The Eternal Dilemma Of The Hogwarts Sorting Hat
There’s something that struck me a few years ago:
The Hogwarts Sorting Hat grapples with an eternal dilemma! Now I don’t exactly consider myself a Potterverse fan. I approve of its existence, sure. Fandom is a fine thing. I got into the Methods of Rationality for a while.
But I’ve barely even dipped my toe in the vast frothy waters of the Potterverse fandom and the fandom-ming of its fans. I have no idea how deeply and extensively various tribes of fans have picked apart the magical nuances of the Sorting Hat. Maybe the dilemma this post explores got identified and squelched and dismissed years ago. Maybe me simply bringing it up will induce waves of scorn and “yo check out grandad, thinks he’s the first to notice the Sorting Hat’s bugs, what’s he going to enlighten us about next? Rickrolling?” No idea. But what the hell. It may interest you as it interested me. Read on:
From what I can tell, the Sorting Hat has not one but two priorities:
(1) Sorting kids into the Houses of their choice, and
(2) (going by the main hall movie scenes): Keeping each House’s student numbers roughly equal.
The Hat must achieve both by sorting each child alphabetically, individually, and publicly.
I’m sure you can see the problem: first-year kids with surnames closer to Z will find their house-sorting wishes are disregarded more than kids with surnames closer to A.
Like, how likely is it that for the current year’s crop of 40 first-years, exactly 10 wish to enter each House? A four-way 25% split? Not very! Consider this situation: 13 wish to go into Gryffindor, 13 to Hufflepuff, 13 to Ravenclaw … and only one to Slytherin. But the Hat will discover this input lopsidedness only during the process of sorting, and not before.
So the Hat processes them alphabetically, we begin with surnames A, B, C. The first kids simply enter the houses of their choice, D, E, F, business as usual, ho hum …
… But by the time we reach, say, K, the Hat realises: Oh crap! this is really lopsided! Slytherin is hurting! Can’t have that! As the alphabet wears on and the opportunities the Hat might have to correct these lopsided ratios droop and diminish, it must start to disregard the wishes of the alphabetically impaired kids to keep the House proportions equal.
Z-kids get ignored. Makes a mockery of the role of the Hat in general, doesn’t it? Easy solution though: you could get around this by allowing the Hat to first silently leap from one kid’s head to another, sizing up the whole lot and withholding judgement … and then batch its sorting decisions in one huge blob at the end. Problem solved.