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so all I have to do is find 100 willing girls, take them all out on a date, then compare, reject or accept based on "simple" calculations... sounds easy enough.
There are 2 main problems with this in applying to the real world: 1. The population dating size is unknown or might be too large 2. That solution is assuming the other person always accepts you...
There's more, the entire setup doesn't really mirror dating in reality. You can talk to people multiple times, and it's not guaranteed that a person with maximum compatibility even exists. But this isn't about applicability anyway, it's just for fun. It's the same when teaching stable matchings from Graph theory, it's not really dating advice either.
@@jimmcneal5292 Of course, if you could represent dating compatibility with a number then some number is logically always bound to be the maximum. I guess what I'm trying to say is that compatibility in real life isn't cleanly ordered, and likely cannot be represented like that, so there may not even be such a thing as an objective best.
@@patryk6769 imagine being rejected just because you are part of the comparison group, doing everything possible in order to show how great you are but in reality it doesn't matter because you will be rejected regardless.
It can be, but in that situation, I don't think it's the best strategy. The company doesn't have to reject a potential employee before interviewing the next. They can (and probably do) interview all applicants, then choose the best of all interviewed applicants. In this hypothetical scenario, the best employees can be selected with 100% accuracy. They wouldn't settle for 37%.
@@Fouriersuirno the thing being maximized is definitely the probability of picking the absolute best person, the strategy happens to also make it likely to get someone pretty good but it's not being optimized for that
His result only maximizes the probability of hitting a singular result 1/n and treats not getting it as a miss. If there were a way to instead of looking for the singular best 1/n look to see which method maximizes the probability of getting something good or maximizes the “expected value” it could be more useful. I think that this is what op was trying to say.
I think we’d need a probability distribution on the compatibility values to even do that. What’s neat about this approach is that it doesn’t even need compatibility to have a value, only that it can be compared.
I decided to write a python code to test the results of rejecting 37 at the beginning and seeing how likely you are to get a perfect, and I got the expected ~37% result. I also would like to note I had it also find the average result it gets (whether that be higher than all rejected but found before perfect, or the last because 100 was in the forced rejections) and got the average result for this was about 81% compatibility, so the odds really are pretty in your favor
@michaeldesanta749 I wouldn't mind sharing the code, but before I do, I need to mention I am not a programmer or software engineer in any way, I have just picked up a bit of python here and there and it might be pretty unoptimized
@brujua7 It isn't, although I could probably find a way to make it. It factors in the 100s that were encountered which being about a 37% chance, skews it pretty heavily in favor of higher numbers
When you consider that you have to choose them, and they would have to also randomly choose you using the same maths, it’s incredibly unlikely that anyone gets together at all. In my friend group and wider group, there’s tons of crushes going around, yet there are no partners, because people keep developing crushes on other people who aren’t the person whose crushing on them, in some super complicated love polygon.
I was thinking the same, but you have to consider that the numbers we are using to evaluate the 100 people are NOT the grade we gave them, those numbers are the compatibility between us and them!
If you can redefine the methodology, you can change the problem. If you're allowed to talk to people more than once you can ask what the minimum number of conversations is to find the best match. Assuming you do 2 1:1 conversations, such that you can compare 2 people, this is a 2-way Alternative Forced Choice (AFC) comparison. At an internship I worked on an algorithm to find the highest ranking test subject 1. using as few comparisons as possible. For example, you do not want to tire from too much dating. 2. with as much distance between subjects. For example, you do not want the other person to tire from too much you. The result was to use merge-sort, which gives O(n log n) comparisons unlike trivial O(n^2) sorts, and doesn't use a sentinel (ex. comparing every person to 1 person, causing you to have a lot of conversations with that 1 person over and over). Even better is that as you approach the end of the study the rankings are pretty much already set before you finish. So you can end early with a "good idea" of a "group" of the highest ranks. Or, you can continue on and find the highest rank. The number of times each person would be compared is ~ log(n), so in the 100 person example, 10 times. Which isn't the end of the world for finding a soul mate. If you want to get really risky, you can up your AFC factor from 2. Comparing 2, 4, 5, .... partners at a time makes things significantly faster. Just be prepared for them to not like it.
Things i learned: 1. Be absolutely sure about your ideal partner. 2. Don't reject someone unless you are sure they aren't the one. 3. Have a good understanding about people and dating. (To minimise rejection) 4. This was a good video to understand statistics, calculus, combination and comparison.
As a biology student, I don't even think I need to make up a comeback to all the jokes he made about us, this video is proof enough that I'm not gonna have problems outcompeting this guy in the dating market
But what if the "scoring" follows a normal distribution curve instead of a linear randomness? And what if one wanted the highest mean score (you are ok with 99 or 98) instead of the absolute best? How would one optimize the outcome then?
I actually have no idea and it is something a lot of people mentioned. I'm sure you could develop a method which would like guarantee something like a 90%+ as opposed to only the best. Please give it a try and lmk if it works :D
Normalizing scores... doesn't do much here at least on in itself because it preserves scores(a.k.a. the absolute best is still the absolute best... and everyone's still compares the same with that person). But the "maybe get K people but go for top T instead of top 1" could change the game. As you increase T you increase your tolerance... or reduce your "good enough" threshold. It would increase your "success" chance... not in the sense you would get the top 1... but the top T; It probably reduces the chance of getting the absolute because you sometimes may settle early. But... it also reduces the chance of rejecting everyone when the top 1 is in the benchmark set.
At first i didn't understand conditions. Basically task sounds like this: 1) You have set of unknown numbers 2) you have to choose biggest number 3) you can create a set of numbers to compare from which you cannot choose 4) you can compare any number to numbers in created set, but if you don't choose it, it goes to compare set and you cannot choose it anymore
Pretty much yeah. It's important to remember none of this proof actually requires someone to be represented by a number. Its more that one person is 'more' or 'less' - or comparative compatibilities. Numbers just make it easier to quantify that visually and intuitively but we wouldn't know what each person would mean to us in the moment. Hope that helped.
I really enjoy when you take a moment to explain that a certain part is difficult to understand and to try to replay it or think it over. As someone with ADHD I often find myself losing my focus half way through the video and ending up not understanding the explanations by the end, so your disclaimers really help me fully grasp the ideas! Great job, I really enjoyed it.
The stock market would be another (maybe even better) application: say you're trying to find the best time to buy a stock over a certain time period (say 100 days for simplicity). The stock price varies randomly over time. You can't go back in time to pick the best stock price; at any point, you have 2 choices: buy the stock now or later. This optimal stopping problem also works for finding the best time to sell a stock.
it is interesting that for such quality, the video has less than 50 views now. You deserve more. Fun video. Honestly had me more gripped than most math videos on youtube that is some of 3b1b included. Good job man!
@@viks3864 What new style are you referring to? Either way, regardless of reception, in absolute terms, the video is good. Keep going. Thanks to you I have solved optimisation problems fed from chat gpt and it was fun. Your effort must be appreciated.
@scienc-ification2539 I normally keep the video completely driven by the topic of the video, not really involving myself or random jokes. I thought I'd make this more light hearted to see how it would be recieved.
Great video! We are really going to need a Mathematical Dating Advice Pt. 2 where we optimise for probabilistic expected value. My go to method would be running Monte Carlo sims but I am curious to see if you can derive a purely symbolic expression as you did here.
actually, the best way to find the 100% compatibility partner is to ask your current date its favorite number. if she/he says 7 or 42, you must choose that one partner.
Great video! By the way, on 16:57 I noticed you used \frac{}{} to write the fraction inside the ln, but if you use \dfrac{}{} instead the parenthesis become the size of what’s inside!
I think highest average is a more substantial thing to optimize. Since 37% the best is cool, but what if the other 63% is the worst, obviously this isnt the case but it shows the importance of the highest average selection.
It's actually a great point. In reality this probably isn't very useful but I liked the maths of this quite a bit. I may look into a way of optimising to get a greater average instead but I have no idea how it would work.
I did, it's infinite cuz your mum can be modelled by the harmonic series as the number of terms tends to infinity. On an unrelated note your mum is a Saint and I'm not sure how the apple fell so far from the tree.
Nice stuff! My only two notes would be that 1: The fact that there’s an approximation in calculating that sum means that there’s should really be an asterisk after anything saying “this is the optimized value” adding that “this number is slightly off, but gets more accurate the higher n gets.” Or something to that effect. And 2, which is a bit more substantial: I think it would make far more sense to maximize for the best expectation value rather than maximize for hitting the best person. With this method there is a substantial chance of the best person being in the comparison group, in which case the odds of who you end up with are the same for everyone (except the most compatible person whom in this scenario is *always* rejected) regardless of compatibility, which seems to me a flaw
They're all the same except for the best one, who has a 0% chance of being gotten, as in the situation they are in the trial group and rejected automatically
I was thinking the same, in fact by this strategy 37% is also the probability of the best person to be in the first group and therefore to reject everyone
Great video. I was just thinking about the fact that there is way more applications for this compared to the ideas discussed in your other videos. I saw quite a similar video by numberphile about this, but I found this a lot easier to understand. Nice video.
Yeah I actually found the numberphile video as inspiration for this one but I tried to expand on their method to try and make it more clear. I'm glad you liked it.
19:24 You absolutely should mention that you bring around a calculator and ask their favorite number if you think that represents you. They will have a better idea of who you are, and if they reject you, then they weren’t meant for you. Great video :)
Honestly, with the sponsorship, the quality and the didatics, I was surprised to see the channel has less than 2k subscribers and the video, less than 6k views. Keep up the good work!
I really loved every part of this. The problem itself seems unrealistic, saying you're randomly and blindly dating people, but it can truly be applied in some problem in real life, albeit strange. The simplification, which I find to be a necessary step in most problems, was done very carefully, the expansion into the greater problem, in order to generalise, was also very smooth and comprehensive. The mathematics are basically just simple calculus knowledge, and if anybody knows calculus this was very easy to understand, and the methods to reach the solution were confusing, but that's normal and you did your best to explain the reason behind what you did. It was very fascinating. Happy new year? Have a great time.
I simulated how the expected rank of the chosen partner varies with r (with n=100 and 1e5 rank orders per simulated r). the maximum of the expected value is way earlier than the maximum for choosing the best partner, at r=8 or r=9 (8-9% of the pool of people). Expected rank of the chosen partner is 91 vs 81 when using r=37.
I always did this, but rounded to 1/3 instead of using integrals and stuff, although it decreases the chance of me getting the absolutely best result it increases the chance of me actually picking something(I don't use this for dating but in general like choosing from different job offers)
Having not watched it, I imagine you'd speak to 33% of the people available, decide on one to be the benchmark, and then keep talking to the rest until one comes along at or above the benchmark, immediately choose that person and you're done.
my probability lecturer actually talked about this 1/e portion on optimizing choice with proof. but u explain these without requiring the audience to have all the prerequisite knowledge is amazing!
I think it would make more sense to maximize average compatibility, since there is surely a better strategy than one that gets an optimal match 37% of the time and a completely random match 63% of the time. A video on more possible strategies, like optimizing the median, average, or 25th percentile would be very cool.
Its not really optimal for dating because: 1. You dont know what "compatible" really means unless first, you accept a few candidates. 2. The most compatible and best quality candidates that would also accept you, are rarer than most candidates and, 3. The max number of candidates is unknown. So, If we account for point 1, then we would need to first accept a few people in the first group or else we will have 0% chance of knowing what true compatible is, then If we account for point 2; It would be a considerable risk if we reject the better more rare candidates, and point 3; we dont really know where exactly 37% is, so we wil have to approximate until we are confident enough on our selection skills. So, essentially the most optimal dating is just doing "normal" dating.
This is a nice approach but it could use some improvements: 1. Aiming at maximising the expected value rather than going for the maximum possible value 2. Including probability of YOU being rejected 3. Assuming a normal distribution instead of linear (as someone else suggested) 4. Giving some extra score to finding your partner earlier.
Wow thank you so so much. I wasn't expecting any donations but I appreciate it more than you know. I'm so glad you enjoyed the video and again thanks - I'll try my best to not upload once a decade xD
17:50 you have a point about e appearing everywhere, but it's important to note that you approximated that harmonic sum with an integral, so the answer is around 1/e, but not exactly 1/e, unless you basically have infinite girls to go on dates with.
I am like overjoyed you made this lmao i remember finding that comment so funny, and even better you took the ask seriously and turned it into a really cool math video !! please keep up the wonderful content !!! :)
Your content looks leagues above mine. Honestly its an honour to have so many people watch my video. I'm so glad you enjoyed it and good luck with your videos too :D
@@viks3864 I'm not sure about that one haha regardless, I'm certain this is only the beginning of your journey here !!! your content deserves many more eyes than you're getting at the moment, and I'm excited to see how your channel grows over time !!
Although this strategy does maximize the chance you get the best partner, I wonder if that means it's actually the best strategy? For instance, there is a 37% chance the best person (100) is in the comparison group. If this is the case, you are stuck with whatever the last number is (would this just be 50 on average? hm). Perhaps with lower comparisons you would reduce this likelihood, and therefore increase the *overall* result? Genuinly have no idea, I'm not a very smart person so maybe this was covered and I was confused by it lol
Yeah I get exactly what you mean. Most people would be happy with a compatibility of 90% + in reality. It's obviously possible to account for this into our method but it's a lot more difficult as we would need to extrapolate from our sample to figure out what 90% + really means. It's a great question though and I was going to mention it but the video was getting way longer than I wanted to as is, so I decided to leave it.
it won't be 50 on average, it will be lower. In the case where 100 is not in the first n/e people, you're bound to choose him or a maximum before him. So in the case where you went all the way to the end, that must mean the best people are at the start, and all of the people afterwards are worse than the maximum of the first n/e people, OR specific edge cases such as 100 is the last person. I didn't study statistics yet so I don't know the exact value, but be sure it can't and won't be 50, but less.
I think an intuitively optimal solution would be to look for the best partner for some number of people but at some point switch up your strategie to also accept the secound best and a bit after that the third best and so on. Until the second to last person, which you should choose if they are over avarage.
My first boyfriend, a mathematician wannabe, told me "only accept the ones better than me from now on, for I am least you should get" when we broke up. Boy was the whole comparison group.
For reference, women in the US, UK and Europe have an average of 7 sexual partners over their lifetime, and men have an average of 8 (according to the first result on Google, I'm no scholar). Making a naïve assumption that the average is a perfect distribution based on people traversing their respective arrays of partners, the total number of partners x in the array would be found by the equation .37x + (.63x)/2 = 8. Hence, x = 8/.685, or around 12. (10 for women.) As such, practically speaking, you should reject around four (maybe five, as a man) sexual partners for use as your test set before you even consider settling down with anyone. After that, any person who makes a better match than all four is a keeper.
Incredible explanation! 🎉 1 question: What if you dont know the exact number of those who you rejected. Like in life you wouldn‘t know that 1 out of the 37 was a 99, you would know it was nearly perfect (chances are, you wouldnt realise its a 99 and not 100 later in life😂. But a few early 90+ numbers will skew the continued rating for how far away a higher number would be. Is there a mathematical way to calculate the same question but with the uncertainty around the exact number included? :D
Hey glad you liked the video! First thing is that I would recommend never using this in the real world lol. Its more a funny way to let me ramble and make the maths feel more intuitive. Also to answer your question - we actually don't need to know the number of each person - for example that someone is 99. All we need to do is compare people - we are looking for the first person better than whatever the best was - the best could be 210 or 12 or in this case 99. Adding numbers to it just makes the comparisons clearer. I hope that made sense although feel free to ask any other questions you had.
Thank you so much :D. At the end of the day my video is still maths so the audience is slightly smaller but I really like the audience who watch so I'm more than happy to make them. Also the quality of my videos still has some ways to go but I think the quality has been gradually improving. Anyways thanks again
The problem with this is that there is also an equal chance that the ideal person is in the sample group - and then with this strategy, you end up *having* to choose the last person, even though they are likely to be a lot worse than other options (e.g. in your example the last person is 22/100). Surely an ideal strategy would take into account that we would rather have say, someone in the top 5% and have a higher success ratio than have a lower success rate only looking for the ideal person (and therefore the majority of the time being left with the last person and therefore a complete lucky dip)
I wonder how much more complicated this would get if you added the real 2 party system. (not politic), where a girl is also simultaneously going after people that SHE is trying to maximally date, so you could also be rejected. Supposing there's a 'soulmate' for every person, it's also possible that you accidentally reject your soulmate since they are in the initial 37%. Wack
Problem with this is you would need to create a model on how the other party would react/strategize, which I don't see a clear way of doing beyond "make them maximally rational" which I think would result in behaviour that doesn't track well to the real world.
The issue with real life dating apps is that loads of people's ideal partner will be one specific person. Not to get too deep into it since no-one cares but it has been shown that in samples of 100, women and men tend to choose only around 10 as their top pick which makes it difficult for apps. With that tangent over, give it a try yourself and let me know if you figure anything out - it's always nice to test your hypothesis.
I think I saw this same problem on QI or Numberphile or something like that. The objective was to find the cleanest public toilet instead of finding the ideal partner.
As an economist, I see the solution much simpler and change initial conditions. Met girls in the place there you might know their behavior, and I'm not about some apps. Deside that you like and go there, bord game club, dancing school. Ask friends if they know someone who fits you. And use more tricks to make randomization not so overwhelming.
Yeah I know it becomes way more complicated. The issue seems to be that a lot of people tend to find the same person as their ideal partner meaning there is a lot of cross over. I know modern dating apps have ways of dealing with this but I am nowhere near smart enough to understand it xD.
Pre filter with clustering algorithms and only match within a cluster or cluster pair. At least that's my initial guess. Bipartite matching algorithms may be O(n^2), but when n is somewhere beyond the thousands and "computation" time takes hours, you still have an interest in reducing the size of the solution space. This does assume people are told where they rank within the pool of applicants, which I'm certain dating apps don't do
Interesting video explaining the Optimal Stopping Theory in the context of dating (where you reject about 37% of the people you meet and then accept the next person you think is better than everyone else you've previously met) in the fact that even in dating, math can help you out with optimizing your experience to give you the best chance of success. I've seen this talked about from other RU-vidrs and before that I didn't know that you could use a math to help you out in this specific scenario. The issue with this is that you do have to have set some sort of quantitative limit on how many people you meet so that you can use this strategy (i.e.: 100 people), otherwise it's much harder to judge when you've rejected 37% of the people you met then pick the next one that's better than everyone else you met previously. Regardless of this, it's still lovely that math gives you a helping hand in the dating world even if you despise the subject itself.
I think this speaks to a fundamental rule of dating. The previous experience with people in general. If you don’t have a good idea what the characteristics of a good person even are, you are unlikely to realize you even found someone worth pursuing.
Girl: " I have to go now, that was a nice date. Wanna meet again maybe next week?" Absolute dating master: "Well, actually, if you look right here, * takes out noteblock * the rating I've given to you is pretty good, but not better than the best rating in my comparison group, so- hey, where are you going?!"
Catchy title of the video, but I think it's worth mentioning that this method can be used for optimising in all problems where you need to choose from a sequential flow of offers, not only for partner finding purposes :) For example, search for accomodation, recruiting etc.
At 16:49 you replaced the summation with an integral. I obviously get where the general I tuition for that came from but was this done with the supposition that r tends to infinity? (for it to be approximately equal) Or are we just taking a good enough approximation.
Yep exactly - the probability of success and percentage we reject is only 1 over e as r and n tend to infinity. It makes sense that the number of people we reject was always bound to be some percentage of n as opposed to an absolute value like 7 so in the formal proof, they just tended n to infinity.
I love how i wouldn't ever actually do this to find a partner in real life, but I still learned a lot of things, mostly how to think about problems like this
My math professor in college brought this up. He also brought up that statistically, men only fall in love 3-5 times in their life and typically only have about 8-10 meaningful relationships. So the 3 or 4th girl you fall in love with was the best option. Then again, he was twice divorced and 40, and this all takes no account into the variance of the poison distro. But it is a funny way to consider the secretary problem.
lol at least it's biology and not... geology. yuck. Nah I'm joking - its good to be passionate about things and if you are passionate about a lot - it just shows you have motivation which can never be a bad thing. You can be a 4 :D
Great video! I have two questions. What happens if the most ideal partner is within the initial rejection region? Do you reject all of the others until the very last option, which you accept? Also, you said that this integral approximation holds for large values. Is the success equation still decently accurate for small samples? Keep them coming! I loved this!
Yep exactly, if the ideal partner was in the rejection region, you would reject everyone until the last person. And again you said it perfectly - for large values success rates and percentage of people rejected get closer and closer to 37% although it is still relatively close for smaller values of n too. Glad you enjoyed it!
Not gonna lie, I thought I had it down to an art at this point. But nope, once again viks has blown me away with top notch quality content. New style of video is 100/10. Do recommend not being as cool as u r tho cos then gonna be no women left for the rest of us.
Why not just (in this theoretical kingdom) just to date all candidates in order and keep one in "top spot" position untill 1) someone else reveals themselve as more compatible at which moment replaces previous "top pick" 2) queue ends and you say "yes" to the top dog Tip: keep 2nd and 3rd place number saved in case that ur ideal relationship fails after some time. So txt them up and see if they are free.
This actually can lead to much more complex questions. First because we can change how we measure succes other than just "get the best person = win, get any other person = lose". Because like, in this method we have 1/e chance of speaking to the very best person among the first ones, and this would lead to we chosing the last person, that is someone completly random. But how to measure succes is completly arbitrary, taking the average is a natural follow up but maybe if we want to lower the chances of getting someone bad, the geometric mean could be better since it "punishes" more an lower result, or if we actually value so much the very best person, an quadratic mean could be better since it "rewards" more a good result And if we want to add one more layer of complexity, we could add a score to each person. This way if we talk to someone that is better than everyone before by a huge amount we can use this information. And finally we could change how the scores distribute. For dating we should use normal dustribution because that's how basically all human chacteristics spreads. But maybe looking at uniform distribution could also be useful, especialy if we are interested in other aplications (keep in mind that this is actually a quite genric scenario). Anyway, adding all of this may have turned it into an unsolvable question in pratice (maybe not idk) but even if we can't prove one algorythm to be the best possible one, we can try to find some efficient and simple ones. This now is actually more of a computer science problem than a mathematical one but still an interesting problem in my opinion Btw (if someone actually reads this entire coment lol) English is not my first language, I usually don't make this disclaymer but there were lots of words in this text I wasn't sure how to write and I didn't search all of them up, so sorry if something is misspelled
I'm a computer engenering sutudent btw, and this coment probably reflects a lot of that lol. Taking an math problem and making it closer to reality to the point that math can't (probably) solve it anymore, but computer science can give good answers
Can you figure out how compatible you are with someone without spending more time together? Also in real life you can sometimes get back with someone you rejected
Before fully watching, my prediction: Talk to the first 25-50 and once you find someone that you feel is better than all spoken to prior, pick them. That way you take a sample and can predict if you have found a positive anomaly
