A Thought on Pascal's Mugging

komponisto

For background, see here.

In a comment on the original Pascal's mugging post, Nick Tarleton writes:

[Y]ou could replace "kill 3^^^^3 people" with "create 3^^^^3 units of disutility according to your utility function". (I respectfully suggest that we all start using this form of the problem.)

Michael Vassar has suggested that we should consider any number of identical lives to have the same utility as one life. That could be a solution, as it's impossible to create 3^^^^3 distinct humans. But, this also is irrelevant to the create-3^^^^3-disutility-units form.

Coming across this again recently, it occurred to me that there might be a way to generalize Vassar's suggestion in such a way as to deal with Tarleton's more abstract formulation of the problem. I'm curious about the extent to which folks have thought about this. (Looking further through the comments on the original post, I found essentially the same idea in a comment by g, but it wasn't discussed further.)

The idea is that the Kolmogorov complexity of "3^^^^3 units of disutility" should be much higher than the Kolmogorov complexity of the number 3^^^^3. That is, the utility function should grow only according to the complexity of the scenario being evaluated, and not (say) linearly in the number of people involved. Furthermore, the domain of the utility function should consist of low-level descriptions of the state of the world, which won't refer directly to words uttered by muggers, in such a way that a mere discussion of "3^^^^3 units of disutility" by a mugger will not typically be (anywhere near) enough evidence to promote an actual "3^^^^3-disutilon" hypothesis to attention.

This seems to imply that the intuition responsible for the problem is a kind of fake simplicity, ignoring the complexity of value (negative value in this case). A confusion of levels also appears implicated (talking about utility does not itself significantly affect utility; you don't suddenly make 3^^^^3-disutilon scenarios probable by talking about "3^^^^3 disutilons").

What do folks think of this? Any obvious problems?

For background, see here.

In a comment on the original Pascal's mugging post, Nick Tarleton writes:

[Y]ou could replace "kill 3^^^^3 people" with "create 3^^^^3 units of disutility according to your utility function". (I respectfully suggest that we all start using this form of the problem.)

Michael Vassar has suggested that we should consider any number of identical lives to have the same utility as one life. That could be a solution, as it's impossible to create 3^^^^3 distinct humans. But, this also is irrelevant to the create-3^^^^3-disutility-units form.

What do folks think of this? Any obvious problems?

I looked back through and see that I indeed did not actually give a number. My sincere apologies for this. Not greater than 1 in 3E22.

(1E31x2E17=2E48 LHC-level collisions since the formation of the Universe, and yet everything we can see in the sky is still there. 3E22 LHC-level collisions, or ~1E6 LHC experimental lifetimes, with Earth itself in 4.5E9 years. "There is no indication that any of these previous 'LHC experiments' has ever had any large-scale consequences. The stars in our galaxy and others still exist, and conventional astrophysics can explain all the astrophysical black holes detected. Thus, the continued existence of the Earth and other astronomical bodies can be used to constrain or exclude speculations about possible new particles that might be produced by the LHC." They do commit the fatal error of assuming that a negligible probability means "impossible", so therefore the paper should of course be ignored.)

1/3E22 seems hugely overconfident.

20Scott Alexander15y

Sorry, I know I said I'd stop, and I will stop after this, but that 3E22 number is just too interesting to leave alone. The last time humanity was almost destroyed was about 80,000 years ago, when a volcanic eruption reduced the human population below 1,000. So say events that can destroy humanity happen on average every hundred thousand years (conservative assumption, right?). That means the chance of a humanity-destroying event per year is 1/100,000. Say 90% of all humanity destroying events can be predicted with at least one day's notice by eg asteroid monitoring. This leaves hard-to-detect asteroids, sudden volcanic eruptions, weird things like sudden methane release from the ocean, et cetera. So 1/1 million years we get an unexpected humanity destroying event. That means the "background rate" of humanity destroying events is 1/300 million days. Suppose Omega told you, the day before the LHC was switched on, that tomorrow humankind would be destroyed. If 1/3E22 were your true probability, you would say "there's still vastly less than one in a billion chance the apocalypse has anything to do with the LHC, it must just be a coincidence." Even if you were the LHC project coordinator, you might not even bother to tell them not to switch on the project, because it wasn't worth the effort it would take to go to the telephone. Let's look at it a different way. Suppose a scientist has a one in a thousand chance of having a psychotic break. Now suppose the world's top physicist, so brilliant as to be literally infallible as long as he is sane, comes up with new calculations that say the LHC will destroy the world. Suppose you ask the world's best psychiatrist, who also is literally never wrong, whether the physicist is insane, and she says no. If your probability is truly 1/3E22, then it is more likely that both the physicist and the psychiatrist have simultaneously gone insane than that the physicist is correct; what is more, even if you have no other evidence bearin