Bounded total utilitarianism (obviously a draft)

I like my utility functions bounded, and my utilitarianisms total. Wait, fuck.

What do

Let’s try to construct a moral theory that is like total utilitarianism when choosing between deterministic universes, but the utility assignments of which are bounded. Let the set of universes be \(S\), and the total utilitarian utility function be \(u\colon S\to \mathbb{R}\). (Feel free to think of this as the total amount of pleasure minus pain in the universe, or whatever other formulation of totalism you prefer.)

The bad

Since our utility function is bounded, we are bound to run into some of the issues discussed in sections 4, 5, 6 of Wilkinson’s In defence of fanaticism

The good

Local non-egyptologicality

Other good properties

Other than being bounded and thus avoiding issues with unbounded utility functions, here are some additional properties of our utility function that some would consider nice. I guess it’s possible to view each of these as just avoiding a problem with unbounded utility functions, but it’s probably helpful to spell these out anyway.

• Robustness to the world-doubling button. rejects this (for sufficiently large values of utility): “Tyler Cowen’s variant of the St. Petersburg paradox is one objection to utilitarianism that I accept as a serious problem. Suppose you are offered a deal - you can press a button that has a 51% chance of creating a new world and doubling the total amount of utility, but a 49% chance of destroying the world and all utility in existence (let’s assume that there are no aliens in the universe, or alternatively that the button also doubles the number of aliens or something). If you want to maximise total expected utility, you ought to press the button - after all, the button is rigged in your favour and so pressing the button has positive expected value.”
• Robustness to Pascal’s mugging. I’m a beggar with the sign “if you give me $1, I will save \(3 \uparrow \uparrow \uparrow \uparrow 3\) people from great suffering”. Should you pay yp? Well, maybe you should and maybe you shouldn’t, but intuitively the decision should not be motivated by you actually expecting me to save \(3 \uparrow \uparrow \uparrow \uparrow 3\) people. With reasonable priors and reasonable updating, bounded totalism agrees with both common-sense verdicts here.

The ugly

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Acknowledgments

I would have been very surprised if no one had proposed this earlier, but a moderate amount of searching turned up nothing except for . Even still, I would be surprised to learn that no one has proposed this earlier. If anyone can point me to someone who has proposed this earlier, I would be happy to