Would it be better to model preference based activity assignment as a Stable Marriage Problem or a Minimum Cost Problem?

Question

Students list preferences for activities.

Overall aim is to get higher preferences as often as possible.

Stable marriage or min cost flow with bipartite graph?

EDITS:

• Context: Secondary school students choosing activities for a 'fun week' at the end of the school year.
• Speed: obviously would be nice to reduce execution time, however it's not an essential thing I need to accommodate for, because after all the kids enter their preferences the member of staff just has to run it once to get all the allocations.
• Can assume the students will not lie about their preferences- they won't know the algorithm used and even if a couple lie it's not too big of a deal.

Answer 1

Min cost flow seems more appropriate because students have preferences, but activities do not. Also this formulation allows an activity to support multiple students (by increasing the capacity on the arcs).

Stable marriage is appropriate when both sides have preferences.