Both your model and the one leading to the single school are misleading in relevant ways: your model doesn't take into account that realistically scores will be perturbed upon iteration; if each school's score is a well-behaved random variable (let's say normal but certainly doesn't have to be), even with small variance, yes, schools will almost always (in the technical sense, if scores are real; in the intuitive sense, if they are not) be removed each iteration until there's a singleton. However, there's the other simplifying assumption that there's isn't going to be massive churn due to new schools being opened. We already see that with charter schools today. (I mean, I think. My opinions on this are formed entirely by reading this, and a few tweets out of context.)
But, yes, people on the internet are wrong.
But he said "not better than average" not "below average"
But he said "not better than average" not "below average"
Also I think the mechanics for shutting down schools requires some consistent below average performance like three consecutive years. So if all the schools take turns being above average then no one has to shut down. Unfortunately they don't teach about being fair and taking turns any more because everyone has to practice for the tests.
3: Hillary Clinton is a woman, actually.
Both your model and the one leading to the single school are misleading in relevant ways: your model doesn't take into account that realistically scores will be perturbed upon iteration; if each school's score is a well-behaved random variable (let's say normal but certainly doesn't have to be), even with small variance, yes, schools will almost always (in the technical sense, if scores are real; in the intuitive sense, if they are not) be removed each iteration until there's a singleton.
I don't think the change in score on iteration makes a difference. Even if the same entity doesn't map to the same score each time, the average of each score must either be equal to all the scores, or greater than at least one score. The fact that in my example the entity -> score mapping is the identity mapping doesn't matter.
If that were true, I would be unemployed.
Could someone explain 11 to me? I can't get any meaning out of it.
Whereas I can conceive of no unclarity in it. Can you really get *no* meaning out of it?
All I'm assuming is that if you have a list of scores, then when you take the arithmetic mean of them, either the mean will be greater than at least one score, or the mean will be equal to all the scores (which are all equal to each other). Is that not true?
Dalriata seemed to be making some point like, but the same school won't always have the same score. I don't see why that's relevant. At any given time, each school will have a score, those scores can be averaged, and if the scores are all equal then none of them is below average and if they aren't then at least one is below average.
But as soon as you have a (reasonable) probabilistic element to the scores the chances that the latter phenomenon will happen over and over again will go to zero.
What is "the latter phenomenon"? At least one being below average?
either the mean will be greater than at least one score, or the mean will be equal to all the scores (which are all equal to each other).
If the odds of them all being equal is anything less than 100%, then the odds of them all being equal n years in a row will quickly go to zero.
Ok. I don't see how that's relevant. I was making a point about the operation of averaging.
However, there's the other simplifying assumption that there's isn't going to be massive churn due to new schools being opened.
Stack ranking for schools?
I had assumed 11 was responding to 1. Is that not the case?
In Lake Wobegon, below-average children are killed. This process is repeated until only one child remains.
Or maybe that's The Hunger Games. I don't know—I always get them confused.
1 and 17 seem right to me. The operation if averaging isn't the only issue. You need to consider measurement error.
Yeah, my point was that the case where all schools have the same score is going to be rare, especially upon iteration. Even if all remaining schools are iid, including having the same mean, they usually won't have the same value as each other in any given round, so some school will be eliminated (and arguably eliminated unfairly, which I think is partially why people find this offensive?).
And honestly, considering the no-randomness scenario, "eliminate all but the set of schools whose score is the highest value" doesn't sound much better than "eliminate all but the school whose score is the highest value." People may have said the latter when they either didn't know about the former or considered it an uninteresting edge case. Hence why I see arguing against it for that a "someone on the internet is wrong" moment and sort of uninteresting. (Even if that someone is Hillary Clinton. See also whatever the hell she said about encryption that was so risible.)
In practice what I think would be likely to happen is that you'd get the churn I mentioned--a bunch of fly-by-night (charter) schools that basically serve to 1) funnel money to shady operators who'll iterate under different names and 2) keep the average value down, thus protecting middling-to-crap schools. Of course, if there are fewer shady operators or they don't hustle as hard even legitimately good schools could be targeted, but I suppose that is a good problem to have. Maybe. Education policy seems way harder than math.
And honestly, considering the no-randomness scenario, "eliminate all but the set of schools whose score is the highest value" doesn't sound much better than "eliminate all but the school whose score is the highest value."
You know, none of it sounds like a good idea. But the reason it's a stupid proposal isn't the putative fact that unavoidably you'll be left with only one school, as a matter of mathematics. As … I said in the post.
You're right, but I still think under a mildly more realistic scenario it'll be with measure one unavoidable. (And having looked up what Clinton actually said, arthegall's point is also relevant that her procedure will leave no schools, unless the replacement rate is high enough.) Who was even claiming the deterministic one school thing, anyway?
(I'm getting a feeling that this is what arguing about angels on the head of a pin feels like. I imagine there's a German word for that.)
Who was even claiming the deterministic one school thing, anyway?
Some people on twitter.
Friggin' people on twitter, always so wrong yet so sure.
You can simulate this stuff in R if you want to do it right.
Just be sure to specify if you want a spherical kid.
They're more right than wrong. Giant ties just don't happen.
That giant ties don't just happen is not a mathematical result.
It does not follow from the iteration of averaging and removing the below-average.
In conclusion, I am right and you are wrong.
You are technically and narrowly correct. So well done.
That repeated exact ties happen very rarely is a perfectly mathematical result. You take a pretty narrow view of mathematics.
It's a good thing I anticipated that response in 35.
I was stubbornly resisting using the Futurama quote.
I don't even know it as a Futurama quote. It did sound vaguely familiar.
If we keep this up, zombie Wittgenstein will hunt us down and rip out our larynxes while chanting "one must remain silent."
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Straight out of a low-budget dystopian SF movie.
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I didn't know that was a Futurama quote either.
I once got into an argument with Terence Tao over a picayune technical point in logic. Finally, he said "Technically, you're correct but..." to which I only replied "The best kind of correct." I'm telling this story because it is my greatest contribution to the mathematical literature.
In the future, each school will be above average for 15 minutes.