(1) Each candidate can only be assigned to a post they have applied for, and only one post at most.
(2) For each post $j$, a maximum of $p_j$ candidates can be assigned to $P_j$.
- Each candidate can only be assigned to a post they have applied for, and only one post at most.
- For each post $j$, a maximum of $p_j$ candidates can be assigned to $P_j$.
(3) Higher scores have to be chosen before than lower ones: A candidate cannot be left without a job if, in any of the posts they applied for, a candidate with a lower score was admitted. In other words: a candidate can be assigned to a post only if all the candidates with higher score than them for that post are also assigned to that post or to any other post (with more priority for them).
(4) Priorities have to be taken into account: A candidate has to be assigned to the post with the highest preference for them, if possible. In other words, if a candidate can be assigned to more than one post, they must be assigned to the post for which they expressed the highest priority among them.
Higher scores have to be chosen before than lower ones: A candidate cannot be left without a job if, in any of the posts they applied for, a candidate with a lower score was admitted. In other words: a candidate can be assigned to a post only if all the candidates with higher score than them for that post are also assigned to that post or to any other post (with more priority for them).
Priorities have to be taken into account: A candidate has to be assigned to the post with the highest preference for them, if possible. In other words, if a candidate can be assigned to more than one post, they must be assigned to the post for which they expressed the highest priority among them.