# Math Help - (Very hard) Need help to solve a real-life problem that requires a "demonstration"

1. ## (Very hard) Need help to solve a real-life problem that requires a "demonstration"

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.

For example:
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
etc

The problem:

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?

PC

2. ## Re: (Very hard) Need help to solve a real-life problem that requires a "demonstration

Originally Posted by kalkito
I need to somehow prove that candidates ought to make their choices *after* the interviews. This is intuitive but how can it be argumented?
If I understood you, you want an argument that establishes that people are happier with the outcome if they're allowed to chance their preferences after the interview.

Obviously, if their preferences don't change after the interview, then the matching is same whether done before or after the interview.

To "prove" your point, you need only produce *one* concrete example where, if the preferences had been changed after the interview, and then the matching had been done (using the same matching algorithm) based on these new preferences, then:
1) the matching would've been different than the matching results based on the original preferences,
and 2) the matching would've led to a higher overall satisfaction than gained by the matching results based on the original preferences.

3. ## Re: (Very hard) Need help to solve a real-life problem that requires a "demonstration

I tried that approach but I was unable to convince the board.
Do you think this situation can be stated/treated mathematicaly?

4. ## Re: (Very hard) Need help to solve a real-life problem that requires a "demonstration

If you assume that there is a minimum hiring "score" that each candidate has to achieve in order for him to be hired then each candidate would be able to estimate their probability of receiving the position.

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

Candidate A receives a score of 80 80 40
Candidate B receives a score of 80 90 80
Candidate C receives a score of 40 80 80

If candidate C is aware that he did poorly in the interview for his first choice, he is likely going to change his preferred choices to Z, Y, X because this would increase the probability of his being placed in job Z(since you said their ranking plays a role on which candidate is selected) I have to go to class but this seems like a good starting point.