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.

Traditional act utilitarianism judges an action permissible just in case it produces as much aggregate utility as any alternative. It is often supposed that utilitarianism faces a serious problem if the future is infinitely long. For in that case, actions may produce an infinite amount of utility. And if that is so for most actions, then utilitarianism, it appears, loses most of its power to discriminate among actions. For, if most actions produce an infinite amount of utility, then few actions (...) produce non-maximal utility, and so most actions are permissible.1 I will argue that potentially infinite futures create no major problems for utilitarianism. Utilitarianism has, I argue, the resources to distinguish among actions all of which produce infinite amounts of utility -- judging some permissible and some impermissible. For brevity of expression I will focus on act utilitarianism, but all the points apply equally well to many other traditional forms of utilitarianism. (shrink)

Suppose that time is infinitely long towards the future, and that each feasible action produces a finite amount of utility at each time. Then, under appropriate conditions, each action produces an infinite amount of utility. Does this mean that utilitarianism lacks the resources to discriminate among such actions? Since each action produces the same infinite amount of utility, it seems that utilitarianism must judge all actions permissible, judge all actions impermissible, or remain completely silent. If the future is infinite, that (...) is, the prospects for utilitarianism look bleak. (shrink)

In 1991 Mark Nelson argued that if time is infinitely long towards the future, then under certain easily met conditions traditional utilitarianism is unable to discriminate among actions. For under these conditions, each action produces the same infinite amount of utility, and thus it seems that utilitarianism must judge all actions permissible, judge all actions impermissible, or remain completely silent. In response to this criticism of utilitarianism, I argued that utilitarianism had the resources for dealing with at least some cases (...) of infinite utility. More specifically, I defended the following principle as being part of the "spirit" of traditional (total) utilitarianism: -/- PMU*: An action a1 has better consequences than an action a2 if and only if there is a time t such that for any later time t' the cumulative amount of utility produced by a1 up to t' is greater than that produced by action a2 up to t'. -/- For the usual finite cases, this principle agrees exactly with the standard approach of comparing totals. For infinite cases, however, it can distinguish among two actions each of which produces an infinite amount of utility. It says, for example, that an action that produces 2 units of utility at each time has better consequences than an action that produces 1 unit of utility at each time -- even though they both produce the same infinite amount of utility. Of course, cases where one action produces more utility than a second at each time are going to be rather rare. PMU* is not limited to such cases, however; it also has bite in cases such as the following: -/- Time a1: 1, 1, 1, 1, 2, 2, 2, 2, 2, ... a2: 3, 3, 3, 3, 1, 1, 1, 1, 1, ... -/- For although the cumulative utility of a1 up to and including the fourth time is only 4 utiles and a2's is 12, a1 starts catching up after that, ties a2 in the 12th time, and stays ahead after that. Thus, PMU* judges a1 as having better consequences than a2. I claimed that PMU* better captured the "spirit" of traditional utilitarianism than the usual sum total view -- on the grounds that almost anyone inclined to defend traditional utilitarianism would, upon reflection, want to hold, for example, that 2 utiles at every time is indeed better than 1 utile at each time. Two responses to my view have since been given in this journal. Luc Van Liederkerke has argued that PMU* violates an anonymity (neutrality, impartiality) condition that is central to utilitarianism. And James Cain has argued that PMU* is not person-centered, and that being so is central to utilitarianism. Here I will reply to the criticisms. Basically, I will acknowledge that each is right about an important point, but deny that this establishes that the core idea underlying PMU* is less plausible than the standard sum-ranking versions of utilitarianism. (shrink)

The note addresses the problem of how utilitarianism and other finitely additive theories of value should evaluate infinitely long utility streams. We use the axiomatic approach and show that finite anonymity does not apply in an infinite framework. A stronger anonymity demand (fixed step anonymity) is proposed and motivated. Finally, we construct an ordering criterion that combines fixed step anonymity and strong monotonicity.