How To Marry The Right Girl: A Mathematical Solution
npr.org
npr.org
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?
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.
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).
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.
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).
[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.
This algorithm is only good if you'd rather have nothing than second best.
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.
> 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.
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'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.
> 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...
As far as I can see this suggests that believing in cohabitation is not a strong factor when it comes to divorce.
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.
Edit: It sounds to me like you are rationalizing and intellectualizing.
"You love me, so you allow me others; but I love you, so I will not take them."
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.
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.
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! :)
Good job Microsoft.
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 )
Don't be in too much of a hurry.
jk, congrats on a successful marriage!
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"
[1]:http://www.americanscientist.org/issues/id.5783,y.2009,no.2,...
(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.)
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.
Am I missing something? Surely...
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).
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. ;)
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.
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.
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.
IMHO, it's remarkable how your primary measures of a woman's worth are housework, childbearing, and physical beauty.
My mother-in-law's skill and dedication in keeping house is reflected in my wife's skill and dedication in writing clean code.
And I did say in my original comment about physical/emotional change people have over time. Some people don't age well emotionally.
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.
Incredible. I'm laughing and crying at the same time.
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.
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.
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."
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 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 ;-)).
Stock prices are not like meeting that special someone.
But when they go down it's usually worse. :(
IOW, strategy is bad, but the stick market isn't worse than the mate/employee interviewing situation.
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.)
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.
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.
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
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.
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 slightly different variant, is how to make it totally random selection http://www.datagenetics.com/blog/june52013/index.html
- 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.
But maybe the difference is that I never plan to actually marry. Makes things easier.
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.
But then again I'm a giant nerd.
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.
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.
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".
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...
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 still think I'm pretty nerdy. For example, I made a light for my bike that flashes in Morse: 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 :)
You start as a giant nerd going to the gym. Over time, you probably become a smaller nerd, or at least a denser one.
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.
What a dilemma!
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 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.)
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 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.
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.
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 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.)
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.
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.
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.
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.
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 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 also earnestly believe that the custody process is affordable and accessible to poor and middle-class men?