<p>siserune, yes I agree that the multiplicative approach works for an individual applicant, with the applicant’s personal probabilities pH, pY, and pP. In the context of this thread, I think I am the one who suggested it.</p>
<p>When I said that the odds would not go up for most applicants as much as one would predict if the admissions processes were modeled as independent, random selections, I meant: if applicant X takes the raw odds, rH, rY, and rP, computed by dividing the number of acceptances by the number of applications, and then computes (1 - rH) (1 - rY) (1 - rP) as the odds of getting into none of H, Y, and P, X will be overestimating X’s own chances, in most cases. This is due partly to the presence in the pool of the special-category applicants you mentioned in #171, note 2. This alone makes the raw odds higher than the actual odds for a generic applicant. But additionally, in saying “most,” I am estimating the number of “fungible” applicants (your term in #171) as double to triple the number in the admitted class, but not much higher, based on admissions-office rhetoric of the type, “We could easily have admitted a second class that was essentially indistinguishable from the class we selected.”</p>
<p>With regard to #172, you make a good point that applicant X does not need to know X’s true values of pH, pY, and pP to know that increasing the number of applications will always give better odds of an acceptance–unless the added app has zero probability of success or an app already submitted has p = 1–and in the latter case, by submitting additional applications, X is still likely to increase the number of acceptances, as you pointed out.</p>
<p>I think chandelle has made a good point in #169, though, with regard to the OP’s question–if the GC is advising the student not to apply to more colleges, and if the GC is writing the recommendations, and and if the GC will be irritated at having to fill out more forms, where is the break-even point of increased odds with multiple apps vs. decreased odds with an annoyed GC?</p>