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Nebu comments on Bayesians vs. Barbarians - Less Wrong
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What about just paying them to fight? You can have an auction of sorts to set the price, but in the end they'd select themselves. You could still use the courage enhancing drugs and shoot those who try to breach the contract.
One might respond "no amount of (positive) money could convince me to fight a war", but what about at some negative amount? After all, everyone else has to pay for the soldiers.
The problem with this idea is that I have a very strong expectation that the barbarians are going to kill me, then no amount of money would convince me to fight. Even if you enforce payment from all the non-fighters, I still wouldn't fight. Better to incur a trillion dollars of debt than to die, right? Especially if everyone else around me also incurs a trillion dollars of debt such that after the war, we all agree that this debt is silly and nullify it.
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.
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.
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.
Well, that's exactly the objection I tried to cover with the second half of my comment.
The thing is that you're assuming that it won't actually be paid so that there effectively is no debt or pay. Under that assumption of course it won't work, since you're not actually doing it.
The debt is not silly, it's a way of saving your country. If you have good debt collectors, and you owe enough you'll want to fight. Use your imagination.
In the few cases where the probability of dying is near one instead of near zero, being as productive as possible and getting just enough money to survive out (third world type real poor, not "poor" american kind) might still be better than dying. In these cases you'd basically have to punish people that can't pay instead of helping them pay as much as they can.
Then you are suffering strongly from the Bystander-effect. http://en.wikipedia.org/wiki/Bystander_effect
One could translate this effect as "the warm fuzzy feeling that there are enough people around which will do the job and oneself doesn't need to bother".
The effect is very strong. So, adjust your thoughts: The barbarians will kill you either way. There aren't enough people which care, so you yourself have to rise to do something. (That also applies to everyday life: If you want something done, especially in a busy and people-rich environment, do it yourself.)