Yet another counterexample to act utilitarianism

It is wrong to torture a stranger for 99 minutes in order to avoid 100 minutes of equal torture to oneself.

Utilitarianism, egoism and promises

Suppose Alice and Bob are perfect utilitarians or perfect amoral egoists in any combination. They are about to play a game where they raise a left hand or a right hand in a separate booth, and if they both raise the same hand, they both get something good. Otherwise, nobody gets that good. Nobody sees what they’re doing in the game: the game is fully automated. And they both have full shared knowledge of the above.

They confer before the game and promise to one another to raise the right hand. They go into their separate rooms. And what happens next?

Take first the case where they are both perfect amoral egoists. Amoral egoists don’t care about promises. So the fact that an amoral egoist promised to raise the right hand is no evidence at all that they will raise the right hand, unless there is something in it for them. But is there anything in it for them? Well, if Bob raises his right hand, then there is something in it for Alice to raise her right hand. But note that this conditional is true regardless of whether they’ve made any promises to each other, and it is equally true that if Bob raises his left hand, then there is something in it for Alice to raise her left hand.

The promise is simply irrelevant here. It is true that in normal circumstances, it makes sense for egoists to keep promises in order to fool people into thinking that they have morality. But I’ve assumed full shared knowledge of each other’s tendencies here, and so no such considerations apply here.

It is true that if Alice expects Bob to expect her to keep her promise, then Alice will expect Bob to raise his right hand, and hence she should raise her right hand. But since she’s known to be an amoral egoist, there is no reason for Bob to expect Alice to keep her promise. And the same vice versa.

What if they are utilitarians? It makes no difference. Since in this case both always get the same outcome, there is no difference between utilitarians and amoral egoists.

This means that in cases like this, with full transparency of behavioral tendencies, utilitarians and amoral egoists will do well to brainwash or hypnotize themselves into promise-keeping.

In ordinary life, this problem doesn’t arise as much, because as long as at least one person is more typical, and hence takes promises to have reason-giving force, or if public opinion is around to enforce promise-keeping, then the issue doesn’t come up. But I think there is a lesson here and in the previous post: for many ordinary practice, the utilitarian is free-riding on the non-utilitarians.

Open theism and utilitarianism

Here’s an amusing little fact. You can’t be both an open theist and an act utilitarian. For according to the act utilitarian, to fail to maximize utility is wrong. It is impossible for God to do the wrong thing. But given open theism, it does not seem that God can know enough about the future in order to be necessarily able to maximize utility.

Act and rule utilitarianism

Rule utilitarianism holds that one should act according to those rules, or those usable rules, that if adopted universally would produce the highest utility. Act utilitarianism holds that one should do that act which produces the highest utility. There is an obvious worry that rule utilitarianism collapses into act utilitarianism. After all, wouldn't utility be maximized if everyone adopted the rule of performing that act which produces the highest utility? If so, then the rule utilitarian will have one rule, that of maximizing the utility in each act, and the two theories will be the same.

A standard answer to the collapse worry is either to focus on the fact that some rules are not humanly usable or to distinguish between adopting and following a rule. The rule of maximizing utility is so difficult to follow (both for epistemic reasons and because it's onerous) that even if everyone adopted it, it still wouldn't be universally followed.

Interestingly, though, in cases with infinitely many agents the two theories can differ even if we assume the agents would follow whatever rule they adopted.

Here's such a case. You are one of countably infinitely many agents, numbered 1,2,3,..., and one special subject, Jane. (Jane may or may not be among the infinitely many agents—it doesn't matter.) Each of the infinitely many agents has the opportunity to independently decide whether to costlessly press a button. What happens to Jane depends on who, if anyone, pressed the button:

• If a finite number n of people press the button, then Jane gets n+1 units of utility.
• If an infinite number of people press the button, then Jane gets a little bit of utility from each button press: specifically, she gets 2^−k/10 units of utility from person number k, if that person presses the button.

So, if infinitely many people press the button, Jane gets at most (1/2+1/4+1/8+...)/10=1/10 units of utility. If finitely many people press the button, Jane gets at least 1 unit of utility (if that finite number is zero), and possibly quite a lot more. So she's much better off if finitely many people press.

Now suppose all of the agents are act utilitarians. Then each reasons:

My decision is independent of all the other decisions. If infinitely many other people press the button, then my pressing the button contributes (2^−k)/10 units of utility to Jane and costs nothing, so I should press. If only finitely many other people press the button, then my pressing the button contributes a full unit of utility to Jane and costs nothing, so I should press. In any case, I should press.

And so if everyone follows the rule of doing that individual act that maximizes utility, Jane ends up with one tenth of a unit of utility, an unsatisfactory result.

So from the point of view of act utilitarianism, in this scenario there is a clear answer as to what each person should do, and it's a rather unfortunate answer—it leads to a poor result for Jane.

Now assume rule utilitarianism, and let's suppose that we are dealing with perfect agents who can adopt any rule, no matter how complex, and who would follow any rule, no matter how difficult it is. Despite these stipulations, rule utilitarianism does not recommend that everyone maximize utility in this scenario. For if everyone maximizes utility, only a tenth of a unit is produced, and there are much better rules than that. For instance, the rule that one should press the button if and only if one's number is less than ten will produce nine units of utility if universally adopted and followed. And the rule that one should press the button if and only if one's number is less than 10¹⁰⁰ will produce even more utility.

In fact, it's easy to see that in our idealized case, rule utilitarianism fails to yield a verdict as to what we should do, as there is no optimal rule. We want to ensure that only finitely many people press the button, but as long as we keep to that, the more the better. So far from collapsing into the act utilitarian verdict, rule utilitarianism fails to yield a verdict.

A reasonable modification of rule utilitarianism, however, may allow for satisficing in cases where there is no optimal rule. Such a version of rule utilitarianism will presumably tell us that it's permissible to adopt the rule of pressing the button if and only if one's number is less than 10¹⁰⁰. This version of rule utilitarianism also does not collapse into act utilitarianism, since the act utilitarian verdict, namely that one should unconditionally press the button, fails to satisfice, as it yields only 1/10 units of utility.

What about less idealized versions of rule utilitarianism, ones with more realistic assumptions about agents. Interesting, those versions may collapse into act utilitarianism. Here's why. Given realistic assumptions about agents, we can expect that no matter what rule is given, there is some small independent chance that any given agent will press the button even if the rule says not to, just because the agent has made a mistake or is feeling malicious or has forgotten the rule. No matter how small that chance is, the result is that in any realistic version of the scenario we can expect that infinitely many people will press the button. And given that infinitely many other people will press the button, if only by mistake, the act utilitarian advice to press the button oneself is exactly right.

So, interestingly, in our infinitary case the more realistic versions of rule utilitarianism end up giving the same advice as act utilitarianism, while an idealized version ends up failing to yield a verdict, unless supplemented with a permission to satisfice.

But in any case, no version of rule utilitarianism generally collapses into act utilitarianism if such infinitary cases are possible. For there are standard finitary cases where realistic versions of rule utilitarianism fail to collapse, and now we see that there are infinitary ones where idealized versions fail to collapse. And so no version generally collapses, if cases like this are possible.

Of course, the big question here is whether such cases are possible. My Causal Finitism (the view that nothing can have infinitely many
items in its causal history) says they're not, and I think oddities such as above give further evidence for Causal Finitism.