Why you should ask out your crush: A brief mathematical note
by greenturtle3141, Feb 14, 2022, 10:26 PM
This is a very short short-notice note that I'll probably edit / expand in the future, because I don't have much free time at the moment and the only appropriate time to post this is, of course, Valentine's Day. So here we go.
The key idea is that if you are proactive, then you maximize your chances of getting what you want. This idea is portrayed almost perfectly by a little something in math called the Gale-Shapley algorithm.
The Problem (Stable Marriage)
With apologies to those of other gender identities, let us suppose that there are
men and women. Each man has some preference list for the women, and each woman has a preference list for the men. For example, let's say 
. Let's say the men are Albert, Bob, and Charlie, and the women are Dana, Eve, and Flora.
A possible preference list for the men could be:
A possible preference list for the women could be:
The Stable Marriage Problem asks: Can you always pair up these men and women such that the marriages are stable? In unstable matching is one where there is a man
and a woman 
that are NOT matched, and yet prefer each other over their current partners.
Example: Suppose we match up the above three men and women ala (Albert, Eve), (Bob, Dana), and (Charlie, Flora). This is NOT a stable marriage, .
The Gale Shapley Algorithm
The answer to the Stable Marriage Problem is yes, and one proof of this uses an algorithm that the men and women could follow to come up with a pairing of marriages that must be stable.
I'll expand upon this (and make it easier to digest) at a later date, but for now I'll just link the wikipedia page: https://en.wikipedia.org/wiki/Gale%E2%80%93Shapley_algorithm.
Here are the key points though:
1. This algorithm works!
It results in a stable marriage. In the marriages that occur at the end of the algorithm, it's guaranteed that no two people will prefer each other over their assigned partners. This solves the Stable Marriage Problem.
2. If the men are the proposers, then the algorithm favors the men.
That is, the resulting set of marriages is "best for all men" and "worst for all women".
3. If the women are the proposers, then the algorithm favors the women.
The reverse holds true! In general, those that propose will get the optimal outcomes.
The lesson here, folks, is that being proactive (being a proposer/ask-outer) yields good results, and being passive (waiting to be proposed/asked out) yields worse results.
In conclusion, you should ask out your crush.
The key idea is that if you are proactive, then you maximize your chances of getting what you want. This idea is portrayed almost perfectly by a little something in math called the Gale-Shapley algorithm.
The Problem (Stable Marriage)
With apologies to those of other gender identities, let us suppose that there are
men and women. Each man has some preference list for the women, and each woman has a preference list for the men. For example, let's say 
. Let's say the men are Albert, Bob, and Charlie, and the women are Dana, Eve, and Flora.A possible preference list for the men could be:
- Albert: Dana > Eve > Flora
- Bob: Eve > Flora > Dana
- Charlie: Dana > Flora > Eve
A possible preference list for the women could be:
- Dana: Charlie > Albert > Bob
- Eve: Charlie > Albert > Bob
- Flora: Albert > Charlie > Bob
The Stable Marriage Problem asks: Can you always pair up these men and women such that the marriages are stable? In unstable matching is one where there is a man
and a woman 
that are NOT matched, and yet prefer each other over their current partners.Example: Suppose we match up the above three men and women ala (Albert, Eve), (Bob, Dana), and (Charlie, Flora). This is NOT a stable marriage, .
The Gale Shapley Algorithm
The answer to the Stable Marriage Problem is yes, and one proof of this uses an algorithm that the men and women could follow to come up with a pairing of marriages that must be stable.
I'll expand upon this (and make it easier to digest) at a later date, but for now I'll just link the wikipedia page: https://en.wikipedia.org/wiki/Gale%E2%80%93Shapley_algorithm.
Here are the key points though:
1. This algorithm works!
It results in a stable marriage. In the marriages that occur at the end of the algorithm, it's guaranteed that no two people will prefer each other over their assigned partners. This solves the Stable Marriage Problem.
2. If the men are the proposers, then the algorithm favors the men.
That is, the resulting set of marriages is "best for all men" and "worst for all women".
3. If the women are the proposers, then the algorithm favors the women.
The reverse holds true! In general, those that propose will get the optimal outcomes.
The lesson here, folks, is that being proactive (being a proposer/ask-outer) yields good results, and being passive (waiting to be proposed/asked out) yields worse results.
In conclusion, you should ask out your crush.
This post has been edited 4 times. Last edited by greenturtle3141, Feb 14, 2022, 11:37 PM
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