Please help me solve this situation or point me in the right direction. (please bear with my poor english)
There are n candidates to be placed in n job positions.
Each candidate selects 3 positions wich are ordered according to his/her preference.
* Candidate cannot change this order *
Each candidate is then interviewed in his/her 3 chosen positions.
Job interviewers order candidates.
Candidates will be placed in the jobs they rated most highly as long they are placed highly in employer preferences.
Candidate A chooses X, Y and Z in this order
Candidate B chooses X, Z and Y in this order
Candidate C chooses X, Z and Y in this order
X chooses A,B, C in this order
Y chooses A,B, C in this order
Z chooses A,B, C in this order
This results in
A goes to X
B goes to Z
Candidates real preferences are only visible after the interviews (and not before) and beeing unable to change the predefined order results in less optimal placements. for exemple, even If A hates the X position aftr the interview, his placement can't be changed.
I need to somehow prove that candidates ought to make their choices *after* the interviews. This is intuitive but how can it be argumented?
Thanks in advance