Unless I'm missing something, using different scales doesn't actually preclude utilitarian calculations.

There's no obvious natural conversion between fun and pain (hence the question), but any monotonic conversion function that we choose to adopt will give us well-defined values of X and N. We can construct a utilitarianism around any of these possibilities: if X or N are very large or infinite, that just means that we're approaching pure negative utilitarianism, defining utility in terms of minimizing suffering without taking fun into account. Deontological considerations need not apply.

Indeed, of the major utility functions that I'm aware of, this problem only seems to arise within pleasure/pain utilitarianism; as stated, negative utilitarianism doesn't admit to the existence of a finite exchange rate for torture (which seems rather shaky in light of preferences like those expressed in other comments), while preference utilitarianism's results are going to vary by individual and case but are always individually well-defined.

(This comment was originally buried more deeply, but on reflection it seems to have more to do with the OP than with the comment I was replying to.)

N=1,X= -(T+ epsilon) where T is the amount of antifun that a month of torture is.

But I really don't like that answer.

Some thinking out loud follows:

• It's clear to me that I don't want to answer this question, for more or less the same reasons that I don't want to explain how much suffering I would be willing to impose upon you in exchange for X amount of fun for me. Which, of course, doesn't necessarily stop me from doing it, as long as I don't have to admit to it.

• It's relatively clear to me that intuitively I'd give a different answer if I started from a small X and worked my way up by increments asking "Is this enough?" than if I started from a large X and worked my way down by increments asking "Is this too little?" From which I conclude that my intuitions on this subject are not reliable. Which I knew already from earlier conversations about "utilon-trade" scenarios.

• It's clear to me that, while I have a fairly concrete understanding of torture, I have a very fuzzy understanding of fun. So when I say "X=-T + epsilon", I'm comparing concrete-torture-apples to fuzzily-imagined-fun-oranges, and I once again have no reliable intuitions.

• If I screen off all of my real-world understanding of torture, so I can do a fuzzily-imagined-apples-to-fuzzily-imagined-apples comparison, it's a simple optimization question: is 1 (T+ epsilon) - 1 T positive? Why, yes it is. Great, do it! But the minute I unscreen that real-world understanding, I'm back to not wanting to answer that question.

• What I'd prefer to do is unpack "-T amount of fun" into something equally concrete and do the comparison that way, but I don't seem to know how to do that.

This kind of "thought experiment" always reminds me of chapter seven in John Varley's Steel Beach, which narrates a utilitarian negotiation between humans and brontosaurs ("represented" by human ecologists sporting animal attributes) mediated by an omniscient computer.

Central Computer (CC): "It is as close to mental telepathy as we're likely to get. The union representatives are tuned into me, and I'm tuned into the dinosaurs. The negotiator poses a question: 'How do you fellows feel about 120 of your number being harvested/murdered this year?' I put the question in terms of predators. A picture of an approaching tyrannosaur. I get a fear response: 'Sorry, we'd rather not, thank you.' I relay it to the unionist, who tells Callie the figure is not acceptable. The unionist proposes another number, in tonight's case, sixty. Callie can't accept that. She'd go broke, there would be no one to feed the stock. I convey this idea to the dinosaurs with feelings of hunger, thirst, sickness. They don't like this either. Callie proposes 110 creatures taken. I show them a smaller tyrannosaur approaching, with some of the herd escaping. They don't respond quite so strongly with the fear and flight reflex, which I translate as 'Well, for the good of the herd, we might see our way clear to losing seventy so the rest can grow fat.' I put the proposal to Callie, who claims the Earthists are bleeding her white, and so on."

"Sounds totally useless to me," I said, with only half my mind on what the CC had been saying. [...]

"I don't see why you should say that. Except that I know your moral stand on the whole issue of animal husbandry, and you have a right to that."

"No, that whole issue aside, I could have told you how this all would come out, given only the opening bid. David proposed sixty, right?"

"After the opening statement about murdering any of these creatures at all, and his formal demand that all--"

"'--creatures should live a life free from the predation of man, the most voracious and merciless predator of all,' yeah, I've heard the speech, and David and Callie both know it's just a formality, like singing the planetary anthem. When they got down to cases, he said sixty. Man, he must really be angry about something, sixty is ridiculous. Anyway, when she heard sixty, Callie bid 120 because she knew she had to slaughter ninety this year to make a reasonable profit, and when David heard that he knew they'd eventually settle on ninety. So tell me this: why bother to consult the dinosaurs? Who cares what they think?"

The CC was silent, and I laughed.

"Tell the truth. You make up the images of meat-eaters and the feelings of starvation. I presume that when the fear of one balances out the fear of the other, when these poor dumb beasts are equally frightened by lousy alternatives--in your judgement, let's remember . . . well, then we have a contract, right? So where would you conjecture that point will be found?"

"Ninety carcasses," the CC said.

"I rest my case."

"You have a point. But I actually do transmit the feelings of the animals to the human representatives. They do feel the fear, and can judge as well as I when a balance is reached."

"Say what you will. Me, I'm convinced the jerk with the horns could have as easily stayed in bed, signed a contract for ninety kills, and saved a lot of effort."

I have a strongly egalitarian utility function: for scenarios with equal net utility Σ (i.e. sum of normalised personal utilities of individual people) I attach a large penalty to those where the utilities are unevenly distributed (at least in absence of reward and punishment motivations). So my utility is not only a function of Σ, but rather of the whole distribution. In practice it means that X and N will be pretty high.

To set the specific value would be difficult, mainly because I use a set of deontological constraints while evaluating my utility. For example, I tend to discard all positive contributions to Σ which are in sharp conflict with my values: for example, pleasure gained by torturing puppies doesn't pass the filter. These deontological constraints are useful because of ethical injunctions.

So even if 7^^^7 zoosadists could experience orgasm watching just one puppy tortured, the deontological filter accepts only the negative contribution to Σ from the puppy's utility function (*). Now this is not much reasonable, but the problem is that neither can I switch off my deontological checks easily, nor do I particularly want to learn that.

So, to answer 1), I have to guess how I would reason in absence of the deontological filters, and am not much confident about the results. But say that for a month of really horrible torture (assuming the victim is not a masochist and hasn't given consent) with no long-term consequences, I suppose that N would be of order 10^8 with X = a week of a very pleasant vacation. (I could have written 10^10 or 10^6 instead of 10^8, it doesn't actually feel any different).

As for 2), the largeness of N doesn't necessarily reflect presence of deontology. It may result either from the far larger disutility of torture compared to utility of pleasure, or from some discount for uneven utility distribution. In my case it is both.

(*) Even if I did get rid of rigid deontology, I would like to preserve some discount for illegitimately gained utilities. So, the value of Σ, taken as argument of my utility function, would be higher if the zoosadists got exactly the same amount of pleasure by other means and the puppy was meanwhile tortured only by accident.

1) A few thoughts:

a. Intuitively, fun per person feels like it is upper bounded (just like utility of money). I cannot imagine what kind of fun for one person could compensate a month of torture. We will fix X and play with N

b. The difficulty seems to arise from the fact that the mechanical answer is to set e.g., X=1, N = ceil(Y + epsilon) (where minus Y is utility of the torture), yet this intuitively does not feel right. Some thoughts on why:

• Scope insensitivity. We have trouble instinctively multiplying fun by many people (i.e., I can picture one day of fun very clearly, but have trouble multiplying that by millions of people, to get anywhere near compensating for a month of torture). So the mechanical answer would be correct, but our brains cannot evaluate the fun side of the equation “intuitively”.

• Bias towards “fairness”. Having one person suffer and others have fun to compensate doesn’t feel right (or at least assessing this trade-off is difficult)

• Bias towards negative utilitarianism. We instinctively prefer minimizing suffering than maximizing utility.

c. When we scale things down the question seems easier. Suppose we set X = an amazing week of fun I will remember for the rest of my life, bringing me joy to think about it again and again. Now I ask how much torture I would put up for that. This is a question I feel I can intuitively answer. I would trade, say Y = 10 seconds of extreme pain for X (assuming no permanent physical damage).
To move to 1 month of torture we need to assess how the utility of a torture session scales with its duration. If it scaled linearly, 1 month of torture is ~2.6 million seconds of torture, which means we should set N= ~260’000 for X defined above. I feel that after a few days, the scale is sub-linear, but it may be super-linear before that (when you start moving into the permanent psychological damage area). I cannot seem to come up with an answer I am comfortable with.

2) As pointed out by Nornagest, If I give you my utility function (mapping all possible pains and pleasures to a number), I’m not sure how you could tell whether pain and pleasure are being measured “on the same scale” or not?

Most of the usual thought experiments that justify expected utilitarialism

Is this question only intended for people who do not believe expected utilitarialism is not obviously abominable? I mean... it has SUM() built in as the intrinsic aggregation tool. SUM isn't even remotely stable, let alone an ideal to aspire to.

2) If you say X or N must be very large, does this prove that you measure torture and fun using in effect different scales, and therefore are a deontologist rather than a utilitarian?

I confess my knowledge of the subject is non-existant but everything I have seen has discussed utilitarianism as a sub-set of the broader class of teleological theories, and that not all of these would be uncomfortable with the idea of using different scales. And also that deontologists don't have scales for measuring outcomes at all.

a deontologist rather than a utilitarian

The opposite of a deontologist is a consequentialist, not a utilitarian. All utilitarians are consequentialists but not all consequentialists are utilitarians.

(The domain of the above paragraph being restricted to the subset of agents whose moral preferences are described by common one-word terms.)

2) If you say X or N must be very large, does this prove that you measure torture and fun using in effect different scales, and therefore are a deontologist rather than a utilitarian?

Not in and of itself. That proof would also require knowing that this deviates from the actual utility assigned to each state. Without knowing those numbers you can only draw inferences that they are probably deontologists based on estimating the implausibility of the implied utility evaluations.

Mind you, the vast majority of people claiming to be utilitarian do seem to be deontologists, regardless of their verbal expressions to the contrary.