> configurations), the applicant is going to have the least favorable one among the different pairings.
I don’t understand why this would always be true. In your example, Google may indeed like Alice, so they both get their top choice.
I don’t understand why this would always be true. In your example, Google may indeed like Alice, so they both get their top choice.
When Alice and Google are not paired up, then they will always form a “blocking pair” in any matching where they aren’t together so that means any matching that doesn’t have Alice and Google paired is not stable.
I think the confusion is that Alice only has one possible stable employer and thus her worst one happens to be her best one.
If Alice’s top choice wasn’t Google, but some other company, then there might be multiple employers she could be matched with to form a stable pairing.
This algorithm is definitely weird too though because it’s possible for some candidates to be paired with a company they don’t really like, but it’s considered a stable situation because the other companies don’t want them more than their current employees.
I guess in real life, you could try improving yourself and then the matching becomes unstable again if preferences change.
Thus extrapolating to a dating app, it’s possible for someone in the matched pair to not really like the other person. Sounds like a rousingly success.