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How To Marry The Right Girl: A Mathematical Solution (npr.org)
320 points by ColinWright on June 13, 2014 | hide | past | web | favorite | 194 comments



... the best way to proceed is to interview (or date) the first 36.8 percent of the candidates. Don't hire (or marry) any of them, but as soon as you meet a candidate who's better than the best of that first group — that's the one you choose! Yes, the Very Best Candidate might show up in that first 36.8 percent — in which case you'll be stuck with second best, but still, if you like favorable odds, this is the best way to go.

Maybe I haven't had enough coffee this morning. Can someone explain how you would get second best in this case? Wouldn't you never meet a candidate better than the best of that first group and exhaust the rest of the candidates?


It's good that they finally mentioned it at the end - this is a flavor of the optimal stopping problem (http://en.wikipedia.org/wiki/Optimal_stopping). This is a cute application of that strategy, the problem is that mathematics has very little to do with actual relationships, as much so as the assumptions game theory makes about actual relationships (http://crookedtimber.org/2005/10/13/whats-wrong-with-game-th...). Whats more important than trying to play your luck in a relationship is: working through the grit of an actual relationship.

In reality - if you don't put in the actual work any single relationship takes, then none of them will work out, it doesn't matter how large your "sample size" is.


The article blithely describes the "best" strategy, without defining "best." I believe the strategy is only best in the sense of giving the highest probability of ending up with the best candidate--so the second best candidate is considered as bad as the worst.


It also actually maximizes the expected rank of the chosen candidate.


This is not true. To maximize the expected rank, reject the first sqrt(n) candidates, and then pick the next one better than that group. Once you have more than 7 candidates, this means that for maximizing expected rank, you want to reject fewer candidates than if you maximize probability of choosing the best.


Can you link me to a proof? I recall working this out and finding that the solutions were the same whether you were maximizing rank or maximize P(best)


It's pretty easy to see for yourself that the two metrics can't simultaneously be maximized.

Imagine a situation where you've already passed by all of the candidates except for the last two. You meet the second-to-last candidate, and she's at the 99.99% percentile, but there was one single previous candidate that was ranked higher. What do you do?

If you want to maximize the expected value of the rank, you have to pick her, because the odds that the last candidate is better is vanishingly small. If you want to maximize the chance that you pick the maximum rank, you have to pass, because the chance that the second-to-last candidate is the best is zero (since you've already seen one who's better).


Does http://en.wikipedia.org/wiki/Secretary_problem#Cardinal_payo... work? They have a sketch derivation.


This is under this hypothesis: "the interviewer does not learn the actual relative rank of each applicant. He learns only whether the applicant has relative rank 1." I think this is rarely a reasonable hypothesis. Kepler certainly could tell how much he liked each woman, not just whether she was the best so far or not.

Under the (reasonable) hypothesis that you get some information about the relative value of each candidate, I believe spacehome is correct and the optimal strategies ARE different.


Thanks! Looks like I worked it out wrong. Intuitively it makes sense that the results would be different.


Imagine you had 11 candidates like he described, and you interviewed them in random orders. For ease, we will describe them by number, which will also equate to their "goodness" by arbitrary criteria (known to the interviewer only).

One of the worst possible cases would be that you interview them like:

1 2 3 4 5 6 7 8 9 10 11

In this case, you would see them decreasing in "goodness" without ever increasing. You would get to 11 and be stuck with the crappiest whatever possible.

In the average version though, you might get something like:

7 3 4 6 5 8 11 1 10 9 2

Using their strategy, you would check the first 4 candidates (7 3 4 6) and then you would stop when you hit better than max(7 3 4 6) = (3), which in this case would equate to finding (1) at the 8th position.

You are correct that if the best is in the first block it screws everything up. In the specific version you mention, a possible arrangement that triggers could be:

3 9 8 1 5 10 2 6 4 7 11

You would interview the first set with a best of (1). All the rest would then not compare, and you would get (11).


Yeah, 36% chance of getting nothing isn't great. I'd expect that for the last third, you might want to settle for someone who is a bit worse than the best of the test group.

This algorithm is only good if you'd rather have nothing than second best.


(FYI, the scale used in parent's is 1 is best, 11 is worst. Confused me for a bit.)

[Edit - Ignore me. I guess you can't recall rejected candidates.] In your final example though, because you had now interviewed all the candidates, you could go back and offer jobs to the best candidates. The point of interviewing four and then interviewing until you find a better one is that it should keep you from wasting time interviewing the whole list. If you end up doing that anyway, you know who the best was and can hire them.


Yes, that appears to be a mistake. In the 36.8% of cases where the best candidate shows up in that first 36.8%, it would seem the algorithm must keep running until it is forced to select the final candidate, which is essentially a random choice out of all but the very best (assuming ordering has no relation to goodness) -- very different from being "stuck with the second best." However, the rest of the quote -- "but still, if you like favorable odds, this is the best way to go." -- might very well be true.


Presumably the optimal strategy would be to gradually lower your standards the further you go. It's easily proven that the optimal strategy for the second-to-last candidate is to select the candidate if the candidate is above average. So the algorithm as described in the article seems to be missing something.


I think I've got it.

The main thing here to notice is that this is a strategy and not a solution.

If the best options is in the first 1/e * n of group elements of the group you will end up with the last interviewee as the one to choose.

But if you use this strategy many times over max permutations of the group it WILL give you the best output in general.

btw i would like to thank the author for posting this.


No, you're right. You will be stuck with the last one, not the second-best one.


Presuming 'serial dating'. You can actually know several people at once, and get more serious with one once you've evaluated the pool.


That's concurrent, not serial


The parent to your post could be rephrased as:

> That presumes 'serial dating,' but you can actually know several people at once, and get more serious with one once you've evaluated the pool.


I think that's what they were trying to say


It's flat out wrong. You'd end up with the last candidate, not the second best, as you say.


Similarly, isn't there like a 10% chance you're stuck with the 3rd best candidate? Is that still good enough?


The point is, he will not end up even with second best if the best candidate is in the first group. Rather he will end up with the last candidate hitting a dead end just like the example. That's because no one in the second group is better than the best in first group.


Yeah I misread that. That's true, but my point still stands as well. It sounds like using this strategy as it is written yields increasingly poor results as the sample size increases (assuming a total ordering)


Yes, increasingly poor, but converging on 1/e. http://en.wikipedia.org/wiki/Secretary_problem#Deriving_the_...


Immediately reminded me of this:

A store has just opened in New York City that offered free husbands. When women go to choose a husband, they have to follow the instructions at the entrance:

“You may visit this store ONLY ONCE! There are 6 floors to choose from. You may choose any item from a particular floor, or may choose to go up to the next floor, but you CANNOT go back down except to exit the building!

So, a woman goes to the store to find a husband. On the 1st floor the sign on the door reads: Floor 1 - These men Have Jobs

The 2nd floor sign reads: Floor 2 - These men Have Jobs and Love Kids.

The 3rd floor sign reads: Floor 3 - These men Have Jobs, Love Kids and are extremely Good Looking.

“Wow,” she thinks, but feels compelled to keep going. She goes to the 4th floor and sign reads: Floor 4 - These men Have Jobs, Love Kids, are Drop-dead Good Looking and Help With Housework.

“Oh, mercy me!” she exclaims. “I can hardly stand it!” Still, she goes to the 5th floor and sign reads: Floor 5 - These men Have Jobs, Love Kids, are Drop-dead Gorgeous, help with Housework and Have a Strong Romantic Streak.

She is so tempted to stay, but she goes to the 6th floor and the Sign reads: Floor 6 - You are visitor 71,456,012 to this floor. There are no men on this floor. This floor exists solely as proof that you are impossible to please. Thank you for shopping at the Husband Store.


I married the first girl I dated because I waited to date someone I was truly attracted to, that I felt was my mental equal and who could hold a real discussion (plus she's beautiful). We've now been married 27 years ... I hope it's not a fluke!


I've noticed a trend with computer people who married the first person they dated and the marriage being very successful (in terms of longevity at least). I haven't quite figured out why that is but I would say the vast majority of my software engineering friends are like this.

I've been told by women who are in my other circle of friends that they wouldn't want that because then they feel like they aren't the first choice but whatever the guy can get. But then I think about the marriages that have resulted and how happy those people are. Sometimes I wonder if people over think these things.

Forget the Kepler strategy. Forget getting the "best", if there is such a thing. If you click with the other person and both people care for and are kind to each other, then go for it and enjoy love and life.


> married the first person they dated

> the marriage being very successful

> I haven't quite figured out why that is

It is not about software engineers, it is a general correlation to the "numbers" of pre-marital dates.

The lower the number of partners before marriage, the more likely is the marriage to succeed:

> http://socialpathology.blogspot.com/2010/09/sexual-partner-d...


Isn't this data very skewed by the fact that not believing in cohabitation and not believing in divorce are highly correlated? This group includes lots of marriages that I wouldn't consider good outcomes even though they don't end in divorce.


> The most salient finding from this analysis is that women whose intimate premarital relationships are limited to their husbands—either premarital sex alone or premarital cohabitation—do not experience an increased risk of divorce. It is only women who have more than one intimate premarital relationship who have an elevated risk of marital disruption.

As far as I can see this suggests that believing in cohabitation is not a strong factor when it comes to divorce.


I think this is a very important point that is often overlooked.


As I see the data in those green bars (the chart in your linked article), the chance of your marriage surviving ten years falls with each non-marital sexual partner you had before marriage in the way you might expect if your current partner had to go on competing with all your previous partners simultaneously. If she's the only one, she's the best. If she's one of two, the chance of her remaining the best is 1/2. If one of three, only 1/3 chance that she goes on seeming like the best of the lot, etc. (And substitute "he" where appropriate and note that the same calculus is being applied to YOU, too.)

Of course, maybe the marriage survival doesn't require being the best but just >= the past average or some other variation, but that still leaves a curve dropping in a sort of 1/n Zipf Law descent into too-bad-for-you-ness where the competition with the "ex"es never ends. Yikes.


Thank you for that data - I've never seen it before and it's really interesting.


This is very well discussed in Erich Fromm's book "The art of loving". He proposed that in today's society we put too much value on the object of love, and too little in learning how to love. Thus we look intensely for the best possible partner and we may have second thoughts even once we reach a decision, instead of learning how to love and enjoy life.


Eric Fromm also said true love is letting that person you love sleep with other people if it makes them happy. I have been with one person who I felt I loved according to Fromm, but I was not attracted to her--so I guess I never loved? By the way, I think Fromm is right, but I'm just to selfish, and he said that before AIDS. I wonder if he would be so cavileer today?


Intellectuals have been known to give terrible relationship advice. They have their theory and they apply it. You can't hold them responsible when it blows up for you. I don't have advice on what to do, but mix a good dose of common sense and your experience of human nature in with Eric Fromm.

Edit: It sounds to me like you are rationalizing and intellectualizing.


Parents who truly loved their children would let their children pick others as parent figures if it's what would make them happy. I think there's a difference between that love and romantic love.


If that's what you believe, wouldn't you also say that true love is not sleeping with other people if it makes your love unhappy?

"You love me, so you allow me others; but I love you, so I will not take them."


Computer person here, married to the third person I dated. We met our senior year of high school, fell in love, got married a few years after that. This year will be our 20 year anniversary.

I dunno, you meet someone you like, why date more people just because? I never really understood the survey-the-field strategy. Seems like a recipe for disappointment.


In choosing a partner, satisficing beats optimizing any day.


Yep - I married the woman I've been dating since I was 15. We've been together 8 years now (not married the whole time).


well, the pessimistic view, as also expressed by michel houllebecq in his books:

ugly, weird, fat (and come on, look at our industry) people tend to stick to their partners because they know that the alternative is not another partner - but being alone.

truly attractive (varies by gender, between pure aestethics and power, wealth) humans tend to have more relationships - because of pure availability. it is one thing to stay loyal if there is no one actively going after you, but a whole other ballgame once you have suitors.

"is there someone better out there for me?" is the key question that defines longevity of marriage. and fear of being forever alone is a strong bond.

think about it the next time you see a morbidly obese couple living "happily" together.


This somewhat reminds me of when Microsoft announced the Zune. One of the selling points was (in true nerd form) you could send a song to a cute girl nearby. To which Steve Jobs replied, "Or you could just go up and talk to her."

A bunch of mathematicians came up with a formula for finding a wife. @smoyer effectively just went up and talked to her.

Kudos to you sir... and your wife! :)


Didn't they call it something terribly awkward too, like 'spurting?' Oh, no, it was 'squirting': http://www.newsweek.com/zune-should-go-beyond-squirting-1072...


Guy: "I just squirted a song to you" Girl: ... Guy: <forever alone>

Good job Microsoft.


That was one of the worst names for a feature I've ever heard. And I was a happy (for a while) brown Zune owner.


Did you ever own an Aztek?


OT, but as a younger guy I'm curious: how old were you when you met?


When we first met, I was 17 and she was 14 but we were friends for a several years before we even started dating.


My wife and I met when I was 15 and she was 16. After dating other people and a few years later we ended up getting married at 21 and 22. After 13 years, two kids, and watching many hours of "Star Trek" and "Pride and Prejudice" together we are still happily married with hopefully many more years to come.


My wife and I met when I was 18 and she was 16, online (playing the same video game). We married at 20 and 21.98, and are going on 12 years now.

Here's what my wife wrote a previous time this algorithm was discussed:

"To pre-optimize a future wife, focus on being a man of character. Sacrifice for noble goals, exercise self-discipline, show love to family, especially your mother. To optimize an existing wife, continue to do those things, and also spend a lot of time together, be romantic, communicate honestly and frequently (pursue intimacy; resolve to hold no secrets), and ensure a good sex life for her--which for you means generosity and an eye toward emotion."

followup:

"Over ten, fifteen, twenty years of marriage, the single largest factor in who your wife is, is who you are. And vice versa. Her criticisms become your defensive sore spots. Your generocity becomes her avid interest. Your callousness becomes her indifference. Her complacency becomes your disinterest. And on and on. After many years, every groove in your soul matches a cusp in hers, and vice versa. There's feedback. There's resonance. That's why the quality of your wife is 120% you.

You grow to be like who you hang out with. You rise to high expectations or sink to low ones

....

To optimize your wife, optimize yourself. Because marriage is really long, and after just a few years, she's mostly who you've made her."

( Full discussion at https://news.ycombinator.com/item?id=1236686 )


Did you take a very high speed trip between being 18 and 21.98 (as your wife aged 4 [Earth] years and you aged 3.98)?


We lived at different altitudes.


That advice is completely spot on :)


My story is almost exactly like yours. Met at 15, married at 22. We are only married for 1 years now though, though we've been living together for 6 :)


We met when I was 32 and she was 31. Second person I ever seriously dated. I'm 40 now, and everything is looking well.

Don't be in too much of a hurry.


I give it 28 years, tops.

jk, congrats on a successful marriage!


That's how long my parents lasted.


<3


<2 as well


false


The 38% sample allows you to build a model of the population distribution based on which you take your decision.

But this does not mean you have to do this EVERY time. Say you have done a round on interviews before and you are tasked with interviewing for a new position: you might hire the first person you speak with because you know the population model, and they are high up with respect to that.

In common parlance, this is called "being experienced"


In this particular case, it means you've interviewed more people in advance.


This isn't literally about selecting wives.


In that case the term is "divorced".


For those who are interested, this is a nice write-up: Knowing when to stop [1]

[1]:http://www.americanscientist.org/issues/id.5783,y.2009,no.2,...


Thank you. This is a much better article since it actually lays out and explains the reasoning behind the solution, as opposed to blandly stating "it has something to do with e" and padding up the rest of the note with grotesque drawings and minutiae.

(Also I appreciate what seems to me the less stridently gendered tone of the American Scientist article. Just a personal and subjective opinion though, so please be tolerant and try not jump on the hate.)


Can anyone point out the strategy to the example for 2 cards in the range [1,100] and the probability of winning?


This formula is great for "good enough" problems. The way I use it is to mark the first thing that is good enough, but then keep looking for something that is better than that, then stop. Works great for apartments, books and ice cream.

The key is to realize time and effort is finite, and that you can always keep on looking if you don't have a stopping point.


Also, a normal distribution would help, so you don't encounter values way off that would skew the results.


This is great; however, I don't quite understand how you can 'be stuck with' (i.e. choose) the second-best option if the very-best occurs in the first 37%... Surely you wouldn't be able to realise/decide that there is no one better than the best from the first group, if that is the case, until the end — by which point it's too late?

Am I missing something? Surely...


If you follow the rules of the equation, if you get to the end, you're marrying the last person you dated.

However, as noted in the article and by yourself, real life is never so constricting as only allowing you one chance at any particular person.

On the other hand, once you've passed on someone, there's nothing to guarantee that you'll be able to go back (they could be engaged, have moved away, hate your guts for evaluating mates by a mathematical formula, etc).


Hating your guts is so often a dealbreaker in relationships :(


Have you ever dated/married Indian, Catholic, or in more conservative groups?


So that's how you can make someone love you!


What does love have to do with marriage?


The scenario is that passing on a candidate means they might become unavailable, or choosing one means you can't look at the rest. Basically, how to choose the best item when you have to choose and can't change your mind?

Well, you can't guarantee you choose the best, but you can try to maximize the chance of doing better than random.

This models real-world situations such as (the article example) picking a wife from a pool of women, or even something such as who to hire from a pool of job applicants. In these scenarios, job candidate you passed on might take a different job, or the woman you choose to marry means you can't date the rest, or vice versa.

Obviously, if you can examine everyone and then go back and choose, you'd do that.

The irony is Kepler actually did get to go back - he hesitated on #5, she became unavailable, then he went through the rest of his list of women... and went back to re-woo #5. So he got to see all the candidates before choosing. ;)


Suppose the case of interview for a job where half the applicants are unqualified. This algorithm has an ~20% chance of hiring someone unqualified.

This algorithm seems optimized towards getting near-optimum rather then limiting risk. I think for real world problems it'd be much better to lower your standards as you near the end of the pool.


I think that's right. The only way you can choose the second best (and know it) is if the best occurs in the first 36% and the second best candidate is the very last one (if the best occurs in the first 36%, you'll always end up with the very last candidate, since nobody will satisfy the criterion of being the best so far).

You can unknowingly happen to choose the second best if the best candidate occurs among those you never consider because the second best is the best 'so far' when you get to them.

But the way it's described in the article is incorrect, as far as I can tell.


Forget about finding the right girl only. You also need to pay as much attention to her family and HER mother. Your wife will very much likely turn out the way her mother did, in terms of how well she keeps the home in order, raise kids, and AGE as time goes on.

IMHO, it's remarkable how a girl ages the way her mother aged. And some age well while other don't (both in physical/emotional).

So, don't get hung up with the girl only. Think about her family in your 'equation' too.


> Your wife will very much likely turn out the way her mother did, in terms of how well she keeps the home in order, raise kids, and AGE as time goes on. IMHO, it's remarkable how a girl ages the way her mother aged.

IMHO, it's remarkable how your primary measures of a woman's worth are housework, childbearing, and physical beauty.


A woman's worth as a human being and her suitability to marry some particular man are two different things. Most men want attractive wives who are good mothers, just as many women want attractive husbands who are good fathers.


moreover, those attributes can serve as proxy measures for others.

My mother-in-law's skill and dedication in keeping house is reflected in my wife's skill and dedication in writing clean code.


I'm sorry if I offended you that's just a short sample list, really short.

And I did say in my original comment about physical/emotional change people have over time. Some people don't age well emotionally.


It's amazing that's what you took away from a very insightful comment.


Thank you exabrial.

Maybe I should've put this in original comment:

Before marrying, people wonder "do I want to spend rest my life with his woman?" Well there's a good prediction of what your future wife will be like, and that would be her mother.


I can't agree with housework(I don't care), but I do care about how a person treats kids, animals, and the less fortunate. The mother can be a good barometer, especially if the bride is not educated. As to looks, I thought it didn't matter, but I was recently reminded how primitive I really am. I was, I thought, in complete love with a Midwestern girl in the 90's. Eric Fromm type of love! I just was her at DMV and that love was gone. She morphed into her mother. Her voice changed. Her liberal views were buried under layers of the wrong foods, and too much alcohol. I didn't recognize the most beautiful person I had ever come across. She knew I liked her years ago, and abused it--so maybe my repulsion had more to do with that, and not the way she aged? I'll never know?


Every woman becomes their mother. That's their tragedy. And no man becomes his. That's his. - Wilde


This has to be the most insane, cavalierly misogynistic comment I've ever seen.

Incredible. I'm laughing and crying at the same time.


I'm blushing that it came across like that. I just meant to say how a young woman eventually becomes a very similar mirror of her mother as time passes.

I didn't mean to say I or anyone should measure a woman with how she keeps home or raises kids or physical beauty only. It was as sample list.

What I meant to say is you obviously don't want to marry a woman who's a great person today but turns out to be a terrible person tomorrow or 10 years from now (because everyone ages and changes over time). Of course there are unexpected/terrible things like diseases but basically you would want to marry someone you like your whole life. What I've seen is that when a mother in law is cranky and unhappy at older age for whatever reason, the daughter turns out similar.

If you don't care for any of this after my explanation, just note that you are not marrying just a person. You are marrying her family/friends and whatever baggage she may have.


Just a question: have you ever been in a relationship? I'm just curious, because what other evidence do you have for the seemingly bold statement that women become more like their mothers as time goes on?


Well, let's see: 1. a woman shares DNA with her mother. A big chunk of it. 2. she were most likely raised by her mother, and influenced strongly by who she was, the good and the bad. 3. on account of being of the same gender, a mother is usually a primary role model to woman, in the same way many fathers are to men.

I'd say that's plenty of evidence.

I'd also say that the same goes for men, and more recently I've been amazed by how similar my siblings are to me, in comparison to the rest of the world.

Anecdotally, it's true to varying degrees with all women I know, and the similarities only became more visible as I got to know them better.

While I'm not a big fan of the points OP picked to focus on ("how well she keeps the home in order, raise kids, and AGE"), I don't think his statement that women often become like their mothers is so incredibly bold or hard to believe.

While my impressions of a love interest's mother (and to a lesser degree father) are not the deciding factor, they are an important data point, because in every relationship I've had, specific 'issues' that were immediately obvious in her parents eventually bubbled up in her as well. It would be silly to ignore that information.


> While I'm not a big fan of the points OP picked to focus on ("how well she keeps the home in order, raise kids, and AGE"),

I should've put it in this form: "Before marrying, people wonder "do I want to spend rest my life with this woman?" Well there's a good prediction of what your future wife will be like, and that would be her mother."


Yeah, that's more or less how I read it.

I just wanted to make it clear that I was agreeing with you on the general statement, not on the possible interpretation that the things you name are the typical things one should think of of in relation to women.


I am in fact married with kids. And my statement was based on my observations. I can make such statements based on my observations no? Or do I have quote a scientific research?


What? No, seriously, huh? Misogynistic? Saying someone grows up to be like their parents is misogynistic? Come down off your high horse, the clouds up there are making you see things.


Is this advice you give to all lesbians?


There are no lesbians in 1950s Leave-it-to-Beaver-land.


I've always wondered if this is a sensible way to buy shares. Say I wanted to buy Google shares in the next 30 days. I could monitor the price for the first 36.8%, and then choose the best price in the remainder. Does that make sense as a strategy?


No. This method assumes normally distributed potential wives. If a stock was normally distributed (i.e. has volatility) around a stable average, then yes, you could do that - but so can thousands of automated trading algorithms.


No, it doesn't assume that at all. It just assumes that they are i.i.d. (so all permutations of ranks are equally likely). Still probably not a good model of stock prices (which presumably are correlated more with the previous day than ten days ago)


I think the volatility of the stock market adds extra complexity. Presuming you go on dates with 36.8% of your pool, you will have an idea of what you would like in a woman, and from there you can make a proper selection. But with the stock market, you can watch 36.8% of the time, see a rising trend, think it's a good choice, and be totally wrong five days later when their quarterly earnings come out.

I think you'd want better heuristics for investing in the stock market than observing a bit of time (unless, apparently, you're a HFT algorithm ;-)).


In this case a portfolio accumulation strategy known as Value averaging works better. http://en.wikipedia.org/wiki/Value_averaging


Whoa cowboy... this isn't the same at all. We're talking about a whole different ball game here.

Stock prices are not like meeting that special someone.


Yeah, you can at least get something out of exiting from a relationship with a stock. The positions are more varied. The hours are more consistent.

But when they go down it's usually worse. :(


No, it does not. You would essentially just be gambling on the price.


But how is that different from the original problem? Unknown distributions are unknown. Assuming a uniform shuffle of ranked options isn't actually appropriate in most real world situations.

IOW, strategy is bad, but the stick market isn't worse than the mate/employee interviewing situation.


The OP makes the rookie mistake of confusing the Marriage Problem and the Secretary Problem. The Marriage Problem is the famous article by Gayle & Shapely (1964), on optimal matching (two-sided), and is the basis for The Match, used to place medical residents into hospitals. The Secretary Problem is a problem of optimal choice (one-sided).

As an aside, the best thing about the Marriage Problem is that it shows that it is much, much better to be the side making invitations instead of the side awaiting invitations. So being a guy is a pain in (generally) having to invite the woman, but that power translates into guys tending higher in their ultimate stable matching range than women. (Surprise! Hospitals make invitations to residents, not the other way around.)


Meticulously detailed account of Kepler's bride computing process can be found in his letter to unknown nobleman (dated from Linz, 23 October 1613). I've read just fragments of it from "The Sleepwalkers: A History of Man's Changing Vision of the Universe", the book by Arthur Koestler.

Introductory paragraph (p. 399): "Kepler's first marriage had been engineered by his well wishers when he was penniless young teacher. Before his second marriage, friends and go-betweens again played a prominent part, but this time Kepler had to choose between no less than 11 candidates for his hand...".

What follows could hardly IMHO put in any proper mathematical formula. In the best case it has to be modeled by some stochastic process with exponentially increasing number of random variables.

Anyways, the book is more important than that and I cannot recommend it enough. There is nothing else to my knowledge that so convincingly describes how process of scientific discovery can be arbitrary, fragile and random. The mentioned 'choosing ideal bride' episode is merely anecdotal chapter in the book that better explains Kepler's role and importance in the history of science.


Interestingly enough, this is a topic that has been studied in behavioral economics, where the described strategy is known as "satisficing" (as opposed to "maximizing"). The model assumes that when humans try to make choices, rather than trying to pick the "best" choice (the choice with the maximum benefit), they attempt to find the first choice which meets or exceeds an internally set "threshold" benefit and pick it. The relative optimality of the two strategies has not been conclusively decided on, but "satisficing" generally appears to be more in line with how humans naturally behave based on experiments. The details have been given in a paper by Caplin, Dean, Martin [1]

[1] http://www.econ.brown.edu/fac/mark_dean/Pub_Paper_6.pdf


I like this article, and I love Krulwich & Radiolab. Its a lesson in statistics and not in marriage though, just in case you weren't sure. So just for fun, my inner monologue while reading...

Now that's love. "Honey, you were better than the 37% of women I was going to try. It is statistically likely that you're probably the best, or at least second best, of all my immediately available options. Will you marry me?"

I'm somewhat amused that the conclusion is to date (sample) for a while, then start getting serious once you get an idea of what you want. Sounds a lot like what everyone does already, at least the ones whose marriages aren't arranged for them.

Kepler got what he wanted and sampled 100% of his options. He didn't get a statistically likely "Right Girl", he got "The Right Girl", and he never wondered whether or not he got the best one.


I'm surprised that utility doesn't come in here anywhere. Imagine a bimodal distribution, one set of matches that you hate, and a much smaller set of matches that you love. Why try to wait for the best after the first 1/e? Why not just pair off with someone that is 99% as good as #1?


Sadly, correct answers are too complicated to be fluff blog posts.


it does give you a 36.8 percent chance

My understanding is that this also give you 36.8% of not finding a wife at all because the best one is in the learning set. So 36.8% chance of success (picking the best one), 36.8% chance of no wife and 26.4% chance of picking the wrong one. I suppose there are different algorithms for different types of bachelors. Bachelors working under marry-or-lo-your-inheritance conditions are better off using different algorithms.

Using this method on a population of 100 prospective wives, what are the probabilities that: (1) you will pick the best wife (2) you will pick a wife in the top 3.

Thinking of this problem and eating a fun-blog level understanding of them is one of those things that give you "mental thinking models" of the Charlie Munger kind. Very useful.

EDIT: clarity


Actually, if you are following the method described in the article, if the best candidate is in the learning set, you end up with the last one. So it's effectively a 36.8% chance of picking a random one from the "not-best" population.


For endless sample groups there is no chance of failure - there are always more individuals in every category including 'better than the first set of samples'.

Also - I met my wife and continued to date but returned to her, because obviously it would have been futile to try to beat what she had going on. So you don't have to be a slave to the algorithm.


You must ask her immediately or she won't marry you.


For most "computer guys" the real question is "how to be the guy worth marrying."


This solution only applies if you have a finite number of secretaries that is known at the start to interview. Anything else and the equations get freaky. You can also add probability distributions for how many interviewies you expect.


The title is link bait and inaccurate. It's not about "how to marry the right girl". It's about "how to marry the right girl, given an unrealistic set of constraints".


Another version of this is "the last torpedo problem": A submarine with only one torpedo left is hiding in a cave. In front of it an enemy convoy is passing. The number of ships in the convoy is known in advance, but not the individual ships, and through the opening of the cave the submarine can see only one ship passing each time. So the question is how to decide in which ship to fire its last, unique torpedo?


This doesn't work in the event higher quality participants are pairing off earlier (i.e., attractive partners get committed earlier in their lives) or in the event attractiveness isn't life static. The Secretary Problem provides a lot of great insight, but you need to be very careful applying stylized stories to real problems.


this also assumes every candidate is fully willing to accept the offer. what if your first best candidate accepted the offer but was in the 36%. Then the 2nd best candidate after 36% rejected the offer, leaving you with potentially a bad choice in candidates. This seems highly probable too...

If everyone did this, you have to assume the other candidate is doing the same, thus your choice after 36% may end with you being insider their 36% bracket. This works only at a selfish scale and dubious at best.

This only really works for a gameshow situation. You have 20 boxes with money inside. You don't know what is the minimum or maximum amount, you get to look at a box and determine yes/no. So you do the 36%. Then the very next box that is close enough or above the maximum of the first 36% is what you chose.


A bayesian approach. If you know what you real aspirations are act according to it, if you haven't the fanciest idea then use the first 25% as a sample and from that sample estimate the mean and the variance, make a chi-square test to see if the population is normal, now you can compute and estimate for the probability of finding a candidate in the rest of the sample according to your valuation. The length of this interval is related to the risk of your election. If you are not very picky you have a long interval and a high probability to succeed, if you put high stakes then you can get the best girl for you, but you are risking to live alone or to miss good opportunities. (Sorry for the English).


I must apologize because I didn't read the post, but I know that the reasoning is based in permutations and here is the flaw in the argument. Anyone of us could rapidly recognize that a girl is wonderful and without second thoughts promise her eternal love, this kind of knowledge is not encoded in the permutation of numbers. Bayesian reasoning give you this advice: use your knowledge girls are not numbers.


My last comment. Just suppose that you know there is one or more girls that are wonderful for you but you also know that there are a lot that are no way for you. In my case I should without second thoughts get the first wonderful girl. I am risk averse and I don't want to miss this one in a life opportunity. This reasoning takes into account the kind of people you are.


I wrote a blog article about this (contains a bit more math) http://www.datagenetics.com/blog/december32012/index.html

A slightly different variant, is how to make it totally random selection http://www.datagenetics.com/blog/june52013/index.html


Couldn't this be applied to startup ideas? Say you have savings to last you 12 months. Try one startup idea (/MVP) every month for 12/e = 4 months. Then keep going producing 1 MVP per month until you find one that looks more promising than the best of the first four. If the article is right then with a probability of 36.8% you will have found the best idea with some time to spare in your 12 months to make some money with it. No?


No, because you can go back to a better idea anytime you want to do so. If you estimated that you have 12 months of savings and that it takes you a month to build an MVP and six months to take an MVP to ramen profit, you should spend the first six months building six MVPs, then evaluate them and pick the best to work on for another six months.


Ah yes, of course.


Except the number of startup ideas is not fixed, just the number of months, so you haven't exactly found the "best idea" -- more that you've found the best month+idea pairing. It might still be an okay approximation if your goal is to build a good-enough MVP, but it's not exactly the same formula since there are any number of ideas you might have to work with.


Optimal stopping theory can be applied to many things where you need to make a decision without full information, like finding a job for example ... http://www.roletroll.com/blog/the-plight-of-the-long-term-un...


For anyone interested in how the solution is derived, one alternative is to use dynamic programming. For example, see these lecture notes: http://www.cim.mcgill.ca/~decinfo/courses/ecse506/winter-201...


Now I have another alternative to "It's not you, it's me"


This formula doesn't account for non-monogamous configurations. I'd be interested in seeing a mathematical representation of the maximum bonding pairs a person could reasonably handle.


The problem is that in real life the number of applicants is unknown and might change drastically depending on your luck and behaviour over the years.


So how do you select 36.8% of an infinite pool? (3.5 billion is an infinite pool for all intents and purposes)


The pool is way lower:

- Girls in your range (age, available, and close geographically)

- Average time you need to 'learn' a girl (it is, to know the best/cons, and to take a decision if dropping her or not). On some it will take 2 hours, others will take 6 months or even years in some cases.

- Time when you start dating.

- Time when you plan to marry.

- Average time between dates.

So if living in a city big enough, and you start dating at around 18 and plan to marry at around 30, while being skillful enough to get a new date in less than 2 months, you can expect to date around 24 girls. That means you can discard the first 9 dates, and wait until you are almost 22 (3.75 years later) to take things seriously.


I've been on dates with about 20 girls in the last 6 to 7 months alone ... only two different cities. Tinder is a magnificent thing.

But maybe the difference is that I never plan to actually marry. Makes things easier.


Nice tinder plug. From their website it looks like an application to connect smiling people with dogs on beaches.


The size of the pool is the total number of people you expect to evaluate for a given decision.


And really, it isn't 3.5 billion. Reduce by % in relationship, in acceptable age range, straight, living within driving distance...you'd probably be fine.


And I thought my town had a lot of people.


Sounds like some of the girls were practicing some form of queueing theory.


Are there any companies using this strategy for hiring?


Ahh yes, the constant magic of e. More concisely, it can be explained as thus: If you're both on e, you're guaranteed to find the right partner... straight away.


I am sobbing mathematically out of sheer joy !


This is a good way of choosing a song on your iPod while shuffling. Assume you have a tolerance of shuffling through 40 songs before picking one.

You should click through the first 40/e (roughly 15). Then start clicking until you come across a song better then the best one in the first 15.

Listen to that one.


do you actually do that? it sounds interesting in theory but i find it actually quite impossible to "remember" the satisfaction my favorite gives me so that i can reference it against every other track.


Yes. This is my 'walking to and from the gym' strategy.

But then again I'm a giant nerd.


Automatically disqualified as a "giant nerd" by going to a gym.


No way. Going to the gym is one of the nerdiest things you can do if you approach it the right way. I mean it is basically the real life equivalent of grinding levels in an rpg:

You choose a class (endurance, strength, or something in between). You have items and skills which you have to skill up individually (barbells, dumb bells, gymnastics equipment, running, cycling, etc.). The same dilemma exists for leveling up: skill points added to one category are skill points you can't add to another category. Thus if you split your time between strength and endurance you will never achieve as much as someone who exclusively trains one of the two.

The skill curve is even similar to that of a well designed RPG: in the beginning you make a lot of gains quickly but eventually you slow to a halt and it takes months to even gain a few skill points in one item/skill.

The gym in real life is like hardcore mode: If you don't play for a while, your skills degrade as a penalty. However, the skill lost as a penalty is easier to reattain then skill you never had.

There are even boss fights and co-op mode if you decide to compete.

There are too many parallels to list them all here, but I think you get the idea.


Going to the gym in itself is still not a 'nerdy' activity. All you did was describe going to a gym in a very nerdy way by comparing it to an RPG - you could most likely apply this practice to just about any activity one could do.

edit: I do disagree with that statement of the poster to whom you replied, you can still be a pretty big nerd and go to a gym.


> Going to the gym in itself is still not a 'nerdy' activity.

Neither is moving pieces on a chess board until you start to obsess over it, read about it in your free time, track your progress as a player, and constantly try and improved yourself as a chess player. No activity is really "intrinsically nerdy" (whatever that means), that's why I said "if you approach it the right way".


Still, society generally views playing chess as being nerdy, no matter how involved you are with it. They don't make these distinctions you're making. Whether or not they're accurate in their description is another discussion entirely, but I think we can all understand this in the context of the conversation.


You seem to be mixing up [1] geeks and nerds. What you describe is geeky rather than nerdy.

What would be a nerdy approach to gym/fitness? Perhaps doing 10 years of research into what's the most efficient way of maintaining fitness and publishing a paper. Or perhaps building your own gym -- on the orbit, and commuting by a rocket of your own design.

[1] http://slackprop.wordpress.com/2013/06/03/on-geek-versus-ner...


The article says nerds are achievement oriented. That is textbook RPG player. All they care about is the next level, getting a sub 4 minute mile, the 100kg snatch, etc. Going to the gym is entirely achievement oriented.

Side note: I think we're arguing semantics. If you draw a venn diagram of nerds and geek there would be so much overlap it is hardly practical to differentiate except in the rare instance when an activity falls into one category and not the other (which I don't think is the case here).


I reached an age where I was either going to join many of my peers in being weak and overweight, or I was going to do something about it. The something I did is... cycle to work (15 miles a day) and lift weights three days a week before work.

I still think I'm pretty nerdy. For example, I made a light for my bike that flashes in Morse: https://github.com/jgrahamc/bikemorse


> https://github.com/jgrahamc/bikemorse

Now why does that not surprise me at all :)

I think you are in no danger whatsoever of losing your nerd card :)


What? No.

You start as a giant nerd going to the gym. Over time, you probably become a smaller nerd, or at least a denser one.


"To keep the body in good health is a duty... otherwise we shall not be able to keep our mind strong and clear." Buddha


Exclusionism sucks. Please don’t do it ever.


I've never thought of it as an optimization problem at all, until now, but I do a form of this all the time when I'm listening to a playlist with a wide variety and nothing better going on (For instance when running or driving.)

The thing is for something trivial like that, it doesn't actually matter if you remember the satisfaction or not, all that really matters is if you are more satisfied than you think you were with the previous song, accuracy be damned.


I only listen to good songs, though?

What a dilemma!


Then you don't need shuffle, only play.


Shuffle's good for not wearing out good songs.


But if you don't shuffle you get the same ordering of songs every time (which bugs me, at least).


Advise from an old man--I have no reason to lie: Don't ever tell "the one" you love her. If you are somewhat good looking don't marry the first girl who gives it up. She will change mentally and physically. Never tell them you have money, or have the potential to make money. Keep a large portion of your money buried--she might leave you. Twice about having spawn--you have a say these days. If she loves you after you have a nervous breakdown she's a keeper--do anything for her.(Make sure she's not using your bad luck to feel better about herself. Charles Bukowski,'She loved me when I was broke, and humble.' Or disregard this "advise", I spent my twenties looking for the perfect person, and never found her, or was too stupid to know I found the right one? I think the latter. I used to say, "But she's too nice, and conventional?" Yea--I screwed up, but I'm still glad I didn't get married. oh yea, make sure to listen to her talk to her friends and mother; that's the real girl you are living with a long time.


The only way to win this game is not to play


Exactly. Modern marriage is like a game of Russian Roulette for men. The difference is that your odds are worse, and the gun has financial incentive to destroy you.

Divorce rates are over 50%, divorce is initiated by women over 70% of the time, women get custody of children 90% of the time.

Laws like VAWA and the Duluth Model give women a surefire way to have you arrested and charged with zero evidence. Now you have a criminal record and no access to your children - 100% legal! Guess what happens to the suicide and addiction rates of men in these situations?

Enjoy your archaic life-long alimony payments, 'supervised visitation' with your children, drug testing, mandatory psychological evaluations, dumping thousands into a custody battle to end up with 4 days/month with your kids, and a child support system that rewards the payee for alienating your children from you.

Hey, your lawyer's kids will have no problem paying college tuition! Don't worry about yours.

Do you like the things you've earned over your life? Hold on to them by avoiding marriage like the plague its become.


> "Divorce rates are over 50%"

"Divorce rate" is a misleading statistic. It compares marriages in year X to divorces in year X, but divorces in year X can come from marriages in many prior years -- so it's not exactly a direct comparison.

People often mistake it for "the chances of an average marriage ending in divorce", which is a bit lower (the data I've looked at puts it in the 30-40% range.)

But wait, there's more! There are ways to determine, beforehand, which marriages are more or less likely to end in divorce. There are mathematical models based on behavior (James Murray, John Gottman). There are statistics related to various life decisions and behaviors and shared interests. You can dig through all sorts of interesting statistics and figure out your own risk profile if you so desire (see, for example, the General Social Survey at http://sda.berkeley.edu/cgi-bin/hsda?harcsda+gss10 ). People like to act like divorce is just a thing that randomly happens through no fault of your own, and on occasion that's true, but there are a lot of choices you can make to reduce the chances it'll happen to you. (Making choices like my grandparents seems to work out -- one pair celebrated 65 years last month, the other celebrates 67 years this weekend. And yes, the statistics bear out that making similar choices to them results in lifelong marriage a very high percentage of the time.)


Could you explain what you mean by "making choices like your grandparents" ?


not in a single HN comment, no. I can't compress a lifetime of experience (second-hand) into the amount of text I'm willing to write right now with fidelity.

Reading through my HN comment history, and my wife's HN comment history, can give you some insight into what we learned from our grandparents (hers also had lifelong marriages.) Reading through the books published by the mathematicians I mentioned, and digging through the statistics I posted, are additional methods you can use to gain insight into what works. Talking to people you know who've had long and successful marriages (ie, not my grandparents, but yours) can help.


The difference is that your grandmother didn't have a guaranteed payday and a "strong independent single-mother's movement" awaiting her if she decided she was tired of your grandfather.

The quickly disappearing stigma against single-motherhood combined with the demonization of men as deadbeats and child molesters, when paired with massive amounts of state handouts to single mothers (wic, welfare, child support, alimony, state medical insurance, housing subsidy, single-mother scholarships, affirmative action jobs, etc.) has made divorce as inconsequential as possible for women while dramatically raising the consequences for men.

Marriage is broken and men who go into it without understanding the disparity of legal, psychological, and economic outcomes between the genders are in for a rude awakening.


... yes, I'm sure you've identified the only relevant difference.

Which totally explains why my parents and my wife's parents, both married in the 1970s when those social movements were in full bloom, also have wonderful and happy marriages going on 40 and 38 years, respectively.


Are you arguing that our social environment hasn't changed since the 1970's or that our obviously dramatically changed social environment has had no effect on male-female relationships?

Either way, your advice is more of the same feel-good nonsense that we feed our young men, hand-waving away the outcomes of divorce and custody law, and pushing them towards a statistically likely devastating outcome.

It may feel good to preach the traditional loving family of your grandparents, but the data shows that they are the outlier. A much more likely outcome is a split family and emotional and financial devastation for the husband.


I am arguing neither of those things.

I am also not giving "feel-good nonsense" advice, nor hand-waving. I'm suggesting avenues of research that require a level of effort commensurate with the task at hand, namely, creating a long-term stable relationship.

Statistically, relationships with the same attributes as my grandparents' relationships don't fall apart. Statistically, the most likely outcome in that case is "til death do us part". (You really should read some of JD Murray's books/papers. We can predict with a fairly high likelihood which relationships are going to lead to a split family and emotional/financial devastation for the husband, and which are not. But it takes a level of introspection and a level of honesty from friends and observers that most people don't have.)


Again - is it your assertion that our drastically changed social environment has had no effect on the stability of relationships?

I whole-heartedly agree with you that there are many factors that can help predict the success of a marriage. This is somewhat besides the point.

It's shortsighted and a case of "ignoring the elephant in the room" to pretend that a dramatic shift in our social environment is having no effect on the stability marriage or that factors which contributed to past-generation's successful marriages have been unaffected by this shift.


> "is it your assertion that our drastically changed social environment has had no effect on the stability of relationships?"

I have already said explicitly that it is not. Please don't be obtuse.

> "there are many factors that can help predict the success of a marriage. This is somewhat besides the point."

No; it's exactly the point. Your initial comment used misleading statistics to argue that marriage is a "plague" that should be avoided, and you later hinted that my grandfather would have been a victim of this plague if my grandparents had lived in a different era.

I've countered that those statistics don't apply to every situation, and that in fact marriage remains quite a worthwhile pursuit especially for those whose circumstances and life choices put them in the "very high probability of success" category. My grandparents, my parents, and my wife and I are all in this category.

Repeating your assertion that current marriages lead "towards a statistically likely devastating outcome" is useless. The assertion, while true for many couples, ignores the reality that some couples are statistically likely to enjoy the benefits of marriage for their entire lives.


How much of your day would you say you spend thinking about how oppressed you feel?


> Divorce rates are over 50%

This is extremely misleading, though, because the first marriages are much less likely to end in divorce, and subsequent marriages are more likely to end in divorce (with increasing probability for each subsequent marriage).

> women get custody of children 90% of the time.

Women get custody of children far less often when men seek custody. Women get custody more often because women want custody more often.


What a sexist load of garbage. Women /want/ custody and men don't give a shit about their children, right?

The statistic touting men's success rate in seeking custody ignores the price of entry. Men /want/ to be in their children's lives, but must be wealthy to fund a custody battle (while also paying child support and alimony if he was married) in order to do so.

Women are the automatic receivers of custody, it is then the father's "privilege" to hire a family practice lawyer and sue for custody to the tune of thousands of dollars and invasion of his privacy via drug and psychological testing.


> Women are the automatic receivers of custody

No, they aren't. They need to actively choose to seek it just as much as men do, they are just more likely to choose to do so.


You should educate yourself about how the Tender Years Doctrine works as well as how custody is awarded to unwed parents if you think custody is not automatically awarded to the mother.


> You should educate yourself about how the Tender Years Doctrine works as well as how custody is awarded to unwed parents if you think custody is not automatically awarded to the mother.

You should educate yourself about the fact that the tender years doctrine has both been legislatively replaced in most states starting in the 1970s and also struck down by various courts as a violation of the Equal Protection Clause of the federal Constitution and similar provisions of various state Constitution if you think it is relevant now, rather than historically, to policy on child custody.

Unwed parents are a somewhat different case (because the legal presumption of paternity, and the implicit assumption of stable cohabitation, doesn't exist outside of marriage.) Yes, in the case of unmarried parents, the mother has automatic custody, and the father must both establish paternity and make an active claim for custody.


Do you earnestly believe that 9/10 fathers don't want custody of their children?

Do you also earnestly believe that the custody process is affordable and accessible to poor and middle-class men?


This seems like it works on the same principle of the Monty Hall problem, where statistically you win more often by always throwing away your first choice - http://en.wikipedia.org/wiki/Monty_Hall_problem


Sounds similar but the Monty Hall problem isn't just about throwing away your first choice - it's about throwing away your first choice after you've been given more information about the remaining two choices.


Ahh, thank you - that is a very important distinction.


Yay, sexist and inaccurate metaphorical framings for math problems.


How much of your day would you say you spend thinking about how oppressed you feel?


Is there a "you should never get married" solution? ;)




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