In some dark alley. . . Mugger: Hey, give me your wallet. Pascal: Why on Earth would I want to do that? Mugger: Otherwise I’ll shoot you. Pascal: But you don’t have a gun. Mugger: Oops! I knew I had forgotten something. Pascal: No wallet for you then. Have a nice evening. Mugger: Wait! Pascal: Sigh. Mugger: I’ve got a business proposition for you. . . . How about you give me your wallet now? In return, I promise to come (...) to your house tomorrow and give you double the value of what’s in the wallet. Not bad, eh? A 200% return on investment in 24 hours. (shrink)

“Perhaps the most common objection to consequentialism is this: it is impossible to know the future…This means that you will never be absolutely certain as to what all the consequences of your act will be…there may be long term bad effects from your act, side effects that were unforeseen and indeed unforeseeable…So how can we tell which act will lead to the best results overall – counting all the results? This seems to mean that consequentialism will be unusable as a (...) moral guide to action. All the evidence available at the time of acting may have pointed to the conclusion that a given act was the right act to perform – and yet it may still turn out that what you did had horrible results, and so in fact was morally wrong. Indeed, if will never be possible to say for sure that any given act was right or wrong, since any event can continue to have further unseen effects down through history. Yet if it is impossible to tell whether any act is morally right or wrong, how can consequentialism possibly be a correct moral theory?”. (shrink)

We introduce a St. Petersburg-like game, which we call the ‘Pasadena game’, in which we toss a coin until it lands heads for the first time. Your pay-offs grow without bound, and alternate in sign (rewards alternate with penalties). The expectation of the game is a conditionally convergent series. As such, its terms can be rearranged to yield any sum whatsoever, including positive infinity and negative infinity. Thus, we can apparently make the game seem as desirable or undesirable as we (...) want, simply by reordering the pay-off table, yet the game remains unchanged throughout. Formally speaking, the expectation does not exist; but we contend that this presents a serious problem for decision theory, since it goes silent when we want it to speak. We argue that the Pasadena game is more paradoxical than the St. Petersburg game in several respects. We give a brief review of the relevant mathematics of infinite series. We then consider and rebut a number of replies to our paradox: that there is a privileged ordering to the expectation series; that decision theory should be restricted to finite state spaces; and that it should be restricted to bounded utility functions. We conclude that the paradox remains live. (shrink)

000000001. Introduction Call a theory of the good—be it moral or prudential—aggregative just in case (1) it recognizes local (or location-relative) goodness, and (2) the goodness of states of affairs is based on some aggregation of local goodness. The locations for local goodness might be points or regions in time, space, or space-time; or they might be people, or states of nature.1 Any method of aggregation is allowed: totaling, averaging, measuring the equality of the distribution, measuring the minimum, etc.. Call (...) a theory of the good finitely additive just in case it is aggregative, and for any finite set of locations it aggregates by adding together the goodness at those locations. Standard versions of total utilitarianism typically invoke finitely additive value theories (with people as locations). A puzzle can arise when finitely additive value theories are applied to cases involving an infinite number of locations (people, times, etc.). Suppose, for example, that temporal locations are the locus of value, and that time is discrete, and has no beginning or end.2 How would a finitely additive theory (e.g., a temporal version of total utilitarianism) judge the following two worlds? Goodness at Locations (e.g. times) w1:..., 2, 2, 2, 2, 2, 2, 2, 2, 2, ..... w2:..., 1, 1, 1, 1, 1, 1, 1, 1, 1, ..... Example 1 At each time w1 contains 2 units of goodness and w2 contains only 1. Intuitively, we claim, if the locations are the same in each world, finitely additive theorists will want to claim that w1 is better than w2. But it's not clear how they could coherently hold this view. For using standard mathematics the sum of each is the same infinity, and so there seems to be no basis for claiming that one is better than the other.3 (Appealing to Cantorian infinities is of no help here, since for any Cantorian infinite N, 2xN=1xN.). (shrink)

Suppose we wish to decide which of a pair of actions has better consequences in a case in which both actions result in infinite utility. Peter Vallentyne and others have proposed that one action has better consequences than a second if there is a time after which the cumulative utility of the first action always outstrips the cumulative utility of the second. I argue against this principle, in particular I show how cases may arise in which up to any point (...) of time action a1 produces more utility than action a2, yet for each individual involved a2 produces more utility. (shrink)

Recently in the philosophical literature there has been some effort made to understand the proper application of the theory of utilitarianism to worlds in which there are infinitely many bearers of utility. Here, we point out that one of the best, most inclusive principles proposed to date contradicts fundamental utilitarian ideas, such as the idea that adding more utility makes a better world.

Newcomb's problem and similar cases show the need to incorporate causal distinctions into the theory of rational decision; the usual noncausal decision theory, though simpler, does not always give the right answers. I give my own version of causal decision theory, compare it with versions offered by several other authors, and suggest that the versions have more in common than meets the eye.

The Pasadena paradox presents a serious challenge for decision theory. The paradox arises from a game that has well-defined probabilities and utilities for each outcome, yet, apparently, does not have a well-defined expectation. In this paper, I argue that this paradox highlights a limitation of standard decision theory. This limitation can be (largely) overcome by embracing dominance reasoning and, in particular, by recognising that dominance reasoning can deliver the correct results in situations where standard decision theory fails. This, in turn, (...) pushes us towards pluralism about decision rules. (shrink)

An infinite future thus threatens to paralyze utilitarianism. Utilitarians need principled ways to determine which possible infinite futures are better or worse. In this article, I discuss a recent suggestion of Peter Vallentyne and Shelly Kagan. I conclude that the best way forward for utilitarians is, in fact, to by-pass the infinite utility debate altogether. (edited).

I address the problem of indefiniteness in quantum mechanics: the problem that the theory, without changes to its formalism, seems to predict that macroscopic quantities have no definite values. The Everett interpretation is often criticised along these lines, and I shall argue that much of this criticism rests on a false dichotomy: that the macroworld must either be written directly into the formalism or be regarded as somehow illusory. By means of analogy with other areas of physics, I develop the (...) view that the macroworld is instead to be understood in terms of certain structures and patterns which emerge from quantum theory (given appropriate dynamics, in particular decoherence). I extend this view to the observer, and in doing so make contact with functionalist theories of mind. (shrink)

Technological revolutions are among the most important things that happen to humanity. Ethical assessment in the incipient stages of a potential technological revolution faces several difficulties, including the unpredictability of their long‐term impacts, the problematic role of human agency in bringing them about, and the fact that technological revolutions rewrite not only the material conditions of our existence but also reshape culture and even – perhaps – human nature. This essay explores some of these difficulties and the challenges they pose (...) for a rational assessment of the ethical and policy issues associated with anticipated technological revolutions. (shrink)

One resolution of the St. Petersburg paradox recognizes that a gamble carries a risk sensitive to the gamble's stakes. If aversion to risk increases sufficiently fast as stakes go up, the St. Petersburg gamble has a finite utility.

Traditional utilitarianism, when applied, implies a surprising prediction about the future, viz., that all experience of pleasure and pain must end once and for all, or infinitely dwindle. Not only is this implication surprising, it should render utilitarianism unacceptable to persons who hold any of the following theses: that evaluative propositions may not imply descriptive, factual propositions; that evaluative propositions may not imply contingent factual propositions about the future; that there will always exist beings who experience pleasure or pain.