I'm looking for an algorithm or a paper that solves a problem with a particular set of properties.

Imagine you have some number of rooms and some greater number of people. Each person should be assigned to one or more rooms based on a set individual preference. In this way it is reminiscent of rank-choice voting, but the outcome is instead some division of the given resources.

On top of this, it would be nice to provide some overall ranking to the people, think seniority, where some individuals are more likely to get their top preferences than lower ranking individuals.

If anyone knows of any resources that deal with any pieces of this problem I would greatly appreciate it.