layman51
Joined 4 years ago
Joined 4 years ago
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.
An applicant (the receiver) will end up with a "worst" match in the sense that if you look at all "stable" pairings (there can be multiple configurations), the applicant is going to have the least favorable one among the different pairings.
There's an important concept of a "blocking pair", and the Gale-Shapley algorithm is trying to eliminate all blocking pairs, and you could say that pairings are stable when no blocking pairs exist. A blocking pair is a job applicant and employer who aren't matched together, but both prefer each other over their current match.
Suppose that after the algorithm is done with its work, Alice doesn't end up with a job offer from her top choice, Google. This must mean that Google never offered her a job because Alice was just too far down on their list, and Google made a deal with someone else they like better than Alice.
So usually the claims about replacing tutors like in this article come from a place where they usually give a caveat that maybe for highly motivated and ambitious students, they can figure out how to accelerate their learning with AI. But then that undermines the whole argument of transforming education if it wouldn't work with students who are average or below-average in their academic achievement.
That reminds me that there is a library that I believe became a bit viral on social media and now it seems like it receives so many visitors to the surrounding area and it is still quiet, but it is funny because it seems way more crowded and there's way more movement that I remember in the past.
That's why with this post, I sort of wonder whether this is something that these towns really want to have. I am under the impression that in Japan, they generally want visitors, but then they probably end up with issues from people not knowing what to do and even behaving badly.
Going back to chess, I think the situation is similar where you can’t expect an amateur player to get better by trying to play like a strong engine. I think even professional chess players mainly use engines to prepare or memorize variations that are counterintuitive for their opponent. In other words, getting into situations that look wild, but that part of one player’s preparation.
I’m not sure how it is in math, but in chess, it seems like top players can play just like engines when they are in “normal” positions, so that is where I get a bit confused as to where the direction of insight is coming from because it’s been my view that AI is able to make leaps that we would never think of taking and I’m not sure that anyone could actually learn how to do that on their own unless they were willing to keep failing over and over.