Anonymous wrote:
I don't have time to play through your image right now, but your overview is correct. One important note though is that when someone gets assigned a school in round 1 or later rounds, it is only a temporary assignment. If the computer requests a school for a student in a later round and that student has a higher position (because of preference and/or lottery number), the first student will get bumped.

Anonymous wrote:I haven't seen a detailed scenario in this thread, so I created one from my understanding of the lottery algorithm, based on the public information available. If it is incorrect, I'd like to hear from people.

The scenario described in the link below is purposely limited, but I believe it shows the following algorithm:

Step #0: Put all students into an unassigned pool and randomly give each a lottery number for tie-breaking purposes.
Step #1 (Assignment): Assign all students in the unassigned pool to their current highest ranked school.
Step #2 (Reduction): For each school that is over-capacity, rank students by preferences (sibling, locality, lottery number) and un-assign students that are beyond the capacity (by rank).
Step #3: Return unassigned students to the unassigned pool and repeat steps #1-#3 with the students' next highest ranked school until all schools are at capacity.

Note that I'm only considering lottery number and not any other privilege during the reduction step of each iteration. I'm also assuming all students put equal numbers of schools, but those two don't affect the overall logic. At the end of the scenario, student "I" does not get into a school.