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[quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous]Two or three of you in this topic understand both the math and social science aspects of probability estimates. If you guys had usernames, I'd single you out.[/quote]

Why don’t you quote the examples that are correct?  Either the text or time/date sigs will work.  Thanks![/quote]
Without intending to be dogmatic, I'd say that this contributor understands the importance of both math and social science (in this case the social science of college admission) in approaching the question:

[quote]
Look, forecasters don't get the future inflation number or the USD-JPY rate correctly most of the time, but it doesn't stop them from using reason to arrive at a forecast , and they get the direction right most of the time even if not the exact number.

OP is similarly using reason. And the math is correct if you assume a set of qualified students whose stats put them in the range of these schools.

OP used 4% acceptance as an example. You can use Naviance to actually get a sense of probability of not being accepted to a school for your stats (calculate acceptance for that higher stat cluster). So let's say using the Naviance plot of GPA and SAT, your child has a 15% probability of admit at Cornell, and a 15% admit at Dartmouth, (that would be 85% probability of rejection at each). So the probability of rejection FROM BOTH is
0.85*0.85= 0.7225 , i.e. 72%.

If Harvard is a 8% admit probability for your stats, then the probability of reject from ALL THREE is
0.92*0.85*0.85= 0.6647 (66%).

The math is correct...and the correct interpretation is:
1. For those students whose stats put them within the range, applying to more elite schools lowers the likelihood of being rejected by all or put another way improves the probability of being accepted by at least one.
2. But that said , the resultant rejection probability is still high and for most of the best kids rarely gets better than a coin toss.

You don't get shattered when you lose a coin toss. Don't get shattered when your kid doesn't get into an elite.
[/quote]
To this, I'd add a general concept. Questions such as this are accessible to mathematical approaches. You can start with assumptions, however imperfect, in the form of assigned values. Then, with appropriate math, you can get closer than you were before. A feature of probability might even be the expectation that you often will be inaccurate until such time as all the information becomes available and the uncertainty reduces to zero.

On another note, events do not need to be either independent or dependent for probabilistic approaches to be effective. There are mathematical ways to adjust for degrees of dependence. I'd argue as well that there are different ways to define dependence.

Somewhat separately, I'm not understanding the game theory approaches to this question. 
[/quote]

The game theory question and formula, which is the title and main topic of this thread, requires events to be independent to work.

College admissions decisions are, in fact, independent events.

Despite this, the game theory formula which (again) is the title and main topic of this thread will not work because you cannot know the odds of any one student being admitted to any one school.  Therefore the result of the formula - the only reason to use it - is useless, as you are guessing.  This is how probability works.  It's why you can't bet on counting cards in blackjack unless you know how many decks are in the shoe.

I guess we just need to keep repeating this.[/quote]

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