We begin by putting all students in a list of “candidates”, and start with an empty list of “winners”. All
students will eventually be moved from the “candidates” list to the “winners” list, but the order in the
“winners” list will control which students actually get into the program, starting with the first “winner”,
then the second, until all of the available slots are taken up. In the lotteries we’ve done in the past, we
usually ended up taking about the first 30 students in the list. If a student “wins” the lottery and is
chosen, and the student for some reason can’t take the position, we just take the next student in the
sorted list.
If there are, say, 200 students in the lottery, there are actually 199 “drawings”.
For each stage of the drawing:
1. Add up all the weight numbers of the students in the current “candidate” list to get a total
weight.
2. Each student is assigned a probability of being selected at this stage: (the student’s weight)/(the
total of all the weights)
3. The sum total of all the students’ probabilities is 100%.
4. A random number is generated, and used to select one student using the weights.
5. The selected student is moved from the list of “candidates” to the next position in the list of
“winners”
6. The lottery drawing is now repeated with one fewer students.
7. Finally, the very last student goes at the end of the list of “winners”.
So, at each drawing stage, a student with, say 300 points, has three times as much chance of being
selected as a student with only 100 points. And six times as much chance as a student with only 50
points. If the total number of points at some late stage is, for example 1200, and a student has 600
points, that student has a 50-50 chance of being selected at this stage. If this student isn’t selected at
this stage, this student will have more than a 50% chance of being selected at the next stage. As long as
a student has more than zero “points”, the student has a chance of being selected. If all students enter
the lottery with exactly the same number of points, the lottery operates just like the previous lottery
system: each student has exactly the same chance as any other student.
Perhaps a picture will help. To keep it simple, let’s say we have 5 students at this stage:
Al with 100 points
Bea with 150 points
Carla with 66 points
Doug with 80 points
Ed with 90 points
The total number of points is 486
Al’s probability of being selected at this stage is 100/486, or about 20.6%.
To understand this stage, assume a random number is chosen in the range of 0-486.
Assume it comes up as 272. That number is “in Carla’s box”, and Carla is chosen as the next student to
be moved from “candidates” to “winners”. Now there are only four students left, with a total of 420
points. In the next stage, a number between 0 and 420 is generated, the picture is adjusted without
Carla, and the next student is chosen. This repeats until all students have been moved from
“candidates” to “winners”.