[ihaveqvestion]

Can someone explain why the outcomes differ when the roommates are in a different order? Imagine an apartment with one nice room and one terrible room, total rent $1000, and two roommates, one rich, one poor. The poor roommate will always chose the less expensive room, the rich roommate will always chose the nice room unless the price difference is greater than $500.

If the rich roommate is Roommate A, then it converges to a 50/50 split, each paying $500. If the rich roommate is Roommate B, it converges to a 75/25 split, with the rich roommate paying $750. What's going on there?

[EDIT: Also, I've just discovered with three roommates that the results may be displayed without the first roommate ever choosing at all. ???]

[ihaveqvestion]

I think the key may be that the rich roommate actually prefers a room, while the poor roommate does not (according to their assigned valuations) have any room preference at all. So if the poor roommate is second, they make the most choices in this calculator and their lack of preference makes the split even, whereas if the rich roommate is second, they make the most choices and their stronger preference causes them to pay more.

Even so, the order still seems to matter somewhat, and I would have expected it not to matter at all.

[yuliyp]

It doesn't guarantee a perfect allocation, but one that is compatible with everyone's preferences. A is willing to pay up to $750 for the nice room and up to $250 for the bad room. B is willing to pay up to $500 for either room. Any solution where A takes the expensive room for $500-$750 and B takes the cheap room for $250-$500 will leave both content with their choice. B could do better by being strategic and switching his preference to only taking the cheap room for no more than $300, however.

[ihaveqvestion]

Thanks, I think that's what I was misunderstanding.