diff --git a/_posts/2024-08-16-building-an-assignment-algorithm-2.markdown b/_posts/2024-08-16-building-an-assignment-algorithm-2.markdown index 4d46196309..903ed0ca5d 100644 --- a/_posts/2024-08-16-building-an-assignment-algorithm-2.markdown +++ b/_posts/2024-08-16-building-an-assignment-algorithm-2.markdown @@ -69,7 +69,13 @@ Every time slot, attendees are given a slot compromise score according to what c In the end, we decided the compromise for getting the first choice should be 0 (no compromise at all), the compromise for getting the 2nd choice is 2 and the compromise for getting their 3rd choice was 5. Take note of the incremental difference between first to second and second to third - the slot compromise score becomes increasingly worse.
If you would like to know how we calculated these values, click the 'more' button for more details -This is based on the formula \(Cₙ = n + Cₙ₋₁\), where \(C\)ₙ is the compromise for the nth choice and \(C1 = 0\) . Which can also be reformulated to... \[Cₙ = \frac{(n-1)(n+2)}{2}\] +This is based on the formula: +\[Cₙ = n + Cₙ₋₁\] +where \(C\)ₙ is the compromise for the nth choice and \(C1 = 0\). +
+
+This can also be reformulated to: +\[Cₙ = \frac{(n-1)(n+2)}{2}\]
Looking back however, perhaps getting your 5th choice or your 6th choice wouldn’t be much different so perhaps choosing a curve that tends to a fixed value would be better (perhaps of the form \(1-\frac{1}{x}\)), as we have done with surplus difference. In any case, there were only 3 choices per slot for our application, so this worked fine.
@@ -161,7 +167,7 @@ Where: N.B. The Z score is calculated with the median to avoid extreme value skewing.

-And: +And the \(\text{standardisedSurplusScore}\) by the following:

\(\text{if maxSurplus} \neq 0 \text{ and attendee surplus difference} > 0 \text{:}\)