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| ▲ | computably 17 minutes ago | parent | next [-] | | I left another comment with the minimal example, but intuitively: - proposers descend from their 1st choice, while recipients ascend according to their offers; the outcome can't be recipient-biased, because recipients ascend only when proposers are forced to descend - a matching is stable if each pair contains at least one party that cannot find a strictly better match - in particular there are multiple distinct matchings, and if proposer-biased, recipients have no recourse to break the proposer-favored pairs | |
| ▲ | 2muchcoffeeman 2 hours ago | parent | prev | next [-] | | Imagine you are the proposer. You will start at the top of your list and work your way down only if rejected. So you are guaranteed to the best you could possibly do. Imagine
A ranks X,Y,Z in that order
B ranks Y,X,Z in that order
C ranks X,Y,Z X, Y, Z rank A,B,C in that order. A will propose to X and match.
B will propose to Y and match.
C will propose to X and get rejected.
C will propose to Y and get rejected.
C will propose to Z and match. Y will never get a proposal from A. Z will never get a proposal from A or B. Edit: I think I fixed it. | | |
| ▲ | jb1991 an hour ago | parent [-] | | Why will B propose to X first if their first choice is Y? | | |
| ▲ | 2muchcoffeeman an hour ago | parent [-] | | You’re absolutely right. I’m on my phone trying to imagine the scenarios in my head and trying to find the simplest possible example. Maybe 4 participants is too few to clearly see what happens. | | |
| ▲ | computably 40 minutes ago | parent [-] | | (A,X),(B,Y) as the proposals is fine for the point being made. The issue is if we reverse which group is the proposer, we still end up with the same matching, because (A,X) strictly prefer each other. The minimal example with 4 participants is if each person P has unique preferences and P's 1st choice has P as 2nd choice. So in this case just flip X: A:XY
B:YX
X:BA
Y:AB If A,B propose you get AX,BY. If X,Y propose you get BX,AY. Both are stable because the proposers are getting their first choice. | | |
| ▲ | jb1991 13 minutes ago | parent [-] | | I find this algorithm to have a curious definition of the word "stable." |
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| ▲ | jezzamon 2 hours ago | parent | prev [-] | | You have to accept the best offer you get, if there's someone that you would like, you only match with them if all their better options are exhausted. |
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