<p>Continuing from #722,</p>
<h1>732, ““The math is pretty simple if you read Espenshade & Chung’s paper. Espenshade’s simulations are, in essence, adding up the expected number of students admitted in each category. If the probability triples for a given category, the expected admission rate triples.””</h1>
<p>The math is pretty simple. What’s wrong is how you erroneously obtain a race-neutral Asian-student population by multiplying the original Asian-student population with a factor of 3, because of a 1-to-3 Asian disadvantage (to Caucasians in admissions rates). Also quoted from some of your earlier messages,</p>
<p>“”“The idea that the true rate is around 60 percent is something even a US News journalist should immediately grasp is ludicrous, by comparison with available data… Note well that in Espenshade & Chung’s statistical model of admissions, undoing the odds-ratio of 1/3 that they find for the predictor variable “Asian”, would literally be the same as jacking up the Asian admission rate by a factor of 3… It also remains true that a 3-to-1 Asian disadvantage would (e.g., in Espenshade & Chung’s admissions model) imply nonsense such as a “true” 60 percent Asian share of admissions at Harvard,”"</p>
<p>You are building a strawman here and it doesn’t work that way, because the 1-to-3 Asian disadvantage (to Caucasians in admissions rates) is a marginal value only true at the original student demographics. Taking the approximation that URMs can be separately treated, when more Asian applicants are admitted and the Asian-admissions rate increases, simultaneously less Caucasian applicants are admitted and the Caucasian-admissions rate decreases. Race-neutral admissions is reached when both of the admissions rates are about the same. I shall put them in symbols for illustration purposes.</p>
<p>Let A be the original admissions rate for Asian applicants,
Let C be the original admissions rate for Caucasian applicants,
Let a be the race-neutral admissions rate for Asian applicants,
Let c be the race-neutral admissions rate for Caucasian applicants.</p>
<p>3A= C, 1-to-3 Asian disadvantage to Caucasians in admissions rates at the original student demographics
a~ c, both of the admissions rates are about the same at race-neutral student demographics</p>
<p>A< a, Asian-admissions rate increases as admissions become race-neutral
C> c, Caucasian-admissions rate decreases as admissions become race-neutral</p>
<p>Combining the above 4 equations, a~ c< C= 3A, or a< 3A= C, i.e. the race-neutral Asian-admissions rate is necessarily <em>less</em> than 3 times the original Asian-admissions rate here and never reaches as high as the original Caucasian-admissions rate. So a race-neutral Asian-student population <em>cannot</em> be obtained by multiplying the original Asian-student population with a factor of 3. The correct approach is to sum the Asian admits one-by-one with their corresponding admissions rates, until the Asian admissions rate is about the same as the Caucasian admissions rate, when race-neutral admissions is reached. Referring to my earlier message #722, the race-neutral Asian-student population only increases by a factor of (30.4/ 23.9)= 1.27 with URMs and (39.0/ 23.9)= 1.63 if completely race-neutral (Yield is approximated to be about the same across different ethnic groups, so that the admit demographics is about the same as the student demographics). And it should be noted that these multiplication factors represent the ratios between the weighted-averaged admissions rates and the original admissions rate, but <em>not</em> the ratios between the marginal admissions rates (when admissions become race-neutral) and the original admissions rate.</p>
<h1>732, ““At a school like Harvard, where the yield is about the same for all large subgroups of students (a steady 80 percent for blacks, whites, athletes, New Yorkers, etc), tripling the Asian admission rate relative to non-Asians would, therefore, triple the Asian matriculation share, to 50-65 percent depending on how many Asians you believe were attending in 1997.””</h1>
<p>As explained above, the correct multiplication factor is only 1.27 with URMs, for race-neutral admissions. So we are talking about an Asian-student population of only about 30 % for race-neutral admissions, if you assume Harvard has discriminated against Asian applicants to the same extent as the sample of elites in the Espenshade Study.</p>
<h1>732, ““That is wildly implausible when compared to Espenshade’s data on the Asian share of high SAT scores (40 percent), to Berkeley after prop 209, and to Caltech.””</h1>
<p>I suppose you meant “Asian-student population” instead of “SAT scores”. Table 9.1 in the Espenshade Study <em>cannot</em> be applied to Berkeley because the samples are private elites. And it is improper to blindly use the multiplication factors for any school, unless you assume all schools have discriminated against Asian applicants to the same extent. Caltech is generally regarded to run genuinely merit-based admissions, even without URMs. Referring to my earlier message #722, the Espenshade Study actually projected an Asian-student population of 39.0 % for the sample of elites, if completely race-neutral. And this is consistent with the Asian-student population at Caltech.</p>