Solving Marriage Problems

Stable Marriage Problem – Numberphile

Discuss on Reddit: Featuring Dr Emily Riehl. Continues with the more mathematical bit at: The Gale/Shapley paper:…
Video Rating: 4 / 5

0 replies on “Stable Marriage Problem – Numberphile”

How does the end result vary if instead of the Women proposing to men, the
men proposed to the women?

It would definitely vary.

I wonder if the method is biased in a way that it tends to give better
mates to the gender that was active instead of passive in the marriage

Stable yes, but with plenty of unhappiness. All the most wanted people get
married to each other and the least wanted ones have to settle with
themselves. So pretty much the way reality works out… Could be easier if
we just implemented this algorithm, it would save us time and energy and
lots of rejections and disappointment.

If you’re concerned about the fact that these marriages are being described
as necessarily being heterosexual only, realize this: This assumption
defines an important aspect of the problem — namely, that each individual
person must be attracted to exactly half the total population, and that no
person can NOT appear on anyone’s attractiveness-ranking list. If we
allowed for same-sex pairings, a gay man would be able to pick all the
other men in the population except for himself, meaning he’s picked half
the population minus one. The remaining one would have to be a woman. It
necessarily follows then that everyone in the problem would need to be
bisexual, which also is unreflective of reality. So, don’t worry about it
— it’s a math problem, not a commentary on social norms or morality.

You can’t upload the set up part and tease to the maths part at the end
when the second video’s uploaded yet Brady, that’s too cruel.

thank you for not being hetero normative and specifically mentioning the
fact that you’re only including heterosexual marriages, I really appreciate
it so much.

This is a really interesting problem that ultimately shows that those who
reach out first are ultimately rewarded. I think the follow-up video that
shows the theorems is more interesting than the first. But the first sets
everything up.

Hey Brady, you might be interested in knowing that this algorithm was
modified and is now used to determine the where Doctors go to learn their
specialty in the US! It is called the “Match”.

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