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matt comments on Bayesians vs. Barbarians - Less Wrong
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As a soldier you're not facing certain death at any of the relevant decision points (a statistically irrelevant number of exceptions exist to this rule). You're facing some probability of death. When you get into your car or onto your bike you're facing some probability of death. Why do you do that? Commanders don't (irrelevant exceptions exist) send troops to certain death, because, rationalist or not, they don't go. War is not like StarCraft.
Eliezer's point is that, given a certain decision theory (or, failing that, a certain set of incentives to precommitment), rational soldiers could in fact carry out even suicide missions if the tactical incentives were strong enough for them to precommit to a certain chance of drawing such a mission.
This has actually come up: in World War II (citation in Pinker's "How the Mind Works"), bomber pilots making runs on Japan had a 1 in 4 chance of survival. Someone realized that the missions could be carried out with half the planes if those planes carried bombs in place of their fuel for the return trip; the pilots could draw straws, and half would survive while the other half went on a suicide mission. Despite the fact that precommitting to this policy would have doubled their chances of survival, the actual pilots were unable to adopt this policy (among other things, because they were suspicious that those so chosen would renege rather than carry out the mission).
I think Eliezer believes that a team of soldiers trained by Jeffreysai would be able to precommit in this fashion and carry the mission through if selected. I think that, even if humans can't meet such a high standard by training and will alone, that there could exist some form of preparation or institution that could make it a workable strategy.
I'll need to see that citation, actually; it couldn't possibly have been a 75% fatality rate per mission. (When my father says a number is bogus, he's usually right.) Even Doolittle's raid, in which the planes did not have enough fuel to return from Japan but instead had to land in Japan-occupied China, had a better survival rate than one in four: of the 80 airmen involved, 4 were killed and 8 were captured. (Of the eight who were captured, four died before the war ended.)
Correction- it's for a pilot's entire quota of missions, not just one:
Yeah, if it's for an entire quota of missions, the math doesn't work out - each pilot normally would fly several missions, making the death rate per flight less than 50%, so it wouldn't be a good deal.
Let's say somebody who flies out with extra bombs instead of fuel has an overall 0.1% chance of making it back alive through some heroic exploit. Under the existing system, with 25% survival, you're asking every pilot to face two half-lives worth of danger per mission. With extra bombs, that's half as many missions, but each mission involves ten half-lives worth of danger. Is it really all that rational to put the pilots in general in five times as much danger for the same results? After all, drawing the long straw doesn't mean you're off the hook. Everybody's going to have to fly a mission sooner or later.
Thinking in terms of "half-lives of danger" is your problem here; you're looking at the reciprocal of the relevant quantity, and you shouldn't try and treat those linearly. Instead, try and maximize your probability of survival.
It's the same trap that people fall into with the question "if you want to average 40 mph on a trip, and you averaged 20 mph for the first half of the route, how fast do you have to go on the second half of the route?"
How do you answer this question?
Edit: MBlume kindly explained offsite before the offspring comments were posted. Er, sorry to have wasted more people's time than I needed.
It's still an interesting exercise to try to come up with the most intuitive explanation. One way to do it is to start by specifying a distance. Making the problem more concrete can sometimes get you away from the eye-glazing algebra, though of course then you need to go back and check that your solution generalizes.
A good distance to assign is 40 miles for the whole trip. You've gone 20 mph for the first half of the trip, which means that you traveled for an hour and traveled 20 miles. In order for your average speed to be 40 mph you need to travel the whole 40 miles in one hour. But you've already traveled for an hour! So - it's too late! You've already failed.
Yes, that's roughly how MBlume explained it (edited for concision and punctuation):
If that's an actual chat record, I'm getting old for this world. ... okay, on a third read-through, I'm starting to comprehend the rhythm and lingo.
The original had more line breaks and less punctuation, but it's real - what do you mean?
It felt like I was following, say for analogy, a discussion among filipinos who were switching back and forth between English and Tagalog. But re-reading it twice I started to get the flow and terms. E.g. "nodnod" was opaque initially.
Suppose the total trip is a distance d.
So if your average speed is 40 (mph), your total time is d/40.
You have already travelled half the distance at speed 20 (mph), so that took time (d/2)/20 = d/40. Your time left to complete the trip is your total time minus the time spent so far: d/40 - d/40 = 0. In this time you have to travel the remaining distance d/2, so you have travel at a speed (d/2)/0 = infinity, which means it is impossible to actually do.
Let t1 be the time taken to drive the first half of the route.
Let t2 be the time taken to drive the second half.
Let d1 be the distance traveled in the first half.
Let d2 be the distance traveled in the second half.
Let x be what we want to know (namely, the average speed during the second half of the route).
Then the following relations hold:
40 * (t1 + t2) = d1 * d2.
20 * t1 = d1.
x * t2 = d2.
d1 = d2.
Use algebra to solve for x.
To average 40 mph requires completing the trip in a certain amount of time, and even without doing any algebra, I notice that you will have used all of the available time just completing the first half of the trip, so you're speed would have to be infinitely fast during the second half.
I am pretty confident in that conclusion, but a little algebra will increase my confidence, so let us calculate as follows: the time you have to do the trip = t1 + t2 = d1 / 40 + d2 / 40, which (since d1 = d2) equals d1 / 20, but (by equation 2) d1 / 20 equals t1, so t2 must be zero.
I expect a high probability of this explanation being completely useless to someone who professes being bad at math. Their eyes are likely to glaze over before the half way point and the second half isn't infinitely accessible either.
I already had the problem explained to me before I saw the grandparent, but I think you're right - I might have been able to puzzle it out, but it'd have been work.
Well, in the department of actual running, I have some kind of mysterious lung issue that means I need to gasp for air a lot even when I'm sitting still and have been for hours and it only gets worse if I try to do exercise more strenuous than a leisurely walk. (Armchair diagnoses appreciated, incidentally - so far I've stumped multiple doctors and new Google keywords are good.)
Here is something like the thought process that goes through my head when I encounter a problem of this approximate type:
I know what all those words mean. I could come up with a toy scenario and see what's interesting about this problem, that someone bothered to bring it up.
It might be the sort of question where coming up with one toy scenario doesn't answer it because for some reason it doesn't generalize. Like it could have to do with the distance. I don't want to come up with five different distances and work it out for all of them. I'd probably make an arithmetic mistake anyway. I can barely compose a mathematically accurate D&D character, and I'm way more motivated there than here. I'm not interested enough in this to do it in a calculator and then re-read the ticker tape. My eyes are swimming just thinking about it.
And because I'm not good at this, I would be reasonably likely to get it wrong, and then, no matter how much time I'd put into it myself, I would need to ask someone. I could get help if I asked. I am cute and friendly and there are helpful people around. I could get help even if I didn't work on it myself. That would be faster, and then I'd know the answer, and I have to ask anyway, so why not just ask? Why not save the work, and not risk wasting a lot of time on getting a wrong answer and having to stare at all those numbers?
I have to agree that a shorter explanation with just words in it would be bettter for someone with significant aversive math conditioning.
It also doesn't help the explanation when you make an error. That should be d1 + d2.
Acknowledged.
The probability of drawing the long straw twice in a row is four times as high as the probability of making it back twice in a row given 25% survival.
How did Japan convince pilots to be kamikazes?
Chiefly by a code of death-before-dishonor (and death-after-dishonor) which makes sense for a warring country to precommit to. Though it doesn't seem there was much conscious reasoning that went into the code's establishment, just an evolutionary optimization on codes of honor among rival daimyo, which resulted in the entire country having the values of the victorious shoguns instilled.
I'm no history expert, but I remember hearing something about cutting off a finger and promising to kill anyone that shows up missing that finger.
For example, I suspect Jeffreysai would have no trouble proposing that anyone designated for a suicide mission who reneged would be tortured for a year and then put to death.