I've been trying to learn about the Stable Marriage Problem and was wondering what happens if someone doesn't fill in their preference list - at all.
I've read up about the problem with regards to incomplete lists and ties etc. but can't seem to see a specific mention of an empty list. My initial thoughts would be along the lines of this being treated as everyone ranked as a tie but I'm not sure that would be the best way to see things. How would this be handled?
Apologies if this has been asked/answered elsewhere. I also apologise if there is a very obvious answer to this, my brain is currently fried in any case. Thanks in advance for any help.
An empty list is just the extreme case of an incomplete list: the person has indicated that no matches are acceptable to him/her, so it is guaranteed that (s)he will end up unmatched.
By the way, a small terminological note: the term "stable marriage [problem]", when unmodified, ordinarily denotes the original version of the problem, where there are equal numbers of men and women and each person provides a complete ordered list of all members of the opposite sex. So there are no "incomplete lists and ties etc.", and hence no empty lists. Extensions of the stable marriage problem may introduce support for incomplete lists and/or ties and/or different numbers of men and women, in which case they get names like "stable marriage [problem] with incomplete lists" and so on. We could even imagine different extensions that all have "incomplete lists" but assign different meanings to them, though in practice I think all extensions with "incomplete lists" assign them the same meaning.