4. is strange.

Is it equivalent for 2 persons to have 0 utility vis a vis 1 person to have +10 utility and 1 person to have -10 utility, that is to have 1 very rich person and 1 slave ?

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what do you mean by perfectly moral in 1. & 2.?

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You are "hiding" an important assumption that is not necessarily true:

0. There exists a perfectly moral third party.

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They might be basic but all of them are pretty controversial and non-obvious. Maybe I’m confused over the intention of this post.

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First two principles just imply consequentialism. Thus, in order for all of the principles to imply Utilitarianism, the last two principles must be sufficient to imply that Consequentialism implies Utilitarianism. In other words, principles 3 and 4 must imply the following: the act that makes the world best is the act that maximizes utility.

But principles 3 and 4 don't imply that. Because these principles don't rule out the possibility of factors other than utility that make the world better. Presumably by utility you just mean a unit of well-being, as Utilitarianism is a welfarist theory. In that case, the latter two principles are not sufficient to show that non-welfarist considerations are irrelevant.

The last two principles are sufficient to show that, when comparing the goodness of two states of affairs, the state of affairs with greater total utility is better *with respect to utility*. Because I'm reading (4) as just stating that _total_ utility is the only relevant factor when evaluating the goodness of states of affairs. And (3) further implies that _more_ total utility is better than less total utility.

If you added another principle which stipulated that non-utility concerns are irrelevant to the goodness of the world, then we maybe could derive Utilitarianism from these principles. We could do something like this:

1. One should do what perfectly moral third parties would prefer they do.

2. For any possible events, perfectly moral people should prefer the better one occur rather than the worse one.

3. If something is better for some and worse for none, it is better overall.

4. Distribution of utility across people is irrelevant as long as the utility is fixed (so, for example, it’s just as good for three people to have 3 utility as for one person to have 9).

5. The goodness of a given state of affairs is determined solely by the goodness of its utility distribution.

6. (from 1, 2) Agents should do what produces the best state of affairs (consequentialism)

7. (from 3, 4) For any two utility distributions A and B, A is better than B if and only if A has greater total utility.

8. (from 5, 7) For any two states of affairs A and B, A is better than B if and only if A has greater total utility.

9. (from 6, 8) Agents should do whatever produces the greatest total utility.

There's also a few tweaks to make here to make it technically valid (e.g., you use "would" for the first principle but "should" in the second principle), but the general idea is valid. Of course, all of the principles (except for maybe 3) are contestable.

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