Most of the usual thought experiments that justify expected utilitarialism trade off fun for fun, or suffering for suffering. Here's a situation which mixes the two. You are offered to press a button that will select a random person (not you) and torture them for a month. In return the machine will make N people who are not suffering right now have X fun each. The fun will be of the positive variety, not saving any creatures from pain.
1) How large would X and N have to be for you to accept the offer?
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?
There's something that's always bothered me about these kinds of utilitarian thought experiments.
First of all, I think it's probably better to speak in terms of pain rather than torture. We can intelligently discuss trade offs like this in terms of, "I'm going to punch someone" or "I'm going to break someone's leg. How much fun would it take to compensate for that?". Torture is another thing entirely.
If you have a fun weekend, then you had an enjoyable couple of days. Maybe you gained some stories that you can tell for a month or two to your friends who weren't with you. If it was a very fun weekend, you might have learned something new, like how to water ski, something that you'll use in the future. Overall, this is a substantial positive benefit.
If you torture someone for half an hour, not even an entire weekend, it's going to have a much larger effect on someone's life. A person who is being tortured is screaming in agony, flailing around, begging for the pain to stop. And it doesn't. Victims of torture experience massive psychological damage that continues for long after the actual time of the act. Someone who's tortured for half an hour is going to remember that for the rest of their lives. They may have nightmares about it. Almost certainly, their relationships with other people are going to be badly damaged or strained.
I've never been tortured. I've never been a prisoner of war, or someone who was trying to withhold information from a government, military, or criminal organization who wanted it. I have lived a pretty adventurous life, with sports, backpacking, rock climbing, etc. I've had some fairly traumatic injuries. I've been injured when I was alone, and there was nobody within earshot to help me. At those times, I've just lain there on the ground, crying out of pain, and trying to bring myself to focus enough to heal myself enough to get back to medical care. Those experiences are some of the worst of my life. I have an hard time trying to access those memories; I can feel my own mind flinching away from them, and despite all of my rationality, I still can't fight some of those flinches. What I experienced wasn't even all that terrible. They were some moderate injuries. Someone who was tortured is going to have negative effects that are ridiculously worse than what I experienced.
I've spent some time trying to figure out exactly what it is about torture that bothers me so much as a utilitarian, and I think I've figured it out, in a mathematical sense. Most utilitarian calculations don't factor in time. It's not something that I've seen people on less wrong tend to do. It is pretty obvious, though. Giving someone Y amount of pain for 5 minutes is better than giving them Y amount of pain for 10 minutes. We should consider not just how much pain or fun someone's experiencing now, but how much they will experience as time stretches on.
Getting back to the original question, if I could give three or four people a very fun weekend, I'd punch someone. If I could give one person an extremely fun weekend, I'd punch someone. I'd punch them pretty hard. I'd leave a bruise, and make them sore the next day. But if I'm torturing someone for a month, I am causing them almost unimaginable pain for the rest of their life. X and N are going to have to be massive before I even start considering this trade, even from a utilitarian standpoint. I can measure pain and fun on the same scales, but a torture to fun conversion is vaguely analogous to comparing light years to inches.
I don't know about you, but if I didn't have at least one bruise and feel sore after a weekend of extreme fun then I'd start to think I was doing it wrong. ;)