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<p>Your reply is ambivalent. Let’s get to the mathematical heart of the question:</p>
<p>Do you agree or disagree that any probability model of (one individual applicant’s) admission that is NOT multiplicative is invalid? Here “multiplicative” means that probability of any combined outcome such as Prob[Joe is admitted to Stanford, rejected by MIT, waitlisted by Harvard] is equal to a product of the per-school probabilities, in this case Prob[Joe admitted to S] x Prob[Joe rejected by M] x Prob[Joe waitlisted by H].</p>
<p>Several notes:</p>
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<li><p>The word “invalid” above is a euphemism. More honestly one might call the non-multiplicative models “embarrassingly wrong”, “bogus”, or “professionally disqualifying if advocated by a statistics teacher” (as in tokenadult’s FAQ).</p></li>
<li><p>Assume for purposes of this question that all applications are ordinary, regular-round (deadline around January 1, April 1 notification), and there is no athletic recruitment or “special handling” category applicable, that might trigger exchanges or monitoring of information about Joe among the universities. Joe is not the POTUS’ nephew, and he has not been on any school’s radar prior to applying. He is a generic applicant who, from the admissions point of view, is fungible with many others as far as his qualifications and each university’s level of interest in him are concerned.</p></li>
<li><p>I am not assuming that probabilities are necessary represented by a single number. One might quantify Joe’s odds as a range of probabilities (“between 3 and 99 percent chance of admission to Harvard”), or some Bayesian odds-of-odds measure (“equally likely to be any probability between 3 and 99 percent”), or probabilities that vary over time and as a function of the stock market and the weather in Boston. One can still multiply these fancier sorts of probability data. Any such model is fine, but the issue is whether it must satisfy multiplicativity in order to pass the laugh test.</p></li>
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