# Assignment based on ranked preference

Assume that there are n students, who have to be evenly assigned to m groups. For every student, a preference ranking of of the m groups is given.

I partially order assignment by pointwise preference, i.e. one is better or equal to another if for every student, the assigned group is ranked higher or equal.

What algorithm can I use find “locally optimal” solutions, i.e. assignments where there are no strictly better solutions?

I assume there will be multiple locally optimal solutions. Is there a sensible way to order them without giving the students an incentive to be dishonest in their ranking, i.e. without encouraging strategic voting? If so, can that be solved?

And finally: What are the right terms to search for research that solves this and related problems?

• Check out the "stable marriage" problem. Nov 6 '15 at 12:30
• Right, that’s related. I’ll see what I can find starting from there. Nov 6 '15 at 12:49
• Did you end up solving this problem in a satisfiable manner? It appears to be a non-trivial step to go from the SMP to this particular problem. Mar 24 '16 at 15:19
• I did not solve it at all, sorry. Mar 24 '16 at 17:30
• This post describes a similar problem and might be of use to you.
– Pim
Feb 23 '21 at 21:08