Stuart_Armstrong comments on Example population ethics: ordered discounted utility

Stuart_Armstrong 11 Mar 2019 20:47 UTC
4 points
EDIT: I realised I wasn’t clear that the sum was over everyone that ever lived. I’ve clarified that in the post.

Killing people with future lifetime non-negative utility won’t help, as they will still be included in the sum.

Another issue is that two individuals with the same unweighted utility can become victims of the ordering

No. If $a = b$ , then $a + γ b = b + γ a$ . The ordering between identical utilities won’t matter for the total sum, and the individual that is currently behind will be prioritised.
- Evan Clark 11 Mar 2019 21:20 UTC
  1 point
  Parent
  My mistake with respect to the sum being over all time, thank you for clarifying.
  No. If a=b, then a+γb=b+γa. The ordering between identical utilities won’t matter for the total sum, and the individual that is currently behind will be prioritised.
  While the ordering between identical utilities does not affect the total sum, it does affect the individual valuation. a can be prioritized over b just by the ordering, even though they have identical utility. Unless I am missing something obvious.
  - Stuart_Armstrong 13 Mar 2019 12:21 UTC
    2 points
    Parent
    
    a can be prioritized over b just by the ordering, even though they have identical utility.
    
    Nope. Their ordering is only arbitrary as long as they have exactly the same utility. As soon as a policy would result in one of them having higher utility than the other, their ordering is no longer arbitrary. So if we ignore other people $u_{a} < u_{b}$ means the term in the sum is $u_{a} + γ u_{b}$ . If $u_{a} > u_{b}$ , it’s $u_{b} + γ u_{a}$ . If $u_{a} = u_{b}$ , it can be either term (and they are equal).
    
    (I can explain in more detail if that’s not enough?)
    - Evan Clark 13 Mar 2019 19:30 UTC
      3 points
      Parent
      I have realized that I am coming off like I don’t understand algebra, which is a result of my failure to communicate. As unlikely as I am making it sound, I understand what you are saying and already knew it.
      What I mean is this:
      Despite a = b, it could “look like” a < b or b > a if you didn’t have access to the world but only to the (expanded) sum. If you can ask for the difference between the total sum and the sum ignoring a, but not for the actual value of a.
      I can’t think of a non-pathological case where this would actually matter, but it seems like a desirable desideratum that a = b will always “look like” a = b regardless of what kind of (sufficiently fine-grained) information that you have.
      EDIT : After reading your above comment about willingness to sacrifice elegance, I kind of wish I hadn’t said anything at all, considering my comments are all in the interest of what I would consider elegance. To be sure, I think elegance is a legitimate practical concern, but I wouldn’t have engaged with you initially had I known your view.
      - Stuart_Armstrong 14 Mar 2019 12:57 UTC
        2 points
        Parent
        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 $U (W)$ ; small changes to our knowledge of $u_{a}$ and $u_{b}$ make small changes to our estimate of $U (W)$ .
        
        I’m not really sure what stronger condition you could want; after all, when $u_{a} = u_{b}$ , we can always write
        
        $\dots + γ^{n} u_{z} + γ^{n + 1} u_{a} + γ^{n + 2} u_{b} + γ^{n + 3} u_{c} + \dots$
        
        as:
        
        $\dots + γ^{n} u_{z} + \frac{γ^{n + 1} + γ^{n + 2}}{2} (u_{a} + u_{b}) + γ^{n + 3} u_{c} + \dots$ .
        
        We could equivalently define $U (W)$ that way, in fact (it generalises to larger sets of equal utilities).
        
        Would that formulation help?
        
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