Stuart_Armstrong comments on Example population ethics: ordered discounted utility

[Stuart_Armstrong]

Hum, not entirely sure what you’re getting at...

I’d say that $u_a=u_b$ always “looks like $u_a=u_b$”, in the sense that there is a continuity in the overall $U\left(W\right)$; small changes to our knowledge of $u_a$ and $u_b$ make small changes to our estimate of $U\left(W\right)$.

I’m not really sure what stronger condition you could want; after all, when $u_a=u_b$, we can always write

• $\dots +{\gamma }^n{u}_z+{\gamma }^{n+1}{u}_a+{\gamma }^{n+2}{u}_b+{\gamma }^{n+3}{u}_c+\dots$

as:

• $\dots +{\gamma }^n{u}_z+\frac{{\gamma }^{n+1}+{\gamma }^{n+2}}{2}(u_a+u_b)+{\gamma }^{n+3}{u}_c+\dots$.

We could equivalently define $U\left(W\right)$ that way, in fact (it generalises to larger sets of equal utilities).

Would that formulation help?

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