"It's the second one.  This is going to take some effort, actually."

Gregoria is looking confused on purpose. It is kind of terrifying but that's life on Project Lawful for you. "I don't - see how Carissa and Meritxell having an argument is relevant to the probabilities at all. And I don't see how you could possibly get sure enough for it to make sense to do anything other than, uh, expensive fancy Truth Spells or whatever the Crown keeps in store."

"The problem I'm having with thinking up simpler and more realistic examples is that I haven't been in Golarion long enough to learn a lot of probabilities and use them myself on problems with this structure.  The cases where I've resorted to explicit reasoning of this form, have been about weird exotic things I couldn't figure out by simpler methods, like the timing of the Zon-Kuthon attack relative to when I went outside the Forbiddance, or the implications if Carissa mysteriously failed to make her afterlife arrangements."

"Okay, uh, hopefully much simpler example.  Around what fraction of wizard students in your academy had Intelligence 16, 17, 18?"

"....most are fourteen, actually. Most top students are sixteen, seventeen is rare and eighteen's even rarer."

"Side question:  What are privacy customs and deliberate-incentive-structures around that info?  Does everyone know everyone else's Intelligence, or is the info concealed to force people to judge each other by their accomplishments which are thereby more incentivized?"

"Class rankings are posted. Students can say what they heard their Intelligence was, but at the age when you're in school it's not final, so you don't reliably know who's smartest and you do know who is top of the class," says Meritxell. It's her. She is the top of the class.

"Suppose I asked you to guess, if you don't know, if you do know that's obviously fine, what fraction of students in Ostenso wizard academy who graduate at all, will later be determined to have Intelligence 15, 16, or 17."

"More fifteens than sixteens and more sixteens than seventeens," says Meritxell. "Because you start with way more, and not that many wash out. Fifteen's plenty smart enough to be a good wizard."

"Numbers, Meritxell.  I'm not asking you to be perfectly right, I'm asking you to guess, based on what you've seen in your wizard academy that I haven't."

(Keltham has already estimated the ratios between +2.5sd, +3.0sd, and +3.5sd in terms of their improbability, and the ratio should be something like 15:5:1.)

"It'll be - ten fourteens, ten fifteens, a couple sixteens, maybe a seventeen?"

"What was your total class size like?"

"A little over two hundred, in Ostenso. Westcrown's bigger, I think."

"Corentyn's also bigger."

"And the population ratios should be - I've been unwisely trying to work this out inside my head, because it's more impressive that way, even if I have a higher chance of screwing up instead* - one INT 18 to six or seven INT 17s to forty INT 16s to two hundred INT 15s to six hundred fifty INT 14s.  So if you've got equal INT 14 and INT 15 representation, then any individual INT 15 is about three times as likely to get admitted to Ostenso wizard academy than an INT 14.  Does all that sound right?"

He'll write it down on the whitewall in case that helps:

INT 18:       1
INT 17:    6-7
INT 16:     40
INT 15:   200
INT 14:   650

(*)  In particular, Keltham is unthinkingly treating their Intelligence detector's integer output as a perfect floor() function instead of a noisy round() function, though it's not like he'd know that was wrong, and it gets him pretty close.

"That sounds about right?" Meritxell says uncertainly. "They admit the smartest."

"Wait," Asmodia says out loud.  "You just got to Golarion.  How is that something you know?"

"Oh?  That's an interesting question.  Why can't it just be another fragment of Law that I know and you don't?"

"By the way, Asmodia's not allowed to answer that question except by Message to me, somebody else has to try it instead."

"...that's how it is in dath ilan," says Gregoria, "except with the numbers shifted like everyone's got a headband on. Right?"

"Heh.  I suppose that's actually a simpler answer than the one I had in mind.  Why would those ratios be the same between dath ilan and Golarion, though?  What with us having a whole heritage-optimization program, and subsidies for kids expected to produce Civilization-approved positive externalities, and nutrition that doesn't vary much between kids."

"...for the same mysterious reason both worlds have humans at all?"

"Asmodia?"

"If you'd had those numbers memorized, you wouldn't have needed to work them out in your head and risk getting them wrong," Asmodia states.  "So it has to be math.  But it's the wrong kind of thing to be math, I can't figure out how to say it but - the part about Validity -"

"It's not necessarily true across all possible worlds.  You can coherently imagine a population or a wizard academy which looks different.  So, you conclude, it can't be a validity."

"What math did you do?  Or if you don't want to just tell me - can you show me what the calculations were, and then I can see if I can figure out from those what they mean?"

Asmodia could, without benefit of any Detect Thoughts, hear Meritxell thinking earlier about how she was top of the class in Ostenso, and Meritxell needs to be put back in her place.