Example: Say student X has rank order 1, student Y has rank order 2, and student Z has rank order 25. Then say for student X the neighborhood schools they applied to are schools A, B, and C. For student Y it is schools B and D, and for student Z it is schools C, D, E, and F. Because student X has rank order 1, they get priority order 1 for schools A, B, and C. Because student Y has rank order 2, they get priority order 2 for school B since student X is already priority order 1. But student Y gets priority order 1 for school D since student X is not eligible for a priority order there. As this process continues, eventually we get to student Z with rank order 25. Their priority orders may be something like this: C=22, D=10, E=2, and F=17. Now say that school C only has 19 seats. Student Z is not guaranteed a seat at school C, but if three students with higher priority order at school C reject it, then student Z can gain admission.
