Basic algorithm to match students with their courses.

• go through every course
• for each course
  • go through the entire list of voters
  • put every voter, who voted for the course in a list
  • if there are more voters than open spots, remove voters randomly from the list
  • match everyone remaining in the list with the course and mark them as matched
• repeat for second, third, ... choice

This Algorithm only works for a basic situration. An example is a project week at a school:

Students have to choose one project they want to participate in. The projects all have a size limit, which is why there needs to be a voting system. Usually students then get to pick their first, second and third choice.