A community arts course has twenty places and fifty applicants who meet its requirements. Organizers could invent a ranking of enthusiasm, reward the fastest applications, or draw names. A lottery makes selection random within the pool they have chosen to admit.
When school admissions use random allocation, the draw operates within an eligible group of applicants. The random step does not decide who belongs in the pool; that decision has already been made.
Equal chances have a boundary
Imagine the arts course requiring applications through a short online form. Even a perfectly conducted draw excludes people who never heard about it, could not use the form, or misunderstood the deadline. Randomness removes certain judgments from selection without removing the effects of the surrounding process.
The draw also needs understandable administration. A list of eligible applicants, a stated procedure, and a way to handle withdrawals make the result easier to trust. Otherwise, “chosen at random” can become a claim nobody can inspect.
A lottery can be a modest admission that the organizer lacks a defensible reason to rank one qualifying person above another. It gives each a chance while leaving the deeper scarcity untouched: thirty people still need another opportunity.