I first learned about this problem before making the "rainbow connection", but when I put two and two together it was like the stars had aligned; it was too perfect!
but isn't there an assumption here that asexual/aromatic people cannot even be on the preference lists of other people? After all, you can lust after or love someone even though it's not reciprocated. Or am I missing something here?
You did it! You tricked this gay guy who struggles with any math more complex than order of operations to watch a twenty minute math video with genuine interest. Very much proving your point at the end. Well done.
Given the chance of genuine love triangles, I wonder how the problem would change when polyamorous relationships are added. In a way, the residency program example already gave a poly form of the problem with 2 students pairing with the same hospital. Obviously, allowing for arbitrarily high numbers of partners would inevitably become stable once everyone has become one single giant relationship, so it would make sense to focus on smaller limits or trying to minimize the average number of people in one relationship. And yes, "Stable roommates problem" is absolutely hilarious.
Thanks for your comment, and yep, there's a lot to explore there as well! Unfortunately it wasn't something I could do justice to in the video, but I'll take a crack at it now. With the caveat that I know very little about polyamory as compared to other queer identities, I'll mention two broad ways someone can think about polyamorous relationships. One that I think you're alluding to is a group of people who have open relationships. In other words, each person can feel free to have as many or as few partners as they desire, and any person's partners might or might not be in relationship(s) with one another. In this model, the idea of a stable marriage is no longer something we have to care about or solve for, because the main tension in the problem is that people are limited by the partners they can have. In our relationship examples, every person can only have 0 or 1 partners. In the residency program example, each program can only have 0, 1, or 2 students, and each student can only go to 0 or 1 of the programs. In a world of open relationships, two people who like each other more than their current partners (the thing that gave us an unstable matching) can pair off without having to break their existing relationships, so there will never be an issue. Another way to think about polyamorous relationships is that they're exclusive, but the number of partners in any given relationship is unrestricted. It's the difference, for example, between 3 people (P, Q, R) who have each of the others as partners vs. 3 people (P, Q, R) who are all in one relationship together. Again, I'm not an authority on polyamory, but the way I understand this difference is that in the first case, you need to consider the relationships PQ, QR, and PR, but in the second case, you need to think about PQ, QR, PR, and PQR. When I wrote the part of script that mentioned restricting to 0 or 1 partners, I was thinking about this second case, because the underlying math needs to be extended in a pretty significant way to handle it. One way I thought about doing it is to ask P to give a preference list where they rank the three choices, "Q" / "R" / "Q and R"-notice that "Q and R" is distinct from both "Q" and "R". But an issue with this is that in order for the group "Q and R" to prefer P, Q and R have to be in a relationship. I don't know if there's a good algorithm to find a stable matching here, if one even exists.
@@edisonhauptman6886 Many types of polyamorous relationships exist, and from my point of view it would be disingenuous to try and optimize some group of people for the *most stable* sets of relationships, given the analogy of people we're using. The problem itself could have some interesting results when we detach it from this example and, while whichever scenario we create might be relatable back to some polyamorous relationship, another analogy might be more apt. For the PQR dilemma: Whether this distinction is important to the problem depends on if we make it important, such as by making PQR some distinct matching where P has compatibility test with (Q), (R), and (Q and R). Is PQR considered more stable than PQ and PR? and how does that interact with other connections? I'd start by modelling the problem where each member is looking to match with exactly 2, 3, and n others, and change factors from there to see how the optimization rule changes. In terms of relationships however, I personally envision the difference between (PQ, QP, and PR) and (PQR) as Three people who are each in a relationship, but they go out in pairs together, rather than as a trio.
Yeah many of the so-called love "triangles" in fiction are actually just "v"s involving straight people, although even in 2000 some cartoons started putting out love tringles with a straight and 2 bisexual (but more airtime for the characters' lust for the other gender) characters. With queer relationships, we can see even more genuine love triangles.
@@edisonhauptman6886 Another way to model it would be to assume that each person has a limit for how many partners they want, but those relationships need not be complete graphs of that size. So for example, person 5 could want to date up to 2 people while people 3 and 7 might each only want 1 partner (but would be okay with person 5 having 2 partners). Modelling a limit on how much polyamory someone would accept from their "roommates" would make things even more complicated...
This could be a pretty decent set up for a sci-fi story, a world that mathematically matches people and the weird pairings that could come out of it. I find the idea of a state sanctioned stable love triangle or an adequate enough couple to be hilarious.
This is basically describing a fanfic I wrote exactly. The AI couldn't find any viable matches for a girl, and the only reasonable option seemed to be sending her to live with her older sister (and her partners). Sometime after that the older sister came by, complaining that the girl had been assigned a separate room and couldn't spend the nights with them after curfew... That was the day the AI (re)discovered incest.
That sounds similar to the comic L.U.F.F. In there, there is a government-sanctioned dating app that tries to match people. It isn't mandatory, but it does involve a love triangle sanctioned by the app. The comic explores a lot of the consequences of using an AI to essentially force people together, but it's primarily a romance comic, so if you don't like that I wouldn't recommend it.
Reminds me of one discussion in college (one of the super nerdy ones) where we got into the graph theory of all of the various "polycules". You think stable "roomates" problem is tough, now throw in poly queer nerdy college folks and you're now dealing with multipartite directed cyclic graphs :D
fun fact: the “polycule nested spoons problem”, where you try to stack the entire polycule in nested spoons such that two people in direct contact must be romantically involved with each other, is NP-complete. It’s equivalent to the Hamiltonian path problem.
11:30 this is how highschool admissions work in bulgaria. Every child writes a list of preferred schools and schools take the ones with the most points, except each schools calculates points differently. At the end of the year there are 2 national exams: math and bulgarian (both 0-100). The points of the schools have to be out of 500. The most common formula is 2×Math + 2×Bulg + Mark for the whole year (Math) + Year mark (Bulg). Both year marks 0-50. Most top schools however change the formula: math-focused high-schools might take the math 3 times and the bulgarian once, sport-focused ones might take your PE yearly mark (mapped 0-50) instead of maths, and so on. EDI: 15:54 , its the student-focused version
We need a show where the plot cycles through a long set of relationship pairings, and the aces sit back with an infinite supply of garlic bread and watch the chaos unfold 😂
Being Queers is one of those game modifiers that make the game harder but you are more rewarded for succeeding Love life +10% difficulty Public POV of you: -20 Happiness after finding love: +50%
I watched Dr. Riehl’s video years ago, and it’s really stuck with me, both as an interesting math problem and a hilariously unexpected and accurate Pride and Prejudice reference. I really enjoyed this video as well. The residency side of things was incredibly interesting, as it really showcased why this was a problem that needed solving, because it was creating a situation no one involved wanted. From a mathematical perspective, it was also interesting to see how multiple slots doesn’t complicate things, though in hindsight it makes sense as you could potentially treat each “slot” as it’s own suitor, with an identical preference list. From the queer perspective, this is exactly the reason I’ve always felt a queer version of Love Island would be amazing. So much more potential!
The real reason queer relationship dynamics are harder is because you half-flirt with everybody in your friend group and everybody's confused on who likes who
To add to all the other comments about polyamory, I think another factor to consider, that would add yet another layer of complexity, is that for many poly people (and this is my case), "preferences" aren’t really a thing! As in: for many of us there is no real ranking going on when looking who to date. Two or more people could have the same "slot" in the list, if you will. So like if one person (let’s call them P) was 1 person away from being polysaturated (meaning they almost achieved their limit numbers of possible relationships at once), but that person had 2 other people they would want to date, and those two people had the same "slot" in the list, then P would be satisfied with either one of them.
Thanks for your perspective here! For the purposes of the problem, any ties can be settled arbitrarily at any point (though if you settle them differently at different times, you could certainly end up with instability in that regard).
@@rauld434 I know very very little about chemistry and physics but is that the thing where an electron will move between the different uhh layers of an atom only in very specific conditions?
When I saw the title of the video, I was immediately reminded of the Numberphile video. I did not know about this "extension" to the problem, and the video was very enjoyable to watch. I also really liked the positive message at the end of the video. I hope this video will still get more views, because it definitely deserves it!
I do remember the same vid, and also took a time to play round with the idea of making it queer: more precisely, the candidates and choosers being of the same set. Soon became clear you can end up in an unresolvable loop, but hey.
Side note, I never understood why the straight love triangle was called a love triangle, it's more of a "love Y." For me, even as a kid, I always though a love triangle would be A loves B, B loves C, and C loves A
@@bilis2866 I mean ya it's 3, but like, not in the shape of a triangle, the person below your comment put it better than I did, it's more of a "V" than a triangle
I am so glad to see maths educational content that's so inclusive! This would have made a great difference in my life if I saw it a decade or so ago. I am so glad this generation has the chance to grow up with it:)
Hey Alex, thanks for your message! One of my goals with this video was to make math feel like a more inclusive subject, since I think we typically look at it as impersonal. But the way we relate to math (much like anything else) is based on the connections we make to it, and as much as there's beauty in our abstract patterns, math is created and studied by people, and we all bring different perspectives to the table.
I’ve been watching many other SoME2 entries for quite a while now, but this particular entry made my gay heart happy! One thing that I’d be really interested in looking into is the dynamics of polyamory in this; desired numbers/number ranges of partnerships for people, possibly having individuals that aren’t comfortable with their partner (or partners, but I don’t think that’d be as applicable to the real world) and other uncommon relationship dynamics that are still just as valid. Great video by the way!
I am curious as to what would happen if you built (if, indeed, you can build) self-sacrifice into the system. For example, Person 1 prefers Person 2 but knows that Person 2 prefers Person 3, so would prefer that Person 2 is with Person 3 than themselves. That is to say that people (or, if we wanted to complicate things, *some* people) attempt to optimise for the preferences of the people that they would prefer over their own preferences.
The subject material reminds me of the problems with voting systems. In each case, there are many people, and each person has some states of the world which are preferable to them over other states of the world, and the ideal objective is to make a 'most globally preferred' choice. Condorcet voting does seem like it might be suitable if it is generalized: in terms of pairwise voting, when comparing any state of the world where 1 and 2 are a couple, with any state of the world where 1 and 3 are a couple, individual 1 casts a vote "I prefer the former". Of course, once you do some research, you find that Condorcet voting does not eliminate the problem of preference triangles... it just makes them more explicitly blatant, easier to recognize. ... Framing things in this way makes the system even more powerful at keeping everyone happy, now that I think about it a little more. If we allow an individual to express preferences over differences in the state of the world that do not explicitly directly affect them, then in the residents/hospitals story, a couple could vote that they'd prefer to both be at their #3 choices in the same city rather than one be at their #1 choice and the other at their #2 choice at opposite sides of the continent. They could even vote that they'd rather get no residency, if they don't end up near each other. Of course, generally, when pairing roommates up, it seems highly inadvisable to take into account the preferences of an individual who is not one of the pair, and may not even know either person in the pair. So practically, giving someone a vote in meddling in other people's affairs leads to difficulty. But the math works.
I love that you made a connection to voting systems! Yes, this is kind of similar to determining a Condorcet winner. If we imagine all of our relationship-seekers to be candidates in an election, and imagine the preference lists as rank-order ballots submitted by voters (with the people on the left being each voter's first choice, then the next person being the voters' second choice, etc.), then an election between 3, 5, and 7 would run into issues. Of course, in that kind of system, the folks supporting person 1 might not *all* have person 2 as their second choice, so it's not a perfect comparison. But it's still a really neat angle on the problem! As for your comment on couples, the National Resident Matching Program (the system that assigns students to residency programs in the United States) can actually take into account couples' preferences to be close together. Unfortunately, the algorithm we went through in the video can't handle couples' preferences, and in fact a stable matching isn't *guaranteed* when you take them into account. But they've modified the algorithm slightly to adjust for this, and in practice I don't think they run into huge issues.
after seeing this video my first reaction was "hey ! Let"s see what more there is in stock here on this channel" before realizing it was your first and only video. i really like 3blue1brown's content and i think your's is quite similar while still being refreshing in it's own way and i truly would like to see more of it ! GL to you if you want to continue doing videos and i'll definitely check them out !
When this video showed that you can get cyclic preferences in the stable "roommates" problem, my immediate thought was that this was somehow related to the Condorcet paradox - which also relates to a cycle of preferences, but in a voting system instead of a pairing system. You should also be able to define something similar to Arrow's impossibility theorem in the stable "roommates" problem too - that if the pairings are decided by a system based on a ranking of other candidates input by each candidate, there would be no way to determine the pairings without encouraging some candidates to input tactical preferences that differ from their true preferences in order to make their preferred outcome (according to their true preferences) occur.
Maybe a "tier" ranking instead of this linear ranking would solve the instability. Perhaps the blue, pink, and yellow people all like each other enough to date, but because the way they were surveyed FORCED them to put it in a specific order it ended up being unstable
I'm trying to decide what field of mathematics I should go into. But I have proved that there is no way to determine. Unfortunately, since I have not yet studied combinatorics I can not check my work. Therefore I should go into combinatorics to determine if I should go into it. Which means that my proof was wrong since I have determined what field to go into. Which means I have checked my work so I don't need to go into combinatorics. Which means I was right that I don't know where to go and the checking of my work was in error. Since my proof was both right and wrong, I should go into quantum physics. Which I do not want to do but evidently it is my first choice. I have decided to pursue a dual major of quantum physics and not quantum physics. I can not say whether I like this or not, but I can't prove it.
This was really cool and fun to watch! As an educational video creator myself, I understand how much effort must have been put into this. Liked and subscribed, always enjoy supporting fellow small creators :)
@@Данилтычкрейзи Isn't there some limit to the number of relationships humans can have or something? I want to say it's like 200 at varying levels of closeness?
I've been thinking about this issue ever since I heard the original problem (I'm bisexual) but I never got around to actually trying to answer it, so it was amazing when I saw this video on my homepage. Also, "roommates" is just the best title that could be given to this paper.
The reason why this doesn't happen is because if you'd prefer being with no one as opposed to being with some person, you'd reject an attempt to be matched with that person, because you already have a "better offer"-either a more-preferred partner, or no one at all. Put another way, matching you with a partner when you'd rather be with no one is automatically unstable, because you'd unilaterally break off that partnership to be with no one.
@@edisonhauptman6886 I feel like the problem will change slightly if you have the “null” spot as a lower priority choice, i.e. A would want to be with B, C or no one (in that line of priority) as that could influence stable matching (as both matching and not matching them can provide a stable match), thus potentially influencing who stays unmatched
@@waterunderthebridge7950 I encourage you to try this yourself. For example, add a "null" spot at the end of all the students' preference lists in the residency programs example, or add a "null" spot on the residency programs' end. I think you'll quickly see that there's no difference. There are some stable matchings where no one is matched, and the difference between that and matching them to "null" is negligible.
@@edisonhauptman6886 Yeah I would’ve thought there to be not a lot of effect for small groups. I was more thinking that a few individuals with a low priority null preference (not everyone in the group) may contribute to combinations that reduced unmatched individuals, thus contributing to a higher flexibility and ratio of good matches but that may also be somewhat of a human bias
As a poly person that kinda tells me, that my way of holding a relationship is actually beneficial to mono people as well, given that if 3, 7 and 5 could live happily as a poly triangle, 1 and 2 would be decently fine and at least poor 4 would have a chance somewhere, as opposed to an unsolvable mess. Of course this is extremely oversimplified and already fails with the assumption that people are emotionally able to make a proper assessment of their "ranking" in the first place.. But in a perfect world, mixing mono and poly - from what I can intuitively see - would make it a happier place for everybody~ .. Now when can I marry my partners for tax benefits? x)
Hold up, maybe I'm crazy but while you can't make a genuine love triangle with straight people you can make an unsolvable love square with straight people right???
Great question! It turns out we don't run into a problem here. If you have A preferring 1, who prefers B, who prefers 2, who prefers A, then you can match A with 1 and B with 2. While it's true that 1 and 2 will prefer the other person, both A and B will be happy, so there's no instability. (You could also match A with 2 and B with 1, and that will also be stable.)
This is good!! I felt like the video sort of ends in the middle, though. It’s like “look, it’s not always solvable!!!” But we don’t learn anything about *when* it is solvable, or, as many people have mentioned, polyamorous relationships. As for how to specify the polyamory problem: maybe each person has a maximum number of people they can be with, and a maximum number of people they are comfortable with their partners being with? Not really related to how it works in real life, but I don’t think that people can reliably rank everyone in their friend group like this anyways, so I don’t think realism has to be a priority :p
I think a more realistic approach would be to say that someone: 1/ is either OK with their partner dating other ppl, or 2/ is NOT OK with it. That tends to be how it goes irl lol.
Okay I've wanted to make like queer-related/queer-y math videos in the future for when I feel like doing that maybe in SoME3 or something so this is so cool to see, as a trans person I like see very little math content that feels queer-er so this is just v heartwarming and inspiring and the explanations for everything were done really well so thank you for this
Tbh the discussion is more theoretical than practical. Few queer folk are fully conscious of how other prospective mates rank against each other and preferences change according to the circumstances of the proposed relationship. Besides, no one has the time and energy to algorithmically pair up their connections since cooperation would be low. It's a neat thought experiment, though.
The idea is that the algorithm occurs organically and without any real cooperation. Each time two people realize that they would prefer each other to what they currently have, they will (in theory) make that change all on their own. They don't actually need to consult the rest of the group to make that change. The thesis of the video is that while this autonomous algorithm eventually reaches a stable point for straight couples, that's not necessarily the case in general; hence the title of the video.
This is mind-expanding material. A book I read on this topic was equally enlightening. "The Art of Meaningful Relationships in the 21st Century" by Leo Flint
...The scenario of seven people who all have different preferences for eachother and the inclusion of love triangles kind of makes me wonder if there's a connection to be made here between queer relationships and Pokemon typing. But then A's connection with B wouldn't be the same as B's connection with A, so... does that mean we would expand the problem to include not just relationships in general, but who's willing to top or bottom who?
The true revelation is that straight "love triangles" can't actually exist, it's just a love fold since a triangle needs three edges. Love triangles must inherently be queer to work, so basically afaik The Legend of Korra is the only show to present us with an actual love triangle in television so far.
The 'bottom' of the triangle in a more traditional love triangle is essentially there to represent the fact that in a lot of earlier ones the two people pinning after the 'top' of the triangle were often very close themselves, therefor making them have to choose between love and friendship.
I've seen a lot of people describe straight love "triangles" as love corners. This is mostly because a lot of media has the rather concerning tendency of not really taking the woman's opinion into account, so it's more like two men backing a woman into a corner and forcing her to choose. Usually when this isn't the case, the one couple is basically a guarantee, while the other love interest is just the antagonist/current boyfriend that the viewpoint character has to defeat. If the story is from the perspective of the female character, the appeal of the story is often about how attractive the men are rather than actually making a decision, making those stories long as hell (this is common in comics and fanfiction). You honestly get a lot of weird stuff when you write straight love triangles.
If we didn't restrict the number of partners to 0 or 1, could an optimal solution be found, or is that such a fundamentally different problem, that it can't be asked exactly like that?
If you remove an upper limit of partners, judging only by quality of matches the simplest “optimal” solution would just be to group everyone together that wants to have a partner as then everybody would have their most preferred match (maybe sub-partitioned into closed chains of A - B - C - A in case of love polygons). Of course, that might be an unsatisfying solution: The problem would then be how to value to e.g. being paired up with your first choice but also someone you haven’t chosen vs. secondary choices vs. not being paired etc. against each other.
@@grahamrich9956 Regarding people preferring to be with no one, they’ll will always reject any match because they have already found a stable match (i.e. no one)
"but first, let's talk about how medical students become doctors" [vsauce music starts] Edit: I think they should all get into a polycule :) maybe that misses the point but
I'm surprised that an algorithm which would break up the perfect or near perfect matches for the sake of optimising some global statisfaction metric didnt show up or maybe there just wasn't enough time in the video to talk about it?
I am so glad you brought up this point! Solving this problem came with the assumption that we wouldn't want to have any instability-a term defined in such a way that we only have to look locally to check it. We didn't have to use an algorithm like this though. And maybe there is some global utility-maximizing solution that isn't stable. Given the choice between a globally optimal, unstable solution vs. a stable solution that isn't globally optimal, which would you generally prefer? Perhaps the folks who use this algorithm (especially for real-world applications like the National Resident Matching Program) valued the perspective of an individual person experiencing the system that matches them to a program, and thus didn't think too hard about making a globally-optimal algorithm (or maybe an algorithm that maximizes preferences like this is hard to come by; I don't actually know of one off the top of my head). Either way, that was a decision we made, and it's another wonderful example of how our values can inform the math we do!
@@edisonhauptman6886 my thought process behind it is pretty simple, we have algorithm that finds at least two stable solutions that maximize satisfaction of one of two groups (focusing on two groups as the single group model doens't even have a guaranteed stable matching) which is also the worse matching for the othr group so the globally-optimal one would try to find something that is neither best or worse for both groups and maybe it's not nescesarily a question of algorithm (that one may be hard to find) but just proofs or examples of such matchings existing cause the whole thing reminds me (a physicist) of finding an optimal path problem for some reason, where you would try to minimize some sort of function over the path, like energy (there may be some materials about it on some hastag for anyone interested) but that would probably require introduction of satisfaction evaluation beyond ordered list, thus making it more complicated especially for real-life application. Maybe thats why it wasn't explored (?) if I understood you right or was it just not a part of this specific endevour described? As for your question I haven't given this idea enough thought to have a preference but I'd guess it could depend on situation, though the difference would probably require that more precise meteric to distinguish. And a though at the end which poped back into my head after writinhg the rest (and I'm too lazy to try to fit this in), my mind for some reason associated this algorithm with hirsh index (where the two gorups would be publications and citations) but it may just be a wierd thought swirling through my head.
the Algorithm presented this video to me tonight and i'm so fucking glad. Exactly what I wanted to watch. A++ video, what a good explanation AND IT'S GAY ETA: the solution is polyamory and personally i fully support 5, 3, and 7
Can’t the med students at the start agree to the residency and then when another one accepts, just quit the one you already accepted, right? What am I misunderstanding here?
Actually, this doesn't prove that "finding a partner is harder for queers". It proves that a world where everyone is straight can always have stable matchings. But in our world, not everyone is straight, and this makes stable matching harder *for everyone* (regardless of being queer or not)
Great video! And great message at the end on how we can teach math in more inclusive ways. Is there a simple reason why the stable matching theorem breaks down in the queer case? e.g. does someone have to go unmatched in every counterexample? or is it more subtle? I notice the theorem still works in the straight case even if the number of men and women aren't the same.
The trick is that in the straight/two gender case, you can't have an actual triangle, because each woman will only be attracted to men, and each man will only be attracted to women. So if you had a "triangle" of two men and one women, the two men wouldn't be attracted to one another, and so in this example, the lone woman could just choose the man she'd rather be with, and there'd be no instability. In order for there to be instability, you'd need the man she chooses to rather be with the man she didn't choose than with her. Of course, love "triangles" can still be complicated, because one huge assumption we made in the video is that people's preferences won't change. In a sitcom (and in real life), you can become more or less attracted to someone depending on circumstances, and the choice between two people can be very difficult to make. If you're curious to dive into some of the technical details here, the term you'll want to look for is "bipartite graph." That's a fancy way of saying we can sort everyone into two groups, with the condition that all the connections between two people involve one person in each group. If you learn about bipartite graphs in a class (usually Graph Theory or Combinatorics), one of the first things you'll prove is that they can't ever have a triangle, and that's what caused the problem in the queer case. In the straight case, notice that the algorithm we used takes advantage of the fact that we have two distinct groups, and the only connections were between those groups. If we had a way of creating two groups like this in the queer case, then we could apply the Gale-Shapley algorithm like before, and we'd have no problem. But if there's ever a triangle, we could run into trouble.
Calling it the stable „roommates“ problem made me laugh out loud. That is peak queer-related humor.
I first learned about this problem before making the "rainbow connection", but when I put two and two together it was like the stars had aligned; it was too perfect!
Oh my god, they were roommates
genuinely the funniest thing i've seen all day
@@sesemuller4086 And they were roommates?!?!
is this video a joke
As person 6, it makes me inordinately happy to be included in this proof despite the mathematical triviality of it. Thank you.
Aroace supremacy in action
I was a person 6 for a long time, wasn't necessarily happier, but certainly had less problems lol
but isn't there an assumption here that asexual/aromatic people cannot even be on the preference lists of other people? After all, you can lust after or love someone even though it's not reciprocated. Or am I missing something here?
@@pawem8942 I speculate that person 6 was exlcuded from the list of preferences because it would always result in an unstable pairing
@@pawem8942 i noticed this too, but it ultimately has no effect on the math if they were so eh
You did it! You tricked this gay guy who struggles with any math more complex than order of operations to watch a twenty minute math video with genuine interest. Very much proving your point at the end. Well done.
(also I too hate the concept of "love triangles" that are actually just V shaped. If it's not triangle shaped it's hard.)
The traditional Love corners...
True Love Triangle supremacy!
I like to call them Love Lambdas Λ
@@luxill0s stealing that.
Lol I just call them love carrots
I have seen a tumblr post along the lines of "that isn't a love triangle, that's a love corner, and usually the woman is the one backed into it"
Given the chance of genuine love triangles, I wonder how the problem would change when polyamorous relationships are added. In a way, the residency program example already gave a poly form of the problem with 2 students pairing with the same hospital. Obviously, allowing for arbitrarily high numbers of partners would inevitably become stable once everyone has become one single giant relationship, so it would make sense to focus on smaller limits or trying to minimize the average number of people in one relationship.
And yes, "Stable roommates problem" is absolutely hilarious.
Thanks for your comment, and yep, there's a lot to explore there as well! Unfortunately it wasn't something I could do justice to in the video, but I'll take a crack at it now.
With the caveat that I know very little about polyamory as compared to other queer identities, I'll mention two broad ways someone can think about polyamorous relationships. One that I think you're alluding to is a group of people who have open relationships. In other words, each person can feel free to have as many or as few partners as they desire, and any person's partners might or might not be in relationship(s) with one another.
In this model, the idea of a stable marriage is no longer something we have to care about or solve for, because the main tension in the problem is that people are limited by the partners they can have. In our relationship examples, every person can only have 0 or 1 partners. In the residency program example, each program can only have 0, 1, or 2 students, and each student can only go to 0 or 1 of the programs. In a world of open relationships, two people who like each other more than their current partners (the thing that gave us an unstable matching) can pair off without having to break their existing relationships, so there will never be an issue.
Another way to think about polyamorous relationships is that they're exclusive, but the number of partners in any given relationship is unrestricted. It's the difference, for example, between 3 people (P, Q, R) who have each of the others as partners vs. 3 people (P, Q, R) who are all in one relationship together. Again, I'm not an authority on polyamory, but the way I understand this difference is that in the first case, you need to consider the relationships PQ, QR, and PR, but in the second case, you need to think about PQ, QR, PR, and PQR.
When I wrote the part of script that mentioned restricting to 0 or 1 partners, I was thinking about this second case, because the underlying math needs to be extended in a pretty significant way to handle it. One way I thought about doing it is to ask P to give a preference list where they rank the three choices, "Q" / "R" / "Q and R"-notice that "Q and R" is distinct from both "Q" and "R". But an issue with this is that in order for the group "Q and R" to prefer P, Q and R have to be in a relationship. I don't know if there's a good algorithm to find a stable matching here, if one even exists.
@@edisonhauptman6886 Many types of polyamorous relationships exist, and from my point of view it would be disingenuous to try and optimize some group of people for the *most stable* sets of relationships, given the analogy of people we're using. The problem itself could have some interesting results when we detach it from this example and, while whichever scenario we create might be relatable back to some polyamorous relationship, another analogy might be more apt.
For the PQR dilemma: Whether this distinction is important to the problem depends on if we make it important, such as by making PQR some distinct matching where P has compatibility test with (Q), (R), and (Q and R). Is PQR considered more stable than PQ and PR? and how does that interact with other connections? I'd start by modelling the problem where each member is looking to match with exactly 2, 3, and n others, and change factors from there to see how the optimization rule changes.
In terms of relationships however, I personally envision the difference between (PQ, QP, and PR) and (PQR) as Three people who are each in a relationship, but they go out in pairs together, rather than as a trio.
Yeah many of the so-called love "triangles" in fiction are actually just "v"s involving straight people, although even in 2000 some cartoons started putting out love tringles with a straight and 2 bisexual (but more airtime for the characters' lust for the other gender) characters. With queer relationships, we can see even more genuine love triangles.
@@alex_zetsu love angles, the straight men love triangle, lol
@@edisonhauptman6886 Another way to model it would be to assume that each person has a limit for how many partners they want, but those relationships need not be complete graphs of that size. So for example, person 5 could want to date up to 2 people while people 3 and 7 might each only want 1 partner (but would be okay with person 5 having 2 partners).
Modelling a limit on how much polyamory someone would accept from their "roommates" would make things even more complicated...
This could be a pretty decent set up for a sci-fi story, a world that mathematically matches people and the weird pairings that could come out of it. I find the idea of a state sanctioned stable love triangle or an adequate enough couple to be hilarious.
This is basically describing a fanfic I wrote exactly. The AI couldn't find any viable matches for a girl, and the only reasonable option seemed to be sending her to live with her older sister (and her partners). Sometime after that the older sister came by, complaining that the girl had been assigned a separate room and couldn't spend the nights with them after curfew... That was the day the AI (re)discovered incest.
@@Metallicity sounded interesting, until the incest part. Please tell me it's a comedy and not a serious romance story.
Oh, that's Haven! Specifically the RPG on Steam.
That sounds similar to the comic L.U.F.F. In there, there is a government-sanctioned dating app that tries to match people. It isn't mandatory, but it does involve a love triangle sanctioned by the app. The comic explores a lot of the consequences of using an AI to essentially force people together, but it's primarily a romance comic, so if you don't like that I wouldn't recommend it.
I’m gonna write it. Stage play. Maybe.
Reminds me of one discussion in college (one of the super nerdy ones) where we got into the graph theory of all of the various "polycules". You think stable "roomates" problem is tough, now throw in poly queer nerdy college folks and you're now dealing with multipartite directed cyclic graphs :D
I'm gonna start calling polycules "multipartite directed cyclic graphs" lol
Tell me you've read the qntm article on building a database for same-sex marriage. It's a classic.
fun fact: the “polycule nested spoons problem”, where you try to stack the entire polycule in nested spoons such that two people in direct contact must be romantically involved with each other, is NP-complete. It’s equivalent to the Hamiltonian path problem.
My polycule is the example dataset I use for evaluating graph databases.
"Its times like this that i admire folks like person 6"
Aroace pelope: *visible happyness*
11:30 this is how highschool admissions work in bulgaria. Every child writes a list of preferred schools and schools take the ones with the most points, except each schools calculates points differently. At the end of the year there are 2 national exams: math and bulgarian (both 0-100). The points of the schools have to be out of 500.
The most common formula is 2×Math + 2×Bulg + Mark for the whole year (Math) + Year mark (Bulg). Both year marks 0-50. Most top schools however change the formula: math-focused high-schools might take the math 3 times and the bulgarian once, sport-focused ones might take your PE yearly mark (mapped 0-50) instead of maths, and so on.
EDI: 15:54 , its the student-focused version
We need a show where the plot cycles through a long set of relationship pairings, and the aces sit back with an infinite supply of garlic bread and watch the chaos unfold 😂
Why garlic bread and ace people
@@j.kkidding9764 It's a meme :) also cake XD
you guys are attention whores
It went from "queer people" to "residency program" really fast
Being Queers is one of those game modifiers that make the game harder but you are more rewarded for succeeding
Love life +10% difficulty
Public POV of you: -20
Happiness after finding love: +50%
RPG moment
Please critical success
Was expecting straight (hahaha) up sociology, got the first math class in 7 years. Very nice video, 100% would recommend.
they were roommates. god, they were unstable roommates
I watched Dr. Riehl’s video years ago, and it’s really stuck with me, both as an interesting math problem and a hilariously unexpected and accurate Pride and Prejudice reference.
I really enjoyed this video as well. The residency side of things was incredibly interesting, as it really showcased why this was a problem that needed solving, because it was creating a situation no one involved wanted. From a mathematical perspective, it was also interesting to see how multiple slots doesn’t complicate things, though in hindsight it makes sense as you could potentially treat each “slot” as it’s own suitor, with an identical preference list.
From the queer perspective, this is exactly the reason I’ve always felt a queer version of Love Island would be amazing. So much more potential!
The real reason queer relationship dynamics are harder is because you half-flirt with everybody in your friend group and everybody's confused on who likes who
To add to all the other comments about polyamory, I think another factor to consider, that would add yet another layer of complexity, is that for many poly people (and this is my case), "preferences" aren’t really a thing!
As in: for many of us there is no real ranking going on when looking who to date. Two or more people could have the same "slot" in the list, if you will.
So like if one person (let’s call them P) was 1 person away from being polysaturated (meaning they almost achieved their limit numbers of possible relationships at once), but that person had 2 other people they would want to date, and those two people had the same "slot" in the list, then P would be satisfied with either one of them.
Thanks for your perspective here! For the purposes of the problem, any ties can be settled arbitrarily at any point (though if you settle them differently at different times, you could certainly end up with instability in that regard).
This is so close to valence in chemistry I love it
@@rauld434 I know very very little about chemistry and physics but is that the thing where an electron will move between the different uhh layers of an atom only in very specific conditions?
I take it that a person with less than the maximum number of partners is polyunsaturated?
@@zetizahara 😆 I don’t think there is a word for that, so why not! I personally would just say "available" lmao
When I saw the title of the video, I was immediately reminded of the Numberphile video. I did not know about this "extension" to the problem, and the video was very enjoyable to watch. I also really liked the positive message at the end of the video. I hope this video will still get more views, because it definitely deserves it!
I do remember the same vid, and also took a time to play round with the idea of making it queer: more precisely, the candidates and choosers being of the same set. Soon became clear you can end up in an unresolvable loop, but hey.
Side note, I never understood why the straight love triangle was called a love triangle, it's more of a "love Y." For me, even as a kid, I always though a love triangle would be A loves B, B loves C, and C loves A
because is three people involved, triangle = three
It’s more of a love V or even L tbh because the relationship arrows are all independent from another
@@bilis2866 I mean ya it's 3, but like, not in the shape of a triangle, the person below your comment put it better than I did, it's more of a "V" than a triangle
@@waterunderthebridge7950 truuuue, idk why Y was my first thought, V is is better
@@paulinetrivago.7540 is not about the shape, there are 3 characters involved, so you have 3 side of the story
I can’t believe this is the only video you’ve made it’s so good 🥺
Oh my god they were roommates.
Really digestible breakdown of this concept! Very cool to see how math could be inclusive.
I am so glad to see maths educational content that's so inclusive! This would have made a great difference in my life if I saw it a decade or so ago. I am so glad this generation has the chance to grow up with it:)
Hey Alex, thanks for your message! One of my goals with this video was to make math feel like a more inclusive subject, since I think we typically look at it as impersonal. But the way we relate to math (much like anything else) is based on the connections we make to it, and as much as there's beauty in our abstract patterns, math is created and studied by people, and we all bring different perspectives to the table.
I can't wait for a "the liberals are taking over our math" joke
And they were roommates.
I came here to say that but in my heart I knew it was already here
Oh my god, they were roommates...
As a queer math nerd currrently going through a bad breakup, I relate to this video a lot lol
Honestly, a real life love triangle can cause pain, or blossom a polyamory
or both lmao thankfully im still still friends with both of them tho.
stable polycule problem
I’ve been watching many other SoME2 entries for quite a while now, but this particular entry made my gay heart happy!
One thing that I’d be really interested in looking into is the dynamics of polyamory in this; desired numbers/number ranges of partnerships for people, possibly having individuals that aren’t comfortable with their partner (or partners, but I don’t think that’d be as applicable to the real world) and other uncommon relationship dynamics that are still just as valid.
Great video by the way!
I am curious as to what would happen if you built (if, indeed, you can build) self-sacrifice into the system. For example, Person 1 prefers Person 2 but knows that Person 2 prefers Person 3, so would prefer that Person 2 is with Person 3 than themselves. That is to say that people (or, if we wanted to complicate things, *some* people) attempt to optimise for the preferences of the people that they would prefer over their own preferences.
Tbf, 3, 5 and 7 should just form a throuple, that would make all three of them happy :D
Maybe only one or two of them are open to polyamory, but the other two or one aren't... (There's another algorithm to create)
The subject material reminds me of the problems with voting systems. In each case, there are many people, and each person has some states of the world which are preferable to them over other states of the world, and the ideal objective is to make a 'most globally preferred' choice. Condorcet voting does seem like it might be suitable if it is generalized: in terms of pairwise voting, when comparing any state of the world where 1 and 2 are a couple, with any state of the world where 1 and 3 are a couple, individual 1 casts a vote "I prefer the former". Of course, once you do some research, you find that Condorcet voting does not eliminate the problem of preference triangles... it just makes them more explicitly blatant, easier to recognize.
... Framing things in this way makes the system even more powerful at keeping everyone happy, now that I think about it a little more. If we allow an individual to express preferences over differences in the state of the world that do not explicitly directly affect them, then in the residents/hospitals story, a couple could vote that they'd prefer to both be at their #3 choices in the same city rather than one be at their #1 choice and the other at their #2 choice at opposite sides of the continent. They could even vote that they'd rather get no residency, if they don't end up near each other.
Of course, generally, when pairing roommates up, it seems highly inadvisable to take into account the preferences of an individual who is not one of the pair, and may not even know either person in the pair. So practically, giving someone a vote in meddling in other people's affairs leads to difficulty. But the math works.
I love that you made a connection to voting systems! Yes, this is kind of similar to determining a Condorcet winner. If we imagine all of our relationship-seekers to be candidates in an election, and imagine the preference lists as rank-order ballots submitted by voters (with the people on the left being each voter's first choice, then the next person being the voters' second choice, etc.), then an election between 3, 5, and 7 would run into issues. Of course, in that kind of system, the folks supporting person 1 might not *all* have person 2 as their second choice, so it's not a perfect comparison. But it's still a really neat angle on the problem!
As for your comment on couples, the National Resident Matching Program (the system that assigns students to residency programs in the United States) can actually take into account couples' preferences to be close together. Unfortunately, the algorithm we went through in the video can't handle couples' preferences, and in fact a stable matching isn't *guaranteed* when you take them into account. But they've modified the algorithm slightly to adjust for this, and in practice I don't think they run into huge issues.
me before i was bi: SCIENCE
me now: GAY SCIENCE
I am also gay science. :3 Gay science is best science.
I thought I was missing math in my life. You've healed me of this notion. Thank you
Love the aspec representation in this video
6 an aroace icon fr
after seeing this video my first reaction was "hey ! Let"s see what more there is in stock here on this channel" before realizing it was your first and only video. i really like 3blue1brown's content and i think your's is quite similar while still being refreshing in it's own way and i truly would like to see more of it ! GL to you if you want to continue doing videos and i'll definitely check them out !
I came because of the true love triangle thumbnail I stayed because i learned that math can be actually interesting
nice pfp
When this video showed that you can get cyclic preferences in the stable "roommates" problem, my immediate thought was that this was somehow related to the Condorcet paradox - which also relates to a cycle of preferences, but in a voting system instead of a pairing system. You should also be able to define something similar to Arrow's impossibility theorem in the stable "roommates" problem too - that if the pairings are decided by a system based on a ranking of other candidates input by each candidate, there would be no way to determine the pairings without encouraging some candidates to input tactical preferences that differ from their true preferences in order to make their preferred outcome (according to their true preferences) occur.
I've heard about this problem before but never understood it in detail until now. Great video!
Maybe a "tier" ranking instead of this linear ranking would solve the instability. Perhaps the blue, pink, and yellow people all like each other enough to date, but because the way they were surveyed FORCED them to put it in a specific order it ended up being unstable
Aromantic people be chilling rn
Edit: person #6 is aro rep!
I'm trying to decide what field of mathematics I should go into. But I have proved that there is no way to determine. Unfortunately, since I have not yet studied combinatorics I can not check my work. Therefore I should go into combinatorics to determine if I should go into it. Which means that my proof was wrong since I have determined what field to go into. Which means I have checked my work so I don't need to go into combinatorics. Which means I was right that I don't know where to go and the checking of my work was in error.
Since my proof was both right and wrong, I should go into quantum physics. Which I do not want to do but evidently it is my first choice.
I have decided to pursue a dual major of quantum physics and not quantum physics. I can not say whether I like this or not, but I can't prove it.
May I recommend the books "what they teach you in Harvard business school" and "what they don't teach you in Harvard business school"?
Schrodinger's Major
@@brutusthebear9050 No
@@brutusthebear9050 Yes
17:43 Ahh yes, the infamous "love bent-line" authors keep trying to sell as a love triangle :)
This video was really interesting. I hope many more people watch it.
This was really cool and fun to watch! As an educational video creator myself, I understand how much effort must have been put into this. Liked and subscribed, always enjoy supporting fellow small creators :)
answer: polyamory
try it and you'll find out it does not make things simpler.
That's even worse
answer: world wide polyamory. Everyone is in relationship with everyone, so no one can go to another relationship.
@@TheEvilCheesecake it does make things simpler! But that doesn’t mean that it makes them easier. In fact, it makes them harder.
@@Данилтычкрейзи Isn't there some limit to the number of relationships humans can have or something? I want to say it's like 200 at varying levels of closeness?
Calling gay people roommates is literally 1984
I’ve had to wait for this to be recommended to me again to be able to save it
this video was very approachable! which I think is the problem most people who "aren't good at math" have with math
I've been thinking about this issue ever since I heard the original problem (I'm bisexual) but I never got around to actually trying to answer it, so it was amazing when I saw this video on my homepage. Also, "roommates" is just the best title that could be given to this paper.
Hey Edison! Nice video! Haven’t seen you since highschool, but glad to see you’re doing well
Hey Tyler! Great to hear from you, and I hope you're doing well too!
Do you think Irving was secretly thinking "gay" everytime he typed "roomate"?
The hospitals and student problem reminds me a lot of logic puzzles
You should add an "empty element", so that people can prefer having no match, but still accept a match.
The reason why this doesn't happen is because if you'd prefer being with no one as opposed to being with some person, you'd reject an attempt to be matched with that person, because you already have a "better offer"-either a more-preferred partner, or no one at all.
Put another way, matching you with a partner when you'd rather be with no one is automatically unstable, because you'd unilaterally break off that partnership to be with no one.
@@edisonhauptman6886 oh right, thank you for the response!
@@edisonhauptman6886 I feel like the problem will change slightly if you have the “null” spot as a lower priority choice, i.e. A would want to be with B, C or no one (in that line of priority) as that could influence stable matching (as both matching and not matching them can provide a stable match), thus potentially influencing who stays unmatched
@@waterunderthebridge7950 I encourage you to try this yourself. For example, add a "null" spot at the end of all the students' preference lists in the residency programs example, or add a "null" spot on the residency programs' end. I think you'll quickly see that there's no difference. There are some stable matchings where no one is matched, and the difference between that and matching them to "null" is negligible.
@@edisonhauptman6886 Yeah I would’ve thought there to be not a lot of effect for small groups. I was more thinking that a few individuals with a low priority null preference (not everyone in the group) may contribute to combinations that reduced unmatched individuals, thus contributing to a higher flexibility and ratio of good matches but that may also be somewhat of a human bias
Just adding a comment for the TH-cam algorithm the match this to more people
As a stem gay, I love this video.
3,5, and 7 definitely need to be in a poly triple lol
we're REEEEAAALLLY toeing the line here fellas
EDIT: disclaimers pog
This does remember me of the movie "moneyball". Great film about statistical tactics.
As a poly person that kinda tells me, that my way of holding a relationship is actually beneficial to mono people as well, given that if 3, 7 and 5 could live happily as a poly triangle, 1 and 2 would be decently fine and at least poor 4 would have a chance somewhere, as opposed to an unsolvable mess.
Of course this is extremely oversimplified and already fails with the assumption that people are emotionally able to make a proper assessment of their "ranking" in the first place..
But in a perfect world, mixing mono and poly - from what I can intuitively see - would make it a happier place for everybody~
.. Now when can I marry my partners for tax benefits? x)
Absolutely no idea why this video was recommended to me but it’s actually super interesting 🤔
Hold up, maybe I'm crazy but while you can't make a genuine love triangle with straight people you can make an unsolvable love square with straight people right???
I mean it'd be more visually interesting as an hourglass shape but yeah
Great question! It turns out we don't run into a problem here. If you have A preferring 1, who prefers B, who prefers 2, who prefers A, then you can match A with 1 and B with 2. While it's true that 1 and 2 will prefer the other person, both A and B will be happy, so there's no instability. (You could also match A with 2 and B with 1, and that will also be stable.)
This is a crossover i needed
This is good!! I felt like the video sort of ends in the middle, though. It’s like “look, it’s not always solvable!!!” But we don’t learn anything about *when* it is solvable, or, as many people have mentioned, polyamorous relationships.
As for how to specify the polyamory problem: maybe each person has a maximum number of people they can be with, and a maximum number of people they are comfortable with their partners being with? Not really related to how it works in real life, but I don’t think that people can reliably rank everyone in their friend group like this anyways, so I don’t think realism has to be a priority :p
I think a more realistic approach would be to say that someone: 1/ is either OK with their partner dating other ppl, or 2/ is NOT OK with it. That tends to be how it goes irl lol.
Okay I've wanted to make like queer-related/queer-y math videos in the future for when I feel like doing that maybe in SoME3 or something so this is so cool to see, as a trans person I like see very little math content that feels queer-er so this is just v heartwarming and inspiring and the explanations for everything were done really well so thank you for this
Huge polycule goes brrrrrr
Tbh the discussion is more theoretical than practical. Few queer folk are fully conscious of how other prospective mates rank against each other and preferences change according to the circumstances of the proposed relationship. Besides, no one has the time and energy to algorithmically pair up their connections since cooperation would be low. It's a neat thought experiment, though.
The idea is that the algorithm occurs organically and without any real cooperation. Each time two people realize that they would prefer each other to what they currently have, they will (in theory) make that change all on their own. They don't actually need to consult the rest of the group to make that change. The thesis of the video is that while this autonomous algorithm eventually reaches a stable point for straight couples, that's not necessarily the case in general; hence the title of the video.
@@JadeVanadiumResearch this is why I advocate for polyamory
This is mind-expanding material. A book I read on this topic was equally enlightening. "The Art of Meaningful Relationships in the 21st Century" by Leo Flint
...The scenario of seven people who all have different preferences for eachother and the inclusion of love triangles kind of makes me wonder if there's a connection to be made here between queer relationships and Pokemon typing. But then A's connection with B wouldn't be the same as B's connection with A, so... does that mean we would expand the problem to include not just relationships in general, but who's willing to top or bottom who?
How did the Yute-oob not recommend this to me sooner? In the top 5 topics I watch, it's a lot of math and queer content 😭
oh my god they were roommates
Nice! Loved the visuals to help explain the math.
The true revelation is that straight "love triangles" can't actually exist, it's just a love fold since a triangle needs three edges. Love triangles must inherently be queer to work, so basically afaik The Legend of Korra is the only show to present us with an actual love triangle in television so far.
The 'bottom' of the triangle in a more traditional love triangle is essentially there to represent the fact that in a lot of earlier ones the two people pinning after the 'top' of the triangle were often very close themselves, therefor making them have to choose between love and friendship.
nice pfp
I've seen a lot of people describe straight love "triangles" as love corners.
This is mostly because a lot of media has the rather concerning tendency of not really taking the woman's opinion into account, so it's more like two men backing a woman into a corner and forcing her to choose.
Usually when this isn't the case, the one couple is basically a guarantee, while the other love interest is just the antagonist/current boyfriend that the viewpoint character has to defeat.
If the story is from the perspective of the female character, the appeal of the story is often about how attractive the men are rather than actually making a decision, making those stories long as hell (this is common in comics and fanfiction).
You honestly get a lot of weird stuff when you write straight love triangles.
This is what happens if you don't enforce a strict top/bottom distinction
If we didn't restrict the number of partners to 0 or 1, could an optimal solution be found, or is that such a fundamentally different problem, that it can't be asked exactly like that?
Also, love the aro/ace rep with person #6
If you remove an upper limit of partners, judging only by quality of matches the simplest “optimal” solution would just be to group everyone together that wants to have a partner as then everybody would have their most preferred match (maybe sub-partitioned into closed chains of A - B - C - A in case of love polygons).
Of course, that might be an unsatisfying solution: The problem would then be how to value to e.g. being paired up with your first choice but also someone you haven’t chosen vs. secondary choices vs. not being paired etc. against each other.
@@grahamrich9956 Regarding people preferring to be with no one, they’ll will always reject any match because they have already found a stable match (i.e. no one)
@@waterunderthebridge7950 Ah so the solution to make everyone happy is "big ol polycules". That's based lol
"but first, let's talk about how medical students become doctors" [vsauce music starts]
Edit: I think they should all get into a polycule :) maybe that misses the point but
How did I get tricked into watching a math video 😭
AND I'm doing this to procrastinate on math homework
I'm surprised that an algorithm which would break up the perfect or near perfect matches for the sake of optimising some global statisfaction metric didnt show up or maybe there just wasn't enough time in the video to talk about it?
I am so glad you brought up this point! Solving this problem came with the assumption that we wouldn't want to have any instability-a term defined in such a way that we only have to look locally to check it. We didn't have to use an algorithm like this though. And maybe there is some global utility-maximizing solution that isn't stable. Given the choice between a globally optimal, unstable solution vs. a stable solution that isn't globally optimal, which would you generally prefer?
Perhaps the folks who use this algorithm (especially for real-world applications like the National Resident Matching Program) valued the perspective of an individual person experiencing the system that matches them to a program, and thus didn't think too hard about making a globally-optimal algorithm (or maybe an algorithm that maximizes preferences like this is hard to come by; I don't actually know of one off the top of my head).
Either way, that was a decision we made, and it's another wonderful example of how our values can inform the math we do!
@@edisonhauptman6886 my thought process behind it is pretty simple, we have algorithm that finds at least two stable solutions that maximize satisfaction of one of two groups (focusing on two groups as the single group model doens't even have a guaranteed stable matching) which is also the worse matching for the othr group so the globally-optimal one would try to find something that is neither best or worse for both groups
and maybe it's not nescesarily a question of algorithm (that one may be hard to find) but just proofs or examples of such matchings existing
cause the whole thing reminds me (a physicist) of finding an optimal path problem for some reason, where you would try to minimize some sort of function over the path, like energy (there may be some materials about it on some hastag for anyone interested) but that would probably require introduction of satisfaction evaluation beyond ordered list, thus making it more complicated especially for real-life application. Maybe thats why it wasn't explored (?) if I understood you right or was it just not a part of this specific endevour described?
As for your question I haven't given this idea enough thought to have a preference but I'd guess it could depend on situation, though the difference would probably require that more precise meteric to distinguish.
And a though at the end which poped back into my head after writinhg the rest (and I'm too lazy to try to fit this in), my mind for some reason associated this algorithm with hirsh index (where the two gorups would be publications and citations) but it may just be a wierd thought swirling through my head.
Excellent work
Oh nooo I said the same thing about both videos
It's true though!!!
Great video and message!
Here i was, thinking this video will be about quantum symetries and quarks
This is why I don't mess with combinatorics
Number 6 is so me, fr
This was a really informative video thank you
I loved this video, great work!
i love the fact that 6 is aroace
the Algorithm presented this video to me tonight and i'm so fucking glad. Exactly what I wanted to watch. A++ video, what a good explanation AND IT'S GAY
ETA: the solution is polyamory and personally i fully support 5, 3, and 7
Aww and there's even ace representation. Best math video ever
Can’t the med students at the start agree to the residency and then when another one accepts, just quit the one you already accepted, right? What am I misunderstanding here?
Huh, didn't expect this to be a #SoME2 video.
6 is just ace :)
Absolutely rad video!
17:58 thanks
3, 7 and 5 could be a happy triad :3
Actually, this doesn't prove that "finding a partner is harder for queers". It proves that a world where everyone is straight can always have stable matchings. But in our world, not everyone is straight, and this makes stable matching harder *for everyone* (regardless of being queer or not)
6 is the aro GOAT
Amazing video! The way you explain is wonderful
Starting to think I was tricked into watching math
this was insanely interesting
Great video! And great message at the end on how we can teach math in more inclusive ways.
Is there a simple reason why the stable matching theorem breaks down in the queer case? e.g. does someone have to go unmatched in every counterexample? or is it more subtle? I notice the theorem still works in the straight case even if the number of men and women aren't the same.
The trick is that in the straight/two gender case, you can't have an actual triangle, because each woman will only be attracted to men, and each man will only be attracted to women. So if you had a "triangle" of two men and one women, the two men wouldn't be attracted to one another, and so in this example, the lone woman could just choose the man she'd rather be with, and there'd be no instability. In order for there to be instability, you'd need the man she chooses to rather be with the man she didn't choose than with her.
Of course, love "triangles" can still be complicated, because one huge assumption we made in the video is that people's preferences won't change. In a sitcom (and in real life), you can become more or less attracted to someone depending on circumstances, and the choice between two people can be very difficult to make.
If you're curious to dive into some of the technical details here, the term you'll want to look for is "bipartite graph." That's a fancy way of saying we can sort everyone into two groups, with the condition that all the connections between two people involve one person in each group. If you learn about bipartite graphs in a class (usually Graph Theory or Combinatorics), one of the first things you'll prove is that they can't ever have a triangle, and that's what caused the problem in the queer case.
In the straight case, notice that the algorithm we used takes advantage of the fact that we have two distinct groups, and the only connections were between those groups. If we had a way of creating two groups like this in the queer case, then we could apply the Gale-Shapley algorithm like before, and we'd have no problem. But if there's ever a triangle, we could run into trouble.
Oh my God, they were roommates
This is what Love Island meant with LGBT people bringing logistical difficulties
That's the icon from 3Blue1Brown.
Yeah, this still hasn’t revealed how I can move my love life beyond a mere hot, sweaty one night stand in a Japanese bathhouse.
Yooo, that sounds crazy. Spill the tea