PlatypusNinja comments on Total Utility is Illusionary - Less Wrong
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If you look at the sum of all of the actions if you choose option A minus the sum of all the actions if you take option B, then all of the actions until then will cancel out, and you get just the difference in utility between option A and option B. They're equivalent.
Technically, delta utilitarianism is slightly more resistant to infinities. As long as any two actions have a finite difference, you can calculate it, even if the total utility is infinite. I don't think that would be very helpful.
I think the key difference is that delta utilitarianism handles it better when the group's utility function changes. For example, if I create a new person and add it to the group, that changes the group's utility function. Under delta utilitarianism, I explicitly don't count the preferences of the new person when making that decision. Under total utilitarianism, [most people would say that] I do count the preferences of that new person.
You only count their preferences under preference utilitarianism. I never really understood that form.
If you like having more happy people, then your utility function is higher for worlds with lots of happy people, and creating happy people makes the counter go up. If you like having happier people, but don't care how many there are, then having more people doesn't do anything.