Ask yourself if you would want to revive someone frozen 100 years ago.

Yes. They don't deserve to die. Kthx next.

I wish that this were on Less Wrong, so that I could vote this up.

Garrett, since Anonymous reply was a little implicit, the point is that infants have a larger chance of dying before reproducing than young adults, so expected number of future offspring increases during childhood (when at each point counting only non-deceased children).

Aron, almost; it's because they get older, and only future children are relevant. Whether they've had children won't change the value except insofar it changes the chance for future children.

Me: ...so IIUC, we expect a large influence of random variation in the sample.

Bzzzt! Wrong.

Upon more careful reading and thinking, what I understand the authors to be doing is this. They ask 436 Canadian subjects to imagine that two sons or two daughters of different specified ages died in a car accident, and ask which child the subject thinks the parent would feel more grief for. They then use the Thurstone scaling procedure to obtain a grief score for each age (1 day; 1, 2, 6, 10, 13, 17, 20, 30, 50 years).

They say that the procedure gives highly replicable results, and they have that large sample size, so no big sampling effects expected here.

They then correlate this data with reproduction value data for the same ages for the !Kung, which they got from: Howell, N. Demography of the Dobe !Kung, New York: Academic Press, 1979. This is not a random sample, it's for the whole population, so no sampling effects there.

So replication with the same populations should give a very similar result. My original argument still applies, in that the high correlation may in part be due to the choice of populations, but I was completely wrong in expecting sampling effects to play a role.

Also, I realize now that I can't really judge how extreme the correlation is (though I'll happily defer to those who say it is very large): it's too different from the usual kind of correlation in Psychology for my fledgling feeling for correlation values to apply. The usual kind of study looks at two values for each experimental subject (e.g. IQ vs. rating of looks) where this study looks at two values (Canadian ratings and !Kung reproductive value) for each of the ten age groups. In the usual kind of study, correlations >0.9 are suspiciously high, because, AFAIR, if you administer the same psychological instrument to the same subjects twice, a good correlation between the two tests is ~0.8, which means the noise from testing is just too large to get you a correlation >0.9. This obviously doesn't apply to the present study's design.

Eliezer, right, thanks. And I hadn't noticed about the correlations of the subcategories...

Might we get an even higher correlation if we tried to take into account the reproductive opportunity cost of raising a child of age X to independent maturity, while discarding all sunk costs to raise a child to age X?

I haven't done the math, but my intuition says that upon observing the highest! correlation! ever!, surely our subjective probability must go towards a high true underlying correlation and having picked a sample with a particularly high correlation? (Conditioning on the paper not being wrong due to human error or fake, of course -- I don't suspect that particularly, but surely our subjective probability of that must go up too upon seeing the !!!.) If this is correct, it seems that we should expect to see a lower correlation for the modified design, even if the underlying effect is actually stronger.

(If I'm making a thinko somewhere there, please do tell... I hope to Know My Stuff about statistics someday, but I'm just not there yet :))

Do note that the correlation is, IIUC, between the mean Canadian rating for a given age and the mean reproductive value of female !Kung of a given age, meaning that "if the correlations were tested, the degrees of freedom would be (the number of ages) - 2 = 8, not (the number of subjects - 2) as is usually the case when testing correlations for significance", so IIUC, we expect a large influence of random variation in the sample. (The authors don't actually provide p-values for the correlations.) That's not surprising, really; if the highest! correlation! ever! came from an experiment that did not allow for significant influence of random effects (because of really large sample size, say), that should make us suspicious, right? (Because if there were real effects that large, there should be other people investigating similarly large effects with statistically weaker methods, and thus occasionally getting even more extreme results?)

Any chance you'd consider installing jsMath? (Client-side library rendering LaTeX math. Formatting math in plain HTML won't kill you, but there are other things you can do with the same amount of effort that will make you stronger still :-))

We might even cooperate in the Prisoner's Dilemma. But we would never be friends with them. They would never see us as anything but means to an end. They would never shed a tear for us, nor smile for our joys. And the others of their own kind would receive no different consideration, nor have any sense that they were missing something important thereby.

...but beware of using that as a reason to think of them as humans in chitin exoskeletons :-)

Robin, I suspect that despite how it may look from a high level, the lives of most of the people you refer to probably do differ enough from year to year that they will in fact have new experiences and learn something new, and that they would in fact find it unbearable if their world were so static as to come even a little close to being video game repetitive.

That said, I would agree that many people seem not to act day-to-day as if they put a premium on Eliezer-style novelty, but that seems like it could be better explained by Eliezer's boredom being a FAR value than by the concept being specific to Eliezer :-)

*thinks* -- Okay, so if I understand you correctly now, the essential thing I was missing that you meant to imply was that the utility of living forever must necessarily be equal to (cannot be larger than) the limit of the utilities of living a finite number of years. Then, if u(live forever) is finite, p times the difference between u(live forever) and u(live n years) must become arbitrarily small, and thus, eventually smaller than q times the difference between u(live n years) and u(live googolplex years). You then arrive at a contradiction, from which you conclude that u(live forever) = the limit of u(live n years) cannot be finite. Okay. Without the qualification I was missing, the condition wouldn't be inconsistent with a bounded utility function, since the difference wouldn't have to get arbitrarily small, but the qualification certainly seems reasonable.

(I would still prefer for all possibilities considered to have defined utilities, which would mean extending the range of the utility function beyond the real numbers, which would mean that u(live forever) would, technically, be an upper bound for {u(live n years) | n in N} -- that's what I had in mind in my last paragraph above. But you're not required to share my preferences on framing the issue, of course :-))

Given how many times Eliezer has linked to it, it's a little surprising that nobody seems to have picked up on this yet, but the paragraph about the utility function not being up for grabs seems to have a pretty serious technical flaw:

There is no finite amount of life lived N where I would prefer a 80.0001% probability of living N years to an 0.0001% chance of living a googolplex years and an 80% chance of living forever. This is a sufficient condition to imply that my utility function is unbounded.

Let p = 80% and let q be one in a million. I'm pretty sure that what Eliezer has in mind is,

(A) For all n, there is an even larger n' such that (p+q)*u(live n years) < p*u(live n' years) + q*(live a googolplex years).

This indeed means that {u(live n' years) | n' in N} is not upwards bounded -- I did check the math :-) --, which means that u is not upwards bounded, which means that u is not bounded. But what he actually said was,

(B) For all n, (p+q)*u(live n years) <= p*u(live forever) + q*u(live googolplex years)

That's not only different from A, it contradicts A! It doesn't imply that u needs to be bounded, of course, but it flat out states that {u(live n years) | n in N} is upwards bounded by (p*u(live forever) + q*u(live googolplex years))/(p+q).

(We may perhaps see this as reason enough to extend the domain of our utility function to some superset of the real numbers. In that case it's no longer necessary for the utility function to be unbounded to satisfy (A), though -- although we might invent a new condition like "not bounded by a real number.")

(To be clear, the previous comment was meant as a joke, not as a serious addition to the list -- at least not as it stands :-))