 2003), https://doi.org/10.1093/0199257361.003.0009. For related discussions of the notion of "degrees of wrongness" in ethics, see (e.g.) J. L. Mackie, Ethics: Inventing Right and Wrong (Harmondsworth: Penguin, 1977), 205; Bjorn Eriksson, "Utilitarianism for Sinners," American Philosophical Quarterly 34 (1997): 218–19, https://www.jstor.org/stable/20009893; Todd Calder, "Kant and Degrees of Wrongness," The Journal of Value Inquiry 39 (2005): 229, https://doi.org/10.1007/s10790-006-5454-8; and Johan E. Gustafsson, "Consequentialism with Wrongness Depending on the Difficulty of Doing Better," Thought 5 (2016): 108–09, https://doi.org/10.1002/tht3.200. 24 As far as I know, this idea has not been explored in the published literature. 25 Ralph Wedgwood, "Gandalf's Solution to the Newcomb Problem," Synthese 190 (2013): 2643–75, https://doi.org/10.1007/s11229-011-9900-1. 11 construed) in some state of the world compared to a benchmark for that state of the world. Wedgwood identifies the benchmark as an average of the options' values within a given state of the world. He emphasizes that all statewise dominated options and more generally, "all the options that do not deserve to be taken seriously" (2664) should be excluded from consideration at the outset.26 Wedgwood explicitly rejects the idea that the value of an option is its utility. Nevertheless, it is interesting to see how BT (henceforth, BT*) fairs when the value of an option is understood to be its utility. Coming back to our example, we can see that BT* agrees with the verdict that a is choiceworthy for S in situations 1 and 2, but not with the verdict that a is more choiceworthy for S in 1 than in 2. According to BT*, a is equally choiceworthy for S in situations 1 and 2 since b and c are strictly dominated by a in both 1 and 2 and are therefore excluded from consideration at the outset. If b and c are not excluded from consideration and the benchmark is identified as an average of the values (or utilities) of all the available options, then this alternative approach agrees with our verdict: a is more choiceworthy for S in 1 than in 2. Here is a different example: 1: a (100), b (−100), c (−100) 2: a (100), b (−500), c (100) Per the UM Principle, a is choiceworthy for S in both situations 1 and 2. a is also more choiceworthy for S in 1 than in 2-in other words, it is more imperative for S to choose a if she is in situation 1 than if she is in situation 2. In 2, a is merely optional-S misses out on zero utiles by not choosing a, but instead choosing the best alternative to a (i.e., c)-whereas in 1, a is not optional-S misses out on 200 utiles by not choosing a, but instead choosing the best alternative to a (i.e., b or c). Again, a is more choiceworthy in 1 than in 2 because a is more worthy of being chosen over the best alternative to a in 1 than in 2. BT* agrees with both verdicts: a is choiceworthy for S in 1 and 2, and a is more choiceworthy for S in 1 than in 2. However, if the benchmark is defined as an average of the values (or utilities) of all the available options (whether strictly dominated or not), then this alternative approach does not agree with our verdict: a is more choiceworthy for S in 1 than in 2. The two examples just laid out, when taken together, make for an effective counterexample to BT*. Another very similar example: 1: a (100), b (−100), c (−100) 2: a (100), b (−500), c (99) Per the UM Principle, a is choiceworthy for S in both situations 1 and 2. a is also more choiceworthy for S in 1 than in 2-that is, it is more imperative for S to choose a if she is in 26 For critiques of BT, see Robert Bassett, "A Critique of Benchmark Theory," Synthese 192 (2015), https://doi.org/10.1007/s11229-014-0566-3: 241–67 and Rachael Briggs, "Decision‐Theoretic Paradoxes as Voting Paradoxes," Philosophical Review 119 (2010): 1–30, https://doi.org/10.1215/00318108-2009-024. 12 situation 1 than if she is in situation 2. In 2, S misses out on only 1 utile by not choosing a, but instead choosing the best alternative to a (i.e., c), whereas in 1, S misses out on 200 utiles by not choosing a, but instead choosing the best alternative to a (i.e., b or c). Once again, a is more choiceworthy in 1 than in 2 because a is more worthy of being chosen over the best alternative to a in 1 than in 2. BT* agrees with the verdict that a is choiceworthy for S in 1 and 2, but not with the verdict that a is more choiceworthy for S in 1 than in 2. According to BT*, a is equally choiceworthy for S in situations 1 and 2 since b and c are strictly dominated by a in both 1 and 2 and are therefore excluded from consideration at the outset. If b and c are not excluded from consideration and the benchmark is identified as an average of the values (or utilities) of all the options, then a is more choiceworthy for S in 2 than in 1. I take this to be a further counterexample to BT*. One final example: 1: a (100), b (−100), c (100) 2: a (100), b (99), c (100) Per the UM Principle, a is choiceworthy for S in both situations 1 and 2. a is also equally choiceworthy for S in both situations-that is to say, it is just as imperative for S to choose a if she is in situation 1 as it is if she is in situation 2. In both situations, a is merely optional-S misses out on zero utiles by not choosing a, but instead choosing the best alternative to a (i.e., c). To put it another way, a is just as choiceworthy in 1 as it is in 2 because a is just as worthy of being chosen over the best alternative to a in 1 as it is in 2. (BT* agrees with both verdicts.) These four examples serve to illustrate that if there are not any alternatives to a with a greater utility than a, then how choiceworthy a is depends on how much utility S would miss out on by not choosing a, but instead choosing the best alternative to a. The greater the amount of utility S would miss out on by not choosing a, but instead choosing the best alternative to a, the more choiceworthy a becomes. Thus, the benchmark for a must be whichever alternative to a carries the highest utility. What follows is that whether or not there are any alternatives to a which carry a greater utility than does a, the benchmark for a has to be whichever alternative to a carries the greatest utility.27 Therefore, for any agent, S, faced with any decision under certainty and for any option, a, for S, the measure of the choiceworthiness of a for S (relative to any explicitly given utility unit and zero point of utility) is the CU of a (in the state of the world to which S assigns probability 1). The CU of a is the difference in utility between a and whichever alternative to a carries the greatest utility (or one of them in the event that several alternatives are tied). As previously indicated, I will refer to this principle as the CU Principle.28 Like the Utility 27 This means that there is no unique benchmark for a given choice situation. Instead, the benchmark is relative to a specific choice option. The benchmark for a may be some alternative, b, and the benchmark for b may be a. 28 The CU Principle is also true if utilities are taken as primitive rather than derived from a representation theorem. 13 Principle, the CU Principle entails the UM Principle. Henceforth, c‐utiles are defined as units of CU. In light of the CU Principle, the Utility Principle can be falsified. If the Utility Principle were true, then in accordance with the Measurement Principle, it would be the case that for any given decision situation, there is at least one specification of a utility unit and zero point of utility such that it is possible to ascertain how choiceworthy any available option is (for S) by solely considering its utility value in relation to that specification of a utility unit and zero point of utility. In other words, it would be the case that for any given decision situation, there is at least one specification of a utility unit and zero point of utility such that (1) any available option is choiceworthy (for S) if and only if its utility value is equal to or greater than zero (and not choiceworthy otherwise) and (2) the degree of choiceworthiness of any available option (for S) is its utility value. As we will now see, that is not the case. Let us consider the following decision setup: S is faced with three options: a, b, and c. What's more, S assigns probability 1 to a given state of the world. If that state of the world is realized, then S assigns the following utilities to the available options: a (0), b (–100), c (–1,000). Therefore, no matter what zero point of utility is selected, S assigns the following utility intervals between the available options: between a and b, S assigns a positive interval of 100 utiles, between b and c, S assigns a positive interval of 900 utiles and between a and c, S assigns a positive interval of 1,000 utiles. Per the CU Principle, the degrees of choiceworthiness of the available options are as follows: a (100), b (–100), c (–1,000). Therefore, the differences between the degrees of choiceworthiness of the available options are as follows: between a and b, the difference is 200 c‐utiles, between b and c, the difference is 900 c‐utiles and between a and c, the difference is 1,100 c‐utiles. Since the utility intervals and the differences in degrees of choiceworthiness are at variance, we have a decision situation where no matter what zero point of utility (and what utility unit) is selected, it is not the case that the degree of choiceworthiness of any available option is its utility value. In closing this section, it should be mentioned that the idea of calculating differences between the utility of an option under consideration and the utilities of its alternatives in the choice situation has been explored in the economic modeling literature.29 Incidentally, CU should be distinguished from the purely descriptive economic concept of opportunity cost. For any agent, S, let a be the highest‐valued choice option available to S. The CU of a, for S, is the value of whatever additional benefit S would enjoy by choosing a over the highest‐valued alternative to a. By contrast, the opportunity cost of a, for S, is the value of whatever cost S would incur by choosing a over the highest‐valued alternative to a, where this includes the total value of the highest‐valued alternative to a.30 29 Junyi Zhang, Harry Timmermans, Aloys Borgers and Donggen Wang, "Modeling Traveler Choice Behavior Using the Concepts of Relative Utility and Relative Interest," Transportation Research Part B 38 (2004): 215–34, https://doi.org/10.1016/S0191-2615(03)00009-2. 30 Robert H. Frank, "The Opportunity Cost of Economics Education," The New York Times, 2005, http://www.nytimes.com/2005/09/01/business/the-opportunity-cost-of-economics-education.html and David R. Henderson, "Opportunity Cost," The Concise Encyclopedia of Economics, Library of Economics and Liberty, 2008, http://www.econlib.org/library/Enc/OpportunityCost.html. 14 2.4 ECU Theory As I showed in Section 2.2, we require a graded (quantitative) measure of how choiceworthy options are. When we move from decision‐making under certainty to decision‐making under uncertainty, we can, in light of the CU Principle, identify the measure of an option's choiceworthiness as expressing that option's expected choiceworthiness, or ECU, that is to say, the expected value, or the probability‐weighted sum of all possible values, of that option's choiceworthiness, or CU, in the actual state of the world. That roughly encapsulates ECU Theory. As a first approximation, therefore, ECU Theory says that for any agent, S, and for any choice option, a, for S, the measure of the choiceworthiness of a for S (relative to any explicitly given utility unit and zero point of utility) is the ECU of a. The ECU of an option, a, in a decision problem with n states is formally defined as: ECU(a) =∑(U(a, si) − U(bm(a), si))P(si) n i=1 where U(a, si) denotes the utility of option a when state si is actual, U(bm(a), si) denotes the utility of the benchmark for a when state si is actual (i.e., the utility in state si of whichever alternative(s) to a have the highest utility in state si), and P(si) denotes the probability assigned to state si.31 The CU Principle is straightforwardly entailed by ECU Theory. Furthermore, ECU Theory presupposes that the states of the world in any decision problem are probabilistically independent of the agent's choices. ECU Theory, as formulated above, is not quite right though. In accordance with the Measurement Principle, if the measure of the choiceworthiness of options is their ECU, then only options with ECU equal to or greater than zero can be choiceworthy. However, as I will illustrate in Section 2.5, there will always be cases (regardless of what utility unit and zero point of utility are specified) where every option in a decision situation under uncertainty has negative ECU. Since at least one option in a decision situation must be choiceworthy-the one with the highest degree of choiceworthiness (or one of them in the event that several alternatives are tied)-ECU Theory, as defined above, is false in decision cases under uncertainty. By the same line of reasoning as employed in Section 2.3, we reach the following conclusion: for any agent, S, faced with any decision under uncertainty and for any choice option, a, for S, the measure of the choiceworthiness of a for S (relative to any explicitly given utility unit and zero point of utility) is the comparative expected choiceworthiness, or 31 In other words, for any number of alternative options, a, b, c, d, and e, one calculates the ECU of a as follows: for each state of the world, one subtracts a's utility from the utility of b, c, d, or e, whichever of b, c, d, and e maximizes utility in that state, and one multiplies the result by the probability that one assigns to that state; finally, one sums the totals for every state. 15 comparative expected comparative utility (CECU), of a, that is to say, the difference in ECU between a and whichever alternative to a carries the greatest ECU (or one of them in the event that several alternatives are tied). Let us call this principle the CECU Principle. For any two alternative options, a and b, a's CECU is greater than b's if and only if a's ECU is greater than b's, and a's CECU is equal to b's if and only if a's ECU is equal to b's. We are now in a position to precisely define ECU Theory: ECU Theory is the conjunction of the CU Principle (for decisions under certainty) and the CECU Principle (for decisions under uncertainty). To demonstrate how to apply this new decision rule (i.e., ECU Theory) to a concrete decision problem, let us consider the following case: An agent, S, is faced with a choice between two independent options or gambles: one option, a, offering a 0.01 probability of winning a prize worth 1,500 utiles (and nothing otherwise), and one option, b, offering a 0.02 probability of winning a prize worth 700 utiles (and nothing otherwise). According to ECU Theory, S should choose option a, since its CECU is equal to or greater than zero (1– [–1] = 2). The ECUs of options a and b are given by the two equations below. The following notation is used: s1 denotes the state "If S chooses a, then S will not win the prize (0 utiles) and if S chooses b, then S will not win the prize (0 utiles)" (probability: 0.99 × 0.98 = 0.97), s2 denotes the state "If S chooses a, then S will not win the prize (0 utiles) and if S chooses b, then S will win the prize (700 utiles)" (probability: 0.99 × 0.02 = 0.0198), s3 denotes the state "If S chooses a, then S will win the prize (1,500 utiles) and if S chooses b, then S will not win the prize (0 utiles)" (probability: 0.01 × 0.98 = 0.0098), s4 denotes the state "If S chooses a, then S will win the prize (1,500 utiles) and if S chooses b, then S will win the prize (700 utiles)" (probability: 0.01 × 0.02 = 0.0002), P(s1) denotes the probability of s1, and U(a, s1) denotes the utility of option a when s1 is actual. ECU(a) = (U(a, s1) – U(b, s1)) × P(s1) + (U(a, s2) – U(b, s2)) × P(s2) + (U(a, s3) – U(b, s3)) × P(s3) + (U(a, s4) – U(b, s4)) × P(s4) = 1 c-utile ECU(b) = (U(b, s1) – U(a, s1)) × P(s1) + (U(b, s2) – U(a, s2)) × P(s2) + (U(b, s3) – U(a, s3)) × P(s3) + (U(b, s4) – U(a, s4)) × P(s4) = –1 c-utiles One line of argument in support of ECU Theory is that, contrary to EU Theory, ECU Theory agrees with and entails Wedgwood's Gandalf's Principle: the choiceworthiness of an option in a given state of the world should be measured only relative to the values of the other options in that state, and not to the values of the options in other states. According to Wedgwood, to make a rational choice in [cases involving uncertainty], one does not need to consider whether one is in a nice state of nature or a nasty one. All that one needs to consider are the degrees to which each of the available options is better (or worse) than the available alternatives within each of the relevant states of nature. Admittedly, when one is uncertain which state of nature one is in, one must make some comparisons across the states of nature. But since one does not even need to know whether one is in a nice state of nature or a nasty one, it seems that the only relevant comparisons are comparisons of the differences in levels of goodness between the various options within each 16 state of nature with the differences between those options within each of the other states of nature – not any comparisons of absolute levels of goodness across different states of nature.32 Although Wedgwood uses terms such as "better," "worse," and "levels of goodness" in his explication of Gandalf's Principle, the principle can be expressed equally well using replacement terms such as "preferred," "dispreferred," and "levels of utility." Gandalf's Principle is an eminently reasonable principle.33 In a paper critiquing Wedgwood's BT, Robert Bassett concurs: "Gandalf's Principle strikes me as an eminently sensible principle to incorporate into rational decision‐making."34 There is, however, one alternative decision theory which agrees with (and entails) both the CU Principle and Gandalf's Principle and which has some prima facie plausibility-Maximum Likelihood Comparative Utility (MLCU) Theory: for any agent, S, and for any option, a, for S, the measure of the choiceworthiness of a for S (relative to any explicitly given utility unit and zero point of utility) is the most likely value of a's choiceworthiness (or CU) in the actual state of the world. We require a further argument to rule out this decision theory. This brings me to the following decision case: Let us suppose that an agent, S, is faced with three choice options: a, b, and c. S assigns probability 0.51 to a state of the world, A, and 0.49 to a state of the world, B. If state A or state B is realized, then S assigns the following utilities to the set of options: A: a (110), b (80), c (100) B: a (−1,000), b (110), c (100) According to MLCU Theory, a is uniquely choiceworthy for S, since state A is more likely to obtain than state B and the CU of option a in state A is greater than that of any other available option. Yet, it is clear that choosing option a is a mistake, since state B is almost as likely to obtain as state A and the comparative disutility of option a in state B is very high (– 1,110 c‐utiles). I take this to be an effective counterexample to MLCU Theory. 2.5 The Failure of EU Theory In this section, I will assess the cogency of standard rational choice theory (i.e., EU Theory) in view of ECU Theory. Let us begin by giving a precise definition of EU Theory: for any agent, S, and for any number of alternative choice options, a, b, c, d, and e, for S, (1) a is more choiceworthy than b, for S, if and only if a's EU is greater than b's, (2) a is just as choiceworthy as b, for S, if and only if a's EU is equal to b's, (3) (given that utility is assumed to be cardinal) the extent to which a is more choiceworthy than b, for S, is the difference in EU between a and 32 Wedgwood, "Gandalf's solution to the newcomb problem," 2654. 33 For an illuminating discussion of Gandalf's principle, see Wedgwood (2013): 2652–55. 34 Bassett (2015): 241–67. 17 b, and (4) a is choiceworthy for S if and only if a maximizes EU over the space of all alternatives. Decision‐theoretic representation theorems-such as those of von Neumann and Morgenstern, Savage, and Bolker and Jeffrey35-show that if an agent fails to prefer choice options with higher EU, then that agent violates at least one of several axioms of rational preference,36 one of which entails the Independence of irrelevant alternatives (IIA) (as I indicated in Section 2.2). These representation theorems are supposed to provide arguments for EU Theory (as a theory of rational choice), the underlying assumption being that "rational preference" talk can be translated into "choiceworthiness" talk. In what follows, I will demonstrate that such an assumption is false. I will do so by showing that ECU Theory's verdicts sometimes deviate from those of EU Theory. Let a finite decision case be a decision problem where there are only finitely many states and no infinite utilities. In all finite decision cases requiring a choice between only two alternative options, ECU Theory delivers the same verdicts as EU Theory. However, in a number of finite decision cases requiring a choice between more than two alternative options, ECU Theory gives different verdicts from those of EU Theory.37 Let us consider the following example: an agent, S, is faced with five choice options: a, b, c, d, and e. S assigns probability 0.5 to a state of the world, A, and 0.5 to a state of the world, B. If state A or state B is realized, then S assigns the following utilities to the set of options: A: a (2), b (5), c (6), d (8), e (10) B: a (10), b (8), c (6), d (4), e (2) According to EU Theory, b is more choiceworthy than a, for S, since the EU of b (6.5 utiles) is greater than that of a (6 utiles). In fact, according to EU Theory, b is choiceworthy tout court since its EU is greater than that of every other option. EU(a) = (U(a, A) × P(A)) + (U(a, B) × P(B)) = 6 utiles EU(b) = (U(b, A) × P(A)) + (U(b, B) × P(B)) = 6.5 utiles EU(c) = (U(c, A) × P(A)) + (U(c, B) × P(B)) = 6 utiles EU(d) = (U(d, A) × P(A)) + (U(d, B) × P(B)) = 6 utiles 35 John Von Neumann and Oskar Morgenstern, Theory of Games and Economic Behavior (Princeton UP, 1944); Leonard Savage, The Foundations of Statistics (Wiley, 1954); Ethan Bolker, "Functions Resembling Quotients of Measures," Transactions of the American Mathematical Society 2 (1966): 292–312, https://doi.org/10.1090/S00029947-1966-0197671-9; Richard Jeffrey, The Logic of Decision, 2nd ed. (Chicago: U of Chicago P, 1983). 36 Following the formulation of R. A. Briggs ("Normative Theories of Rational Choice: Expected Utility," The Stanford Encyclopedia of Philosophy (Fall 2019 Edition), ed. Edward N. Zalta, https://plato.stanford.edu/archives/fall2019/entries/rationality-normative-utility/). 37 In a number of decision cases where there are infinitely many states with only finite utilities attached (e.g., the St. Petersburg game), ECU Theory inherits the advantages of Mark Colyvan's Relative Expectation Theory over EU Theory. More specifically, in such (infinite) decision cases, ECU Theory delivers the intuitively correct verdicts, whereas EU Theory delivers none (see Mark Colyvan, "Relative Expectation Theory," Journal of Philosophy 105 (2008): 37–44; Colyvan and Hájek (2016): 838–39, https://doi.org/10.5840/jphil200810519). 18 EU(e) = (U(e, A) × P(A)) + (U(e, B) × P(B)) = 6 utiles By contrast, according to ECU Theory, a is more choiceworthy than b, for S, since the ECU of a (–3 c‐utiles) is greater than that of b (–3.5 c‐utiles). In fact, according to ECU Theory, a is choiceworthy tout court, since its CECU is equal to or greater than zero ([–3] – [–3] = 0). ECU(a) = ((U(a, A) − U(e, A)) × P(A)) + ((U(a, B) − U(b, B)) × P(B)) = −3 c-utiles ECU(b) = ((U(b, A) − U(e, A)) × P(A)) + ((U(b, B) − U(a, B)) × P(B)) = −3.5 c-utiles ECU(c) = ((U(c, A) − U(e, A)) × P(A)) + ((U(c, B) − U(a, B)) × P(B)) = −4 c-utiles ECU(d) = ((U(d, A) − U(e, A)) × P(A)) + ((U(d, B) − U(a, B)) × P(B)) = −4 c-utiles ECU(e) = ((U(e, A) − U(d, A)) × P(A)) + ((U(e, B) − U(a, B)) × P(B)) = −3 c-utiles ECU Theory gives different verdicts from those of EU Theory because ECU Theory, contrary to EU Theory, violates the IIA (for choiceworthiness evaluations). According to this principle, for any decision situation, T, and for any choice option, a, in T, if a is choiceworthy in T, then a is also choiceworthy in T if some other option(s) are eliminated from the pool of options in T. Likewise, if a is not choiceworthy in T, then a is also not choiceworthy in T if some other option(s) are added to the pool of options in T.38 Let us consider again the previous decision situation. In such a situation, ECU Theory dictates that a is choiceworthy. However, if options c, d, and e are eliminated from the pool of options, then b is choiceworthy according to ECU Theory, as shown below: A: a (2), b (5) B: a (10), b (8) ECU(a) = ((U(a, A) − U(b, A)) × P(A)) + ((U(a, B) − U(b, B)) × P(B)) = −0.5 c-utiles ECU(b) = ((U(b, A) − U(a, A)) × P(A)) + ((U(b, B) − U(a, B)) × P(B)) = 0.5 c-utiles Here is another example where ECU Theory violates the IIA:39 An agent, S, is faced with two choice options: a and b. S assigns probability 0.001 to a state of the world, A, and 0.999 to a state of the world, B. If state A or state B is realized, then S assigns the following utilities to the set of options: A: a (1000), b (0) B: a (1), b (2) According to ECU Theory, a is choiceworthy tout court, since its ECU is greater than that of any other option. ECU(a) = ((U(a, A) − U(b, A)) × P(A)) + ((U(a, B) − U(b, B)) × P(B)) = 0.001 c-utiles 38 Kenneth Arrow, Social Choice and Individual Values (New York: Wiley, 1951); R. Duncan Luce and Howard Raiffa, Games and Decisions: Introduction and Critical Survey (New York: Wiley, 1967). For a critique of the IIA, see in particular Amartya Sen, "Internal Consistency of Choice," Econometrica 61 (1993): 495–521, https://www.jstor.org/stable/2951715. Sen refers to this principle as "basic contraction consistency (Property ɑ)". See also Wedgwood's critique (2013: 2668–70). 39 Thanks to an anonymous reviewer for suggesting this example. 19 ECU(b) = ((U(b, A) − U(a, A)) × P(A)) + ((U(b, B) − U(a, B)) × P(B)) = −0.001 c-utiles Let us now introduce a third choice option (c) in the decision situation, all else being the same: A: a (1000), b (0), c (900) B: a (1), b (2), c (0) In this new decision situation, b is choiceworthy according to ECU Theory, since b's ECU is greater than that of any other option. ECU(a) = ((U(a, A) − U(c, A)) × P(A)) + ((U(a, B) − U(b, B)) × P(B)) = −0.899 c-utiles ECU(b) = ((U(b, A) − U(a, A)) × P(A)) + ((U(b, B) − U(a, B)) × P(B)) = −0.001 c-utiles ECU(c) = ((U(c, A) − U(a, A)) × P(A)) + ((U(c, B) − U(b, B)) × P(B)) = −2.098 c-utiles This example is particularly telling because option c is statewise dominated by a. Whether state A or state B is actual, option a is strictly preferred to option c. Yet, introducing option c in the decision situation changes ECU Theory's verdict: b, instead of a, is uniquely choiceworthy. ECU Theory thus violates the Irrelevance of statewise dominated alternatives (ISDA).40 This gives rise to a worry. Without the IIA (or the ISDA), it is possible to make up alternatives in any choice set and these manufactured alternatives would be altering the degrees of choiceworthiness of reasonable options.41 This opens the door to strategic manipulation in the decision process. The worry can be partially overcome, however, if we accept Nicholas Smith's theory of Rationally Negligible Probabilities: for any given decision, any outcome with probability ≤ p, where p is very close to 0, can be rationally excluded from consideration in the decision process.42 As such, the very improbable outcomes of manufactured alternatives cannot alter the degrees of choiceworthiness of the other available options in the choice set. Just as ECU Theory delivers verdicts which are at odds with EU Theory, ECU Theory also supplies a more discriminating measure of the intervals in rankings of more than two choice options. Let us consider four choice situations involving decisions under certainty: 1: a (5), b (1), c (1), d (1), e (1) 2: a (5), b (1), c (2), d (3), e (3) 3: a (5), b (1), c (2), d (3), e (5) 4: a (5), b (1), c (2), d (3), e (8) 40 John Quiggin, "Regret Theory with General Choice Sets," Journal of Risk and Uncertainty 8 (1994): 153–65, https://doi.org/10.1007/BF01065370. 41 Thanks to Douglas Lackey for raising this point and for wording suggestions. 42 Nicholas J. J. Smith, "Is Evaluative Compositionality a Requirement of Rationality?" Mind 123 (2014): 457–502, https://doi.org/10.1093/mind/fzu072; idem, "Infinite Decisions and Rationally Negligible Probabilities," Mind 125 (2016): 1199–212, https://doi.org/10.1093/mind/fzv209; Adam Chalmers, An Offer You Can't (Rationally) Refuse: Systematically Exploiting Utility‐Maximisers with Malicious Gambles, 2017, Thesis, http://hdl.handle.net/2123/16131. 20 The difference in CU between a and b is greater in situation 1 ((5 – 1) – (1 – 5) = 8 c‐ utiles) than in situation 2 ((5 – 3) – (1 – 5) = 6 c‐utiles), situation 3 ((5 – 5) – (1 – 5) = 4 c‐utiles) and situation 4 ((5 – 8) – (1 – 8) = 4 c‐utiles), whereas the difference in utility between a and b is the same in all four situations (4 utiles). Therefore, compared to utility, CU is a more discriminating measure of the extent to which a is more choiceworthy than b in situations 1–4. What's more, there do not appear to be any contrary cases where CU (or CECU) gives a less differentiated picture than does utility (or EU). What the foregoing comparisons between EU Theory and ECU Theory show is that rational preference is not a reliable indicator of choiceworthiness. That is because whereas the criterion of rational preference satisfies the IIA (by stipulative definition), the criterion of choiceworthiness (i.e., ECU Theory) violates that principle, as demonstrated above. Thus, not only do representation theorems not support EU Theory, but EU Theory also fails as a theory of rational choice. EU Theory's verdicts track what it is rational to prefer (in accordance with the IIA), but do not always track what it is rational to choose, that is, what is choiceworthy. It is important to emphasize that the proposed criterion of choice (i.e., choiceworthiness) is independent from the standard choice criterion (i.e., rational preference). The latter is not shown here to violate the assumptions, for example, the IIA, which are needed to derive utilities from preferences via a representation theorem. ECU Theory stands vindicated. In recent years, several alternatives to EU Theory have been proposed, for example, Mark Colyvan's Relative Expectation Theory (RET), Paul Bartha's Relative Utility Theory (RUT), and Lara Buchak's Risk‐Weighted Expected Utility (REU) Theory.43 In all finite decision cases, RET and RUT deliver the same verdicts as EU Theory. As for REU Theory, it can deliver the same verdicts as EU Theory, depending on the risk attitude of the agent equipped with the REU decision rule. These alternative "rational preference" tracking decision theories are therefore subject to the same objection as that leveled here against EU Theory: they fall short as theories of rational choice. 2.6 ECU Theory and the Problem of Act Versions Johan Gustafsson has argued that choice options in a decision problem should be construed as sets of acts such that one could jointly intentionally perform, at any time t, all the acts in the set, but no additional acts.44 One of the reasons given by Gustafsson is that if one construes choice 43 Colyvan, "Relative Expectation Theory"; Paul Bartha, "Taking Stock of Infinite Value: Pascal's Wager and Relative Utilities," Synthese 154 (2007): 5–52, https://doi.org/10.1007/s11229-005-8006-z; idem, "Making do Without Expectations," Mind 125 (2016): 799–827, https://doi.org/10.1093/mind/fzv152; Lara Buchak, Risk and Rationality (Oxford UP, 2013). 44 Johan E. Gustafsson, "Combinative Consequentialism and the Problem of Act Versions," Philosophical Studies 167, no. 3 (February 2014): 585–96, https://doi.org/10.1007/s11098-013-0114-x. 21 options as individual acts, then one runs into the Problem of act versions.45 Consider the following two examples: Example 1: Fred is agoraphobic and will experience a lot of anxiety if he starts working out at the gym (–25 utiles), more so than if he does not work out at the gym (0 utiles). Nevertheless, Fred is out of shape, is single and is in need of companionship, and he has a fair chance of finding a girlfriend if he works out at the gym and tries to find a girlfriend (inside or outside the gym) (100 utiles), more so than if he works out at the gym and does not try to find a girlfriend (–50 utiles), if he does not work out at the gym and tries to find a girlfriend (50 utiles) and if he does not work out at the gym and does not try to find a girlfriend (status quo) (–100 utiles). Let us suppose that Fred assigns credence 1 to the state of the world as described above. Although the utility of the act 'Fred works out at the gym' is lower than that of the act 'Fred does not work out at the gym', the utility of at least one version of the act 'Fred works out at the gym'-that is, 'Fred works out at the gym and tries to find a girlfriend' (–25 + 100 = 75 utiles)- is greater than the utility of all versions of the act 'Fred does not work out at the gym'-that is, 'Fred does not work out at the gym and tries to find a girlfriend' (0 + 50 = 50 utiles) and 'Fred does not work out at the gym and does not try to find a girlfriend' (0 + –100 = –100 utiles). Thus, intuitively, Fred should start working out at the gym. However, if choice options are construed as individual acts, then ECU Theory counsels Fred not to work out at the gym. Example 2: It is raining outside, but Ann will feel invigorated if she takes a brisk walk around the block (10 utiles), more so than if she stays inside (2 utiles). However, Ann has an injured toenail which causes her a great deal of pain when she tries to walk with her rain boots on. She will therefore experience a great deal of pain if she goes out for a walk wearing her rain boots (–30 utiles), more so than if she stays inside wearing her rain boots (–2 utiles). Luckily, Ann has a very comfortable pair of shoes which do not cause her any pain. However, there is a problem: it is raining very hard and her feet will get soaked. Ann will experience considerable discomfort if she goes out for a walk not wearing her rain boots (–15 utiles), more so than if she stays inside not wearing her rain boots (0 utiles). Let us suppose that Ann assigns credence 1 to the state of the world as described above. Although the utility of the act 'Ann stays inside' is lower than that of the act 'Ann goes out for a walk', the utility of at least one version of the act 'Ann stays inside'-that is, 'Ann stays inside and does not wear her rain boots' (2 + 0 = 2 utiles)-is greater than the utility of all versions of the act 'Ann goes out for a walk'-that is, 'Ann goes out for a walk and wears her rain boots' (10 + –30 = –20 utiles) and 'Ann goes out for a walk and does not wear her rain boots' (10 + –15 45 See also Lars Bergström, The Alternatives and Consequences of Actions (Stockholm: Almqvist & Wiksell, 1966); and Hector-Neri Castaneda, "A Problem for Utilitarianism," Analysis 28, no. 4 (1968): 141–42, https://doi.org/10.1093/analys/28.4.141. 22 = –5 utiles). Thus, intuitively, Ann should stay inside. However, if choice options are construed as individual acts, then ECU Theory counsels Ann not to stay inside, but instead to go out for a walk. Therefore, to be intuitively plausible, ECU Theory should be minimally cashed out as follows:46 For any agent, S, faced with any decision under certainty or uncertainty and for any number of mutually exclusive and jointly exhaustive options, or sets of acts, a, b, c, d and e, such that, for each set, S could jointly intentionally perform, at any time, t, all the acts in the set, but no additional acts, ▪ a is more choiceworthy than b, for S, at t, if and only if the CU/CECU of S jointly intentionally performing a at t is greater than the CU/CECU of S jointly intentionally performing b at t, and ▪ a is just as choiceworthy as b, for S, at t, if and only if the CU/CECU of S jointly intentionally performing a at t is equal to the CU/CECU of S jointly intentionally performing b at t. This implies the following derivative decision rule for individual acts:47 For any agent, S, faced with any decision under certainty or uncertainty and for any two mutually exclusive acts, a and b, ▪ a is more choiceworthy than b, for S, at any time, t, if and only if a is logically entailed by every set of acts such that, for each set, S could jointly intentionally perform, at t, all the acts in the set, but no additional acts and such that, in accordance with ECU Theory, the set of acts would be more choiceworthy for S, at t than each set of acts such that S could jointly intentionally perform, at t, all the acts in the set, but no additional acts and such that the set of acts logically entails b, and ▪ a is just as choiceworthy as b, for S, at any time, t, if and only if a is not more choiceworthy than b, and a is logically entailed by every set of acts such that, for each set, S could jointly intentionally perform, at t, all the acts in the set, but no additional acts and such that, in accordance with ECU Theory, the set of acts would not be less choiceworthy for S, at t than each set of acts such that S could jointly intentionally perform, at t, all the acts in the set, but no additional acts and such that the set of acts logically entails b. 46 Inspired by Gustafsson, 593–594. 47 Inspired by Gustafsson, 595. 23 Chapter 3: Should You Be Skeptical of Climate Change: Letter to a Climate Skeptic This is a short letter in response to a Reddit post on climate change skepticism (see below): Until recently, I never read much about climate change other than standard newspaper stuff. I think I have heard most of the arguments for it. I've also heard people say stuff like "everyone who actually studies/is an expert on climate change agrees". Well, Judith Curry studies it and doesn't. As I read through this presentation, it seems balanced and well thought out. In fact, searching through "climate sceptic" sites on the web, I find surprisingly sensible-seeming people with logical arguments and data references. This walkthrough is a good example.48 So can anyone tell me; am I missing something obvious? Why are the arguments for climate scepticism wrong? Any feedback is appreciated.49 Dear Skeptic, I think that you are honest and fair-minded. Your skepticism of consensus climate change science is understandable, but it is misplaced. Since you are not an expert on the science of climate change, you are rationally required to believe consensus climate change science.50 But you might ask, "Why should I believe that the climate science claims made by proponents of climate change mitigation are consensus climate science?" Signatory governments to the Paris climate change agreement51 base their support for climate change mitigation on the Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change (IPCC).52 A key finding of the AR5 is quoted below: 48 Judith Curry, "The debate: my presentation," Climate Etc., June 12, 2018, https://web.archive.org/web/20180630062836/https://judithcurry.com/2018/06/12/the-debate-mann-titley-moorecurry/. 49 u/HCAndersAnd, "What is wrong with these arguments?," Reddit (r/climatechange), June 12, 2018, https://www.reddit.com/r/climatechange/comments/8qnq31/what_is_wrong_with_these_arguments/. 50 For any proposition, p, a layperson with respect to p is rationally required to believe p if and only if p is believed by the majority of experts on p. See Chapter 1 ("How to Acquire Rational Belief Attitudes"). See also David Coady and Richard Corry, The Climate Change Debate: An Epistemic and Ethical Enquiry (London: Palgrave Macmillan, 2013), https://doi.org/10.1057/9781137326287. 51 "The Paris Agreement," United Nations Climate Change, accessed July 2, 2018, https://unfccc.int/process-andmeetings/the-paris-agreement/the-paris-agreement. 52 Yun Gao, Xiang Gao, and Xiaohua Zhang, "The 2 °C Global Temperature Target and the Evolution of the LongTerm Goal of Addressing Climate Change-From the United Nations Framework Convention on Climate Change to the Paris Agreement," Engineering 3, no. 2 (April 2017): 272–78, https://doi.org/10.1016/J.ENG.2017.01.022. Gao, Gao, and Zhang note that, In 2008–2014, the IPCC's Fifth Assessment Report (AR5) made a comprehensive assessment of the climate system change, risks, emission budget, and mitigation pathway choice of 2°C global warming on the basis of the research results available. After scientific assessment and a series of 24 Projections of changes in the climate system are made using a hierarchy of climate models ranging from simple climate models, to models of intermediate complexity, to comprehensive climate models, and Earth System Models. These models simulate changes based on a set of scenarios of anthropogenic forcings. [...] Relative to the average from year 1850 to 1900, global surface temperature change by the end of the 21st century is projected to likely exceed 1.5°C for RCP4.5, RCP6.0 and RCP8.5 (high confidence). Warming is likely to exceed 2°C for RCP6.0 and RCP8.5 (high confidence), more likely than not to exceed 2°C for RCP4.5 (high confidence), but unlikely to exceed 2°C for RCP2.6 (medium confidence). Warming is unlikely to exceed 4°C for RCP2.6, RCP4.5 and RCP6.0 (high confidence) and is about as likely as not to exceed 4°C for RCP8.5 (medium confidence). {12.4}53 You should believe that the above statement (call it X) is consensus climate change science because (i) X is clear and unambiguous and (ii) X is quoted from the work of the IPCC, and there is a consensus among recognized organizations of experts with expertise in climate science that "the work of the IPCC represents the consensus of the international scientific community on climate change science."54 Suppose however that X was consensus climate science at the moment of publication of the AR5, but X is no longer consensus climate science, and you have polling or other unequivocal evidence to support this. It then follows that (i) you should disbelieve X if consensus temperature projections have shifted since publication of the AR5 or (ii) you should withhold belief about X if there are no longer any consensus temperature projections and no such projections are believed by even the majority of climate scientists. Suppose instead that X was not consensus climate science at the moment of publication of the AR5 (and that X is not currently believed by even the majority of climate scientists). This would be the most significant and egregious failure of science communication in history. All the climate scientists who were involved in signing off on X's wording would have experienced a lapse or would have engaged in deception. This would have happened in a report, the AR5's Summary for Policymakers, that is designed to guide laypersons in making informed policy decisions on climate change. This is very improbable. political pushes, one of the three goals reached at the 2015 Paris Climate Change Conference was stated as "Holding the increase in the global average temperature to well below 2°C above preindustrial levels and pursuing efforts to limit the temperature increase to 1.5°C above preindustrial levels" [3]. 53 IPCC, Summary for Policymakers, In Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, edited by T.F. Stocker, D. Qin, G.-K. Plattner, M. Tignor, S.K. Allen, J. Boschung, A. Nauels, Y. Xia, V. Bex, and P.M. Midgley. Cambridge: Cambridge University Press, 2013, http://www.climatechange2013.org/images/report/WG1AR5_SPM_FINAL.pdf#page=18. 54 "The Science of Climate Change," Science 292, no. 5520 (May 18, 2001): 1261, https://doi.org/10.1126/science.292.5520.1261. See also "Scientific consensus: Earth's climate is warming," Global Climate Change: Vital Signs of the Planet, Earth Science Communications Team at NASA's Jet Propulsion Laboratory, accessed June 30, 2018, https://climate.nasa.gov/scientific-consensus/. 25 Therefore, unless you have polling or other unequivocal evidence that X is no longer consensus climate science, the likelihood that X is currently consensus climate science is significantly greater than the likelihood that X is not currently consensus climate science. And so, it is rational to believe that X is consensus climate science. In conclusion, if you were a dissenting expert on the science of climate change-that is, if you regarded yourself as such or if you were a practicing climate scientist who disagreed with the conclusions of your peers on climate change science-then you would be entitled to your own view on those conclusions. But, judging from your question, you are clearly not a dissenting expert. As such, I hope to have convinced you that, unless and until you become an expert, you are rationally required to believe the statement quoted above from the IPCC's AR5.55 Chapter 4: Should You Invest in Life-Extension Medical Research? The right to choose to live or to die is the most fundamental right there is; conversely, the duty to give others that opportunity to the best of our ability is the most fundamental duty there is. -Aubrey de Grey Should you invest in healthy life-extension medical research? Aubrey de Grey thinks that you should. De Grey56 is a biomedical gerontologist and the Chief Science Officer and Cofounder of SENS Research Foundation,57 a 501(c)(3) public charity that funds biomedical research into "regenerative medicine to repair the damage underlying the diseases of aging."58 For the past 20 years or so, de Grey has been researching and promoting regenerative medicine solutions to the problem of aging. In 2007, de Grey published the book Ending Aging: The Rejuvenation Breakthroughs that Could Reverse Human Aging in Our Lifetime.59 Ending Aging details how age-related decline and illness could be reversed in the near future if sufficient investments were made in what de Grey calls "SENS" research. SENS (or "Strategies for Engineered Negligible Senescence") refers to a set of regenerative medicine approaches developed by de Grey which directly target age-related tissue damage at the microscopic level. While some gerontologists believe that the 55 I noted three earlier uses of this "Letter to a climate skeptic" format: Mike Kaulbars, "Letter To A Climate 'Skeptic'," News Junkie Post, June 14, 2010; David Morrison, "Letter to Climate Skeptics," Skeptic 16, no. 2 (2011), 10; and Steph Newman, "An open letter to climate change sceptics," 1 Million Women, July 1, 2016. 56 Aubrey de Grey, "CV," SENS Research Foundation, accessed July 3, 2018, http://www.sens.org/sites/srf.org/files/AdG-CV.doc. 57 SENS Research Foundation, accessed July 3, 2018, http://www.sens.org/. 58 "About SENS Research Foundation," SENS Research Foundation, accessed July 3, 2018, http://www.sens.org/about. 59 Aubrey de Grey and Michael Rae, Ending Aging: The Rejuvenation Breakthroughs That Could Reverse Human Aging in Our Lifetime (New York: St. Martin's Press, 2007). 26 maximum lifespan can be extended through metabolic interventions,60 de Grey thinks that metabolism is too complex to be effectively controlled for the foreseeable future. Just as we can keep vintage cars looking and operating like new by repairing broken parts or replacing them with new ones, de Grey points out that we can keep humans in a youthful state indefinitely by periodically removing or repairing damaged tissues at the cellular and molecular levels. While de Grey's "SENS" proposal to extend healthy human life remains controversial among gerontologists, SENS Research Foundation's 30-member expert Advisory Board has endorsed de Grey's conclusions that, Recent biotechnological progress indicates that many aspects of aging may indeed be effectively treatable by regenerative medicine in the foreseeable future. We cannot yet know whether all aspects will be, but extensive scrutiny has failed to identify any definite exceptions. Therefore, at this point there is a significant chance that such therapies would postpone age-related decline by several years, if not more, which constitutes a clear case for allocating significant resources to the attempt to develop those therapies.61 On this basis, de Grey has argued that investments in regenerative medicine to extend healthy human life are morally imperative. One of his arguments can be put as follows: What gives us the right to decide for future generations whether they should or should not live healthily past the age of 120 years? If we refrain from investing in healthy life-extension technologies today because of moral concerns, then we are in effect denying future generations (our children and grandchildren) the right to live healthy lives past our current maximum lifespan. What is considered moral today might be considered loathsome tomorrow, either because circumstances have changed or because values have shifted.62 So if we decide today not to implement those technologies because of overriding moral concerns, then we are rationally entitled not to do so, but what we are not rationally entitled to do is to prevent future generations from benefiting from those technologies should they deem them morally obligatory. Therefore, we can have a reasoned debate about whether it would be moral to implement healthy lifeextension technologies today (and de Grey has forcefully argued that it is morally obligatory to do so), but what we cannot rationally refrain from doing is investing in healthy life-extension technologies today for the benefit of future generations (our children and grandchildren) should they deem those technologies morally necessary. This suggests a more general principle of ethics and rational choice: Values and preferences may change over time. Therefore, to the extent that no current values or preferences 60 Eric Zorn, "A 150-year-old human? Neither side is folding in The Great Longevity Wager," Chicago Tribune, July 13, 2018, http://www.chicagotribune.com/news/opinion/zorn/ct-perspec-zorn-longevity-aging-olshanskyaustad-20180715-story.html; S. Jay Olshansky, "Is Life Extension Today a Faustian Bargain?," Frontiers in Medicine 4, no. 215 (November 29, 2017), 1–3, https://dx.doi.org/10.3389%2Ffmed.2017.00215. 61 "Research Advisory Board," SENS Research Foundation, accessed July 3, 2018, http://www.sens.org/about/leadership/research-advisory-board. 62 Eric Schwitzgebel, "Will Future Generations Find Us Especially Morally Loathsome?," The Splintered Mind, June 30, 2018, https://schwitzsplinters.blogspot.com/2018/06/will-future-generations-find-us.html. 27 are violated, a robust decision rule should leave open as many choice opportunities as possible to accommodate future changes in values or preferences.63 Bibliography "About SENS Research Foundation." SENS Research Foundation. Accessed July 3, 2018. http://www.sens.org/about. Alston, William. "Concepts of epistemic justification." The Monist 68, no. 1 (1985): 57–89. https://doi.org/10.5840/monist198568116. Arnauld, Antoine, and Pierre Nicole. 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