Scholarship Composite Score, Sports Quota and the Temptation to Lower the Cutoff
A state-level scholarship for a one-year pre-engineering programme awards a single seat. The composite score is 0.40 × Mathematics + 0.30 × Reasoning + 0.20 × English + 0.10 × Computer Awareness, each subject marked out of 100. The published cutoff is 84.50. The prospectus says: 'A candidate with a recognised state sports certificate receives 3 marks added to the composite score before rounding to the nearest integer.' Ties are broken by higher Mathematics, then higher Reasoning. Three shortlisted candidates are: A - Mathematics 88, Reasoning 76, English 82, Computer 90; B - Mathematics 84, Reasoning 88, English 78, Computer 86, with a state sports certificate; C - Mathematics 90, Reasoning 70, English 85, Computer 80. The committee must recommend one name and record the arithmetic. A's parent has written that A 'has the highest Mathematics score, so should be preferred'.
1. Compute the composite score for each candidate under the published rules and recommend one candidate. Show every step, including the effect of rounding.
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A: (0.40(88)+0.30(76)+0.20(82)+0.10(90)=35.2+22.8+16.4+9.0=83.4). No quota, so 83.4, which rounds to 83.
B: raw composite (0.40(84)+0.30(88)+0.20(78)+0.10(86)=33.6+26.4+15.6+8.6=84.2). Add the sports quota: (84.2+3=87.2), which rounds to 87.
C: (0.40(90)+0.30(70)+0.20(85)+0.10(80)=36+21+17+8=82.0), which rounds to 82.
The cutoff is 84.50. A has 83.4 and C has 82.0, so neither reaches it. B reaches 87.2 after the quota and is the only eligible candidate. The tie-break is irrelevant because there is no tie. Recommendation: B.
2. A's parent argues that A should be preferred because A has the highest Mathematics score. Evaluate this argument against the prospectus.
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The argument confuses a component with the selection rule. Mathematics is weighted 0.40, and A's 88 gives 35.2 marks, while B's 84 gives 33.6 - a gain of only 1.6 composite marks. B more than recovers this on Reasoning: B's 88 versus A's 76 gives (0.30(12)=3.6) extra marks. B also gains 0.4 on Computer Awareness, while A gains 0.8 on English. The net raw difference is (84.2-83.4=0.8) in B's favour before the quota.
The prospectus uses Mathematics only as the first tie-break, and only when composite scores are equal. Here the scores are not equal: B has 87.2 after the quota and A has 83.4. 'Highest Mathematics score' is not an independent selection criterion. The parent may argue that the quota is unfair, but that is a policy objection, not a violation of the published rule. The committee should not override the composite score on this ground.
3. Suppose B's sports certificate is later ruled invalid and the committee considers lowering the cutoff to 84.0 to fill the seat. Is that defensible? What would you advise?
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Without the quota, B's composite is 84.2, A's is 83.4 and C's is 82.0. At a cutoff of 84.0, B would qualify; at the published 84.50, nobody would qualify.
Lowering a cutoff after seeing the results is retroactive and damages predictability. It is defensible only if the original notification said the cutoff was provisional, or if a documented review procedure allows revision. Otherwise the safer course is to keep 84.50 and, if the seat must be filled, issue a fresh transparent notification explaining the revised criterion and apply it to all candidates. If the certificate is invalid, B still has 84.2 and would benefit from a 84.0 cutoff, but that does not make the change procedurally sound. Advice: do not lower the cutoff ad hoc; use a published review rule or re-advertise.