"At this point we're just assuming that you have any guess about what it's worth to them.  Ah, but before I move on along the path, it seems prudent to include any warnings about stuff they warned us hard about, so..."

Civilization emphasizes really hard to kids at this point that, when you reject a 7:5 split with probability <6/7, you're not trying to spitefully punish the person, just make sure that their incentive curve slopes slightly downward as it moves away from what you think is fair.  If you were trying to spite them in accordance with base instinct, you'd reject with probability a bit greater than 5/7, so that they lost almost as much as they tried to gain at your expense (even spiteful entities, obviously, will still subtract epsilon from their spiteful punishments to avoid the possibility of infinite resonating spitefights that even they don't want).

Keltham has no particular reason to think Chelaxians are likely to make that particular error, but dath ilan emphasizes it hard to children, so it's probably important or a plausible error that somebody might otherwise make.

"....because there's no benefit in spitefully punishing shoesellers or fellow-students for wanting to trade with you?"

"What would the benefit be?  I think the point of the warnings is that there's this thing built into human nature where our ancient ancestors mated and reproduced under conditions where people hitting each other and hitting back was much more of an equilibrium, and now we have instincts that are about that.  But incentivizing fair strategies in the Ultimatum game is not about that, it is a different structure that reflects a different bit of math than the non-ideal pseudo-equilibrium bit of math that got incarnated into hitting people back when they hit you.  But-but it involves somebody else doing something you think is unfair, and then you make sure you do something that causes them to lose some expected value, even if that thing is just not trading with them.  So it's the sort of thing that could map onto the hitting-back instinct, if you weren't specifically warned not to map it onto the hitting-back instinct."

"Imagine that room full of children if you told them that, any time somebody made them an unfair offer and tried to cheat them, they ought to hit back in a way that made sure the person lost even more value than they tried to steal, to teach them a lesson, no matter how much more that cost their own position in expected value.  Those kids wouldn't grow up to be dath ilan's Civilization.  Possibly they wouldn't grow up to be any civilization at all."

The room full of Chelish students nods seriously. The children would try to hit someone and that someone would cave their skulls in and that'd be a waste of a lot of state resources educating those children.

This is only true if you have a very limited conception of hitting back, Carissa thinks. She isn't sure, not yet, but - it really does feel like there's a way to lock an additional piece on, a way that you can get even cleaner and higher-performing results with fewer deals walked-away-from, less value left on the table. If you're not Good and unwilling to do anything that's punishment, if you think you have some duty to keep people in the game when in reality they were born into the game and the only way out of it is their utter destruction. The whole point of pain - possibly not the whole point of pain, but a lot of it - is that it's a deterrent that can be delivered without destroying any value at all. Dath ilan doesn't have one of those, so all the rules have to assume that there isn't one...

Onward in the sequence.  On the next day the children are introduced to their first sophisticated trading-game with tokens that produce varying quantities of jellychips in the presence of other tokens, and which, brought together in sufficient quantity, can even produce more tokens.

Despite everything the kids have learned, the game collapses quickly and with an escalating level of shouting.  What do you guess the kids do wrong?

" - tried to do central planning without a command structure?"

"...you know, I think that thought never occurred to a single one of us.  To be fair, we weren't paying very much attention at that age to how the Legislative or Executive branches of Governance were set up, but I guess we knew enough to elect a leader with some simple ranked voting system?  It would have made sense to try that, not knowing any better solutions, but we didn't."

"What actually goes wrong is that children with rare tokens decide that rarity is the key determinant of fair cost, children with tokens that directly produce a lot of jellychips decide that direct jellychip production should be the starting anchor on price, and children with tokens that can help produce more tokens think their tokens are way more valuable than anything else around."

It is good to hear dath ilani children described doing normal things like rationalizing their getting more stuff than other people. 

"Now, this is a problem mainly of the kids not having full power in their forward reflectors - that's the part of the brain that implements Wisdom, sort of, obviously it's more complicated than that.  Adults could just notice that internal self-favoring influence and switch it off.  When we get to the point of being able to run experiments like this in Cheliax with 18 Intelligence 7-year-old kids who've otherwise had an optimized upbringing, I predict that tapping them all with an Owl's Wisdom and telling them to try to avoid self-favoring biased estimates will be enough to get trade restarted."

"But that just leaves the obvious question - a biased estimate of what?  What defines the fair amount for each child to get, based on the tokens they hold, if we assume in-game that it's fair for them to start out holding those tokens?  There's no object-level effort, in this game, it's just about putting tokens down next to each other.  Nobody can be said to be trying any harder, nobody can be said to be trying any more efficiently.  The outcomes are perfectly predictable and perfectly measurable.  So what's fair?  How would Cheliax solve that problem?  - or how would you do it, if you think you know a way better than Cheliax's standard."

"You could - try to calculate what can be accomplished by all the tokens together, and then all the tokens minus any specific one, and that's that person's - share - though there's no reason to pay everyone that much - you could normalize it -"

"Not bad!  Especially for a first suggestion!  Now suppose I arrange matters such that every token's marginal contribution, defined exactly as you defined it, is zero.  Each of 12 people gets a token.  Any number of tokens from 0 to 10 will produce 0 jellychips, any group of 11 or 12 tokens produces 12 jellychips.  What now?"

"...well if you were a god you could calculate the token's marginal value in all possible subsets of all of the tokens and do something with that. Which I mention only because sometimes apparently if gods can do it dath ilan can too," Gregoria says. She's pretty sure once you've sold your soul you can just say things like that.

"If all the tokens are identical like that you probably just want to split evenly - I know that was just for the example but it'd simplify the math you have to do in the version Gregoria just proposed, if you treat interchangeable tokens as having the same payout -"

That was a faster progression to the Law-inspired answer than Keltham was expecting.  Maybe something about the exact way Keltham asked the question managed to prompt that answer?  Or maybe it really is the sort of thing where most arbitrary aliens will arrive at the same answer, which is a small piece of good news about the general cooperativity of Reality.

"Yes indeed; sometimes you can take an ideal-agent calculation whose naked specification is too large for even gods to compute, and either simplify it to an exact answer, or get a good and fast approximation of it."

Keltham whiteboards a sum over every possible permutation of 12 tokens, pausing to explain dath ilani math symbols like 'all permutations' and 'initial string up to first appearance of this symbol'.  For every possible order in which the tokens could be arranged, consider the marginal production that token adds, on the step it's added.  (0-10 produces 0, 11-12 produces 12.)  Then, divide that sum by the number of permutations.

"This sum has 479 million, 1 thousand, 6 hundred terms," Keltham says.  "I've already finished adding them up.  How are you doing on that?"

See if he'd said that yesterday no one would've bet against him being a sadist.

"The sum is also 479 million, 1 thousand, and whatever it was," Asmodia says.  People who aren't Keltham can tell that she's not saying it as triumphantly as she should be; to Keltham she is liable to sound exactly like the same cheerful person as always.

"Mm.  And you got that by?"

"Dividing 479 million, which is what you said, by twelve, and then multiplying by twelve."  If the others can't figure anything out from that it's their own damn problem.

- that'd work if every term is one? But they just agreed it wasn't?? But it - averages out to one? But how would you prove that?

No one voices any confusion, because they're too Chelish for that.

(Summary of what the fuck is up with Asmodia, from whoever is mindreading her, please.)

The poor dear really didn't want to go to Hell, tried praying to a nonspecific Good god to get her out of it in case Cheliax was lying about Good gods not doing that, and had an accordingly unpleasant evening afterwards.  If they'd known this group was going to be anything more than a welcoming gift for Keltham, they would have done better screening on her.

Does Sevar want to pull the trigger on replacing Asmodia?  There were over-one-half responses to Keltham that could allow one of the girls to later reveal she's a shapechanged adult.

She's considering it.

It's more lying.

(and - a thing Keltham'll be mad about even if she manages to bring him around on Evil generally, someone directly ending up worse off, if he ever does find out)

(probably that doesn't matter because they're not going to be able to bring Keltham around anyway)

On the other hand you really, really don't want bitter children with nothing to lose around your highly sensitive research project. 

The thing she wants is to talk to Asmodia but this isn't a non-heresy work situation at the Worldwound where sometimes someone just needs a drink and the casual but almost generous observation that they aren't special (and that therefore there are people who've survived being like them), there's too much at stake to go off her gut. 

Do we have a replacement candidate. Give them that math problem and see if they get it right.

Oh, Asmodia has plenty to lose now.  She did sign away her soul, as wasteful as that was, and her Hell can always get worse.

They'll try the obvious replacement candidates on that math problem.

(That is a significant ask, though.  Asmodia had the best scores in math, if not in wizardry generally, for this whole group.  If Asmodia had graduated normally she'd have been tracked for spell research and ritual support after her Worldwound tour, not Security.  Target-replacing Security operatives aren't usually tracked for mathematical talent; they're not usually replacing mathematicians.)

"The result has to be that," Ione states, "because everybody got the same kind of token, there are 12 jellychips to divide, there are 12 tokens, and obviously everybody should get one jellychip.  So if we're dividing by the number of permutations, the numerator has to be the number of permutations too."

"Well, yes," says Meritxell, "but if the reason we're learning it this way at all instead of just coming up with 'one jellychip a piece', which three-year-olds could do, is the permutations approach then we should be solving the sum instead of just noticing it has to get us the three-year-old answer. It does, though, since eleven in twelve of them are 'zero' and the twelfth is 'twelve'. ...I'm not sure that even gods are doing the full math all the time but maybe it's usually nearly that symmetrical."