A Note on University Admission Tests: Simple Theory and Empirical Analysis.

4 To be precise: suppose student A applies to university X only, student B to university X as first choice and to university Y as second choice, and student C to university Y only. From Assumption 1, we can therefore write the student's payoff maximising probability of admission as: HT <math display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mfenced close=")" open="("><mrow><mi> </mi><mo»=</mo><mi>T</mi><mo>-</mo><msub><mi>x</mi><mi>s</mi></msub><mo>-</mo><mi>a</mi><mo>-</mo><msub><mi>e</mi><mi> </mi></msub><mfenced close=")" open="("><mi>T</mi><mo>,</mo><mi>a</mi></mfenced></mrow></mfenced><mo>=</mo><mn>1</mn><mo>-</mo><mi>F</mi><mfenced close=")" open="("><mrow><mi>T</mi><mo>-</mo><msub><mi>x</mi><mi>s</mi></msub><mo>-</mo><mi>a</mi><mo>-</mo><mi> </mi><mo>+</mo><mi> </mi><mi>T</mi><mo>-</mo><mi> </mi><mi>a</mi><mi>T</mi></mrow></mfenced><mtext>.</mtext></math> ht Graph (3)This is the latent probability in a binomial regression model. Naturally, we require (i) HT <math overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi> </mi><mi>P</mi><mfenced close=")" open="("><mo>-</mo></mfenced></mrow><mi> </mi><mi>T</mi></mfrac><mo>=</mo><mo>-</mo><mi>f</mi><mfenced close=")" open="("><mo>-</mo></mfenced><mfenced close=")" open="("><mn>1</mn><mo>+</mo><mi> </mi><mo>-</mo><mi> </mi><mi>a</mi></mfenced><mo> </mo><mn>0</mn></math> ht , and (ii) HT <math overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi> </mi><mi>P</mi><mfenced close=")" open="("><mo>-</mo></mfenced></mrow><mi> </mi><mi>a</mi></mfrac><mo>=</mo><mi>f</mi><mfenced close=")" open="("><mo>-</mo></mfenced><mfenced close=")" open="("><mn>1</mn><mo>+</mo><mi> </mi><mi>T</mi></mfenced><mo> </mo><mn>0</mn></math> ht . [Extracted from the article]