"Hello; nice to meet you both."

Kevin offers a friendly wave from Marcy's other side, as does Abigail from a few seats further down where she's discussing alchemy with a sophomore.

Mari smiles at Marcy, turns to Kevin.

"I was hoping to get a chance to talk with you about Johan, who is doing maintenance for our freshmen. Some of my upperclassmen want him to take on two more people. He doesn't want to tell them no; I want to know if it would be safe. If not, I'll tell them no for him."

"Well, it kind of depends on how good he is, right? Both at the maintenance and at keeping up on his homework. Also, does he not want to tell them no because he wants what they're offering for the shifts, or because he doesn't want to be seen saying no?"

"He didn't know enough about it at the start to do a good job; I had to tell him things I learned from András, the senior maintenance person in Buda, before I came. But I haven't seen him working and I thought you might have. No problems with the homework yet, so far as I know, but it is still early and adding two more people — and they might want more — could change that.

"I think he doesn't want to offend our seniors. If you think ten is too many for a freshman to handle, or for him to handle, I will tell Imre that he can't have him. When it's time to get Johan out the gates Imre will be gone. I won't be."

"Ouch, yeah, I didn't realize he already had eight, I've only seen him a couple times. I'm thinking of going up to six but ten is kind of a lot."

"Thank you. I thought that might be the case from what András told me."

She turns back to Marcy.

"That was one of the reasons I was glad Franklin invited us. Also ..."

She glances with a smile at Ellen talking with Franklin about game theory.

"Have you looked at game theory? I was in the library with Mari and there was a boy who wanted to know about it — African, nice, it seemed like he didn't know much but was very bright and learning everything. He was even teaching himself Mandarin, which I haven't tried to do although maybe I should. Mari found Von Neumann and Morgenstern for him right on the shelf — she's good at finding things. I read the first few chapters last year and I thought maybe I could find it and read some more after he was finished with it — I wrote down where it was in the library, which might work."

"Game theory is awesome! A lot of math is useful for practical things, but game theory is the only math that's useful for politics."

"Sounds like they're getting along well, yes. Did you know each other outside?"

"We met a month and a half ago in a park in Budapest — I was there with my little sister. The second day a scratcher showed up — for some reason  the mundanes who are usually there were all somewhere else, and my escorts were paying attention to each other instead of us. I had a yanker that might have gotten me and Anna back to the Buda gate but before I had decided whether to trigger it I saw that Ellen was trying to head the scratcher off from us — casting, I don't know what, and when it tried to go around her moving to block it. Eventually someone, I think her escort, killed it, and Liza and Tamás noticed and showed up and made a fuss over us, and by the time that was over she was gone. When we got back to Buda I told my father what had happened.

"He knew who she was because her mother had been bargaining for one of our spare slots. He gave Ellen the slot instead of charging for it, and then her mother gave me the graduation outfit he had been planning to ask in exchange — she is a weaver, I think a famous one.

"So we became friends. Ellen is amazingly good at some things — she is fire affinity and trained at killing mals for a year before induction and she knows more math than anyone else I know, including adults. But I was the first friend she had — she was home schooled in a house and yard that her parents protected with wards of woven fire, and she hardly knew anyone but them. Her birthday was three days before induction, so she's almost a year younger than I am. Half the time I feel as though I'm taking care of her — it took her a while to realize that people don't always tell the truth, and when she thought another girl might be a maleficer but wasn't sure, she just asked her. But she thinks she's protecting me, and half the time I think so too.

"She's my favorite person."

"If Von Neumann had solved game theory it would be useful for all sorts of things — politics and economics and wars and games, everything that involves strategic behavior. But after he solved two player zero sum games, which are the easiest case, he spent the rest of the book looking for a general solution and not finding one. At least that's what Apa says — I never got much past the first few chapters.

"Other people since have tried other things but they either give ambiguous answers in the general case like Nash Equilibrium or depend on assuming away commitment strategies like Subgame Perfect Equilibrium or have something else wrong with them. Game theory gives you fun ways of thinking about problems but they don't tell you what the answer is, what will happen. Apa, who is very smart, says that when he is looking for problems to work on, problems that defeated John von Neumann go at the bottom of the pile."

"But maybe when I grow up ...

"Do you count statistics as math? It's useful for politics, at least the kind that involves elections. I read a book about that, about using statistics to figure out who was going to win an election or where to spend your money on winning one."

"Wow, what a way to meet someone. I can definitely relate to the part about protecting someone else half the time and the other half they're protecting you. Except we all grew up together and I know exactly who in the squad is the best at any given thing, and so does everyone else, so anything that needs doing gets done as well as any of us can so it.

Kevin practically has eyes in the back of his head; he can be totally focused on one thing one moment and reacting to something on the far side of the room the next. And he's probably the best artificer even if he can't explain where his mad genius ideas come from.

Franklin is the best at math, and the best at generating mana, and the best at coming up with interesting ways to use his affinity for stuff you would never think it would work for. Probably the best of us at paranoia, too.

Abigail is our alchemist, but she's also--well, we joke that she's the sane one. She's always got her own act completely together and she's always looking out for the rest of us too. If one of my plans has a flaw in it, she's the one who points it out.

And I'm the languages and essays and ranged combat one. My affinity is projectiles so I'm doing a mix of incantations and artificing classes.

It sounds like you and Ellen got really lucky, being good at different things like that. How many people from Buda are there in your year?"

If Mari is the only one, that would explain why Ellen is her favourite person instead of someone she grew up with, though even if not she did save her life so it's not completely crazy.

"Game theory is pretty useful even incomplete, though. And it's tied in to economics, which lets you model everything from who to sell homework to to when the bathrooms are going to be crowded."

I do count statistics as math! I haven't thought much about using it for politics, because what kind of running for election would I even do, but being able to think in terms of conditional probabilities is great for planning and risk assessment. Clausewitz says that war is the domain of chance, right, and the Scholomance isn't much different. Anything where one cares about something doesn't know everything about it, which is everything one cares about, is amenable to statistics." 

She smiles at Franklin.

"That's true. Game theory is a useful way of thinking as long as you don't insist on everything being rigorous. I haven't ever done any politics so I think of it in terms of things I have read about, like elections.

"Getting back to using math for politics, I read one paper on multi-dimensional voting theory. The idea was to arrange voters and candidates in an n-dimensional space where each voter voted for the candidate that was closest to him and you use how people voted to deduce how voters and candidates are arranged. Once you know where I am, who I voted for tells you about where he is, and once you know where a candidate is, who voted for him tells you where they are.

"It looks like a chicken and egg problem, where you have to know one half of the answer to find the other half, but the authors thought they had a way of doing it. I suppose if you had enough time you could just try all possible arrangements until you found one that fit the data, but there is probably a cleverer way."

She pauses a moment to think, then shakes her head.

"I don't think anyone's actually done it, but it is a way math could be used for politics. When I told Apa about it his idea was that the same approach could be used for books and readers. Readers report which books they liked or didn't like and how much and you use that to construct a space of readers and books that fits the data. If there is a book close to my location that I haven't read that means I'll probably like it.

"I don't think statistics is very useful in here because we don't have enough data, at least I don't, but probability theory is related to statistics and works for the sort of thing you are talking about. It isn't game theory until other people get involved, or maybe mals, or maybe the school itself if you think of it as a person."

"There are three other Buda freshmen. Sandor is very bright and hates the world; he could be very useful if he decides to join the human race and survives graduation and stays in Buda. I've been hoping to manage the first part by getting him to notice that Ellen is at least as bright and doesn't hate the world but I don't think it has happened yet.

"The other two are well trained and reasonably competent and I am hoping to get both of them through four years with some help from our upperclassmen and out alive, but nothing like your team. It sounds impressive.

"Any tips on how it came out that way that Buda could use to build teams in the future, other than being lucky in who you have?"

Franklin smiles back at Ellen and nods thoughtfully. "Hmm. That sounds like a more formalized version of reading the books your friends like and prioritizing the books of the friends with similar taste. And it sounds like it gets around the problem where if nobody you know has read a book so you never realize you'd like it, though I suppose someone still has to do the categorization at some point. But if you had a way to do it objectively you'd only have to do it once. Whether mals are relevant to game theory is an interesting question; I guess it depends on whether they think about humans as individuals who make decisions. Some of the smarter ones might."

"I'm not going to pretend none of it's luck; we had a great mix of affinities and general skills this year. But a lot of it is just spending fourteen years in each other's pockets. Training together, having fun together, getting used to being able to tell each other anything and relying on each other for anything. And, I don't know how much other enclaves teach this but I think we do more of it than some--learning what it means to be the sort of person who can make promises and really mean them, and why it is the self-interested thing to do to look out for your teammates as much as yourself."

Ellen overhears the last part of the other conversation, responds:

"It is the self-interested thing to be the sort of person who keeps promises and looks out for your teammates as much as yourself. But unless the teammates are in your utility function, which of course Mari is, it isn't actually the self-interested thing to do it. That's the point of commitment strategies and why subgame perfect equilibrium is a poor description of how people act and why Ulysses tied himself to the mast if what he did when he heard the sirens would have been in his self-interest which of course it wouldn't have been which is why he did it which is why that story isn't really a good way of explaining commitment strategies, even though  books always use it.

"And the sort of person who keeps promises is just a special case of the sort of person who can use commitment strategies. Which is usually useful because it expands the strategy space, but not always."

She turns back to Franklin.

"Because sometimes there are commitments you don't want to be able to make."

She thinks of something else.

"And you don't have to have someone categorize books, that's the point of it. The data tells you where books and readers are located."

Mari waits until Ellen is finished before continuing the conversation with Marcy.

"Getting all the age mates to train together is something we could do but I don't know how you would teach them what sort of person to be. Maybe assign the team to games, or better to doing things in the real world, where being that sort of person works. But how do you persuade them that it still works when it isn't a game and the stake is your life? Habit?"

"Having each other in our utility function is important too, yes, that's part of why we can't just instantly set up the same thing with someone else in the Scholomance. And cases where one ends up regretting the ability to make commitments are a lot rarer in practice than cases where it's useful. Human psychology makes things complicated in a lot of ways; in a perfectly abstract situation the same math applies to trade partners as graduation allies. Trade is more of an iterated game than graduation but even graduation isn't a single moment because of all the preparations. But the psychology is different."

Marcy nods to Ellen to indicate that the interjection was welcome before focusing on Mari again. "Training together helps, having a lot of things be evaluated by how well we do as a group helps, competing as a group against other groups helps. Competing against each other some is fine so long as it's friendly. As for how to convince them it's the same when it's not a game--" she furrows her brow thoughtfully. "Well, why wouldn't it be? It isn't as if the practice wasn't serious and important and ultimately life-or-death. I suppose some of it could be momentum; once you have generations of people doing it you can see that it works. Which isn't how the math works, of course, but observation works just as well as a way to learn things."

"Does it work for all the year groups? Is that who your group was competing against?"

"The reason it might not work at the end is that a repeated prisoner's dilemma falls apart on the last play and then the rest unravels. Is the critical fact that there isn't a last play because most of you expect to get out and will still be in the enclave and interacting with each other? That might not work for Indies."

"Does it work across age groups? Will your sophomores be willing to risk death to protect one of you, one of you to protect them? What about after you are back in the enclave? If there aren't enough in an age group for an alliance big enough to get out at graduation, do you try to bring in someone else and fit him into the group or just go with three or four? What if there are too many in an age group for one alliance?

"One of the things we do — father did and I plan to do — is find people we want here, include them in our alliances, then invite them into the enclave — or, if there isn't room, as allied Indies. Father says the Scholomance is a stress test for people and we should use it.

"You can't do that if you come in with a full alliance team of clavemates. At least not very well."

She turns to Ellen.

"If we could find Pest and get the gates open, there would always be room, for a long time."

"We only swear an oath to each other within the year group, but we still trust the other years to look out for us and we'll look out for them. When a year group doesn't look like it will make a good graduation alliance within itself, we do what the other enclaves do and have each person join a different alliance, and then if it makes tactical sense the alliances train together and go out the gates near each other. It doesn't always work out, of course, sometimes one person's group is doing a timespear and another person's group is doing something stealth-based and there's no way to coordinate that.

We're always on the lookout for good indies either way, of course, and our year has a guaranteed spot to offer, but it's rare for us to make agreements with more than one person per year. I'd need stats I haven't actually memorized to know if that's because we have a higher birthrate than you or we're expanding our space more slowly or we recruit more adults or if we're actually recruiting the same number of graduates and just less likely to have an informal thing with allied indies.

Though, also, you mention the Scholomance as a stress test--I think one reason to recruit adults is that you can learn how people behave in the Scholomance, and then wait a couple years and see how they behave outside. It trades off against someone else grabbing the best ones, but that's part of what graduation alliances are for.

Also, you're looking for a lost Pest enclave? I hadn't heard about that, may I ask what the story is there?"