Selection Board Aggregate and Reserved Vacancies
A selection board in Abuja has 24 vacancies and 96 candidates. The aggregate is 40% written, 30% aptitude, 30% interview. Written is marked out of 100. Aptitude is marked out of 80 and must be scaled to 100. Interview is scored by three raters, each out of 20; the board uses the mean of the three, scaled to 100. Fifteen vacancies are open to all corps; nine are reserved for combat corps candidates. Candidate A (combat) has written 68, aptitude 56, interview ratings 14, 16, 12. Candidate B (combat) has written 74, aptitude 60, interview ratings 13, 13, 17. Candidate C (non-combat) has written 71, aptitude 64, interview ratings 15, 15, 14. The board must fill all 24 vacancies and may not exceed the reserved number. A tie is broken by written score, then aptitude.
1. Compute the aggregate score of each candidate to two decimal places. Show the scaling and weighting.
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Use: aggregate = 0.40(written) + 0.30(aptitude scaled) + 0.30(interview scaled).
Candidate A
- Aptitude: 56/80 × 100 = 70.00
- Interview mean: (14 + 16 + 12)/3 = 42/3 = 14.00; scaled = 14/20 × 100 = 70.00
- Aggregate: 0.40(68) + 0.30(70) + 0.30(70) = 27.20 + 21.00 + 21.00 = 69.20
Candidate B
- Aptitude: 60/80 × 100 = 75.00
- Interview mean: (13 + 13 + 17)/3 = 43/3 = 14.333; scaled = 14.333/20 × 100 = 71.67
- Aggregate: 0.40(74) + 0.30(75) + 0.30(71.67) = 29.60 + 22.50 + 21.50 = 73.60
Candidate C
- Aptitude: 64/80 × 100 = 80.00
- Interview mean: (15 + 15 + 14)/3 = 44/3 = 14.667; scaled = 14.667/20 × 100 = 73.33
- Aggregate: 0.40(71) + 0.30(80) + 0.30(73.33) = 28.40 + 24.00 + 22.00 = 74.40
2. Rank the three candidates by aggregate. If one open slot and one reserved slot remain, who should fill each? State any assumption.
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Ranking: C (74.40) > B (73.60) > A (69.20).
C is non-combat, so C is eligible only for the open slot. B and A are combat, so each is eligible for either the open or the reserved slot. To respect both merit and the quota, place C in the open slot because C has the highest aggregate. Place B in the reserved slot because B is the higher-scoring combat candidate. A is not selected on these facts.
Assumption: no other candidate outranks these three for the two remaining slots, and all three are otherwise eligible. Ranking alone does not decide the outcome because eligibility differs: C cannot take the reserved slot, and the board may not use the reserved slot for a non-combat candidate.
3. A board member argues that because A is combat corps, A should be selected ahead of C regardless of aggregate. Evaluate that argument using the stated rules.
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The argument confuses eligibility with priority. The rule creates nine reserved combat vacancies; it does not say that any combat candidate outranks any non-combat candidate for the fifteen open vacancies. The open vacancies are filled on aggregate among all eligible candidates.
If A were placed ahead of C in an open slot, C would be displaced despite a higher aggregate, and the board would be using a reserved-vacancy rule to distort an open-vacancy competition. On the three-candidate facts, C is first and B is second. The quota is satisfied by placing B in the reserved slot, not by promoting A over C. The argument fails unless a separate rule gives combat candidates priority for open slots, and no such rule is stated.