When to stop dating and settle down, according to math
February 28, 2016 8:27 AM   Subscribe

Optimal stopping is a math theory that can be used to solve real world decision problems. In the real world, it is often applied to help decide when to stop dating and get married.
posted by reenum (61 comments total) 24 users marked this as a favorite
 
The critique of this is that n, the quantity of possible people to date, is without defined variance (if we assume it is distributed with a heavy tail). That is, for George Clooney, the n is enormous (hundreds of thousands of people would be willing to marry George Clooney, probably), for the average person, it is smaller, and you don't get to know if you're George Clooney until you learn that you're George Clooney.
posted by hleehowon at 8:30 AM on February 28, 2016 [3 favorites]


I'm pretty sure I'm not George Clooney.
posted by notyou at 8:36 AM on February 28, 2016 [19 favorites]


Or that he's not you?
posted by vernondalhart at 8:44 AM on February 28, 2016 [1 favorite]


I knew my wife was the one when she loudly proclaimed her love for public transportation and timeliness.
posted by grumpybear69 at 8:48 AM on February 28, 2016 [16 favorites]


I am not George Clooney, but my wife would marry him.
posted by nubs at 8:49 AM on February 28, 2016 [6 favorites]


nubs: "I am not George Clooney, but my wife would marry him."

However, your wife married you, so perhaps you are George Clooney.
posted by chavenet at 8:50 AM on February 28, 2016 [19 favorites]


My wife has just assured me - again - that I am not.
posted by nubs at 8:53 AM on February 28, 2016 [65 favorites]


If one were on the other side of the formula ( the job applicant), the winning move would be to aim for the first interview after the 37% cull. It'd be difficult to learn that, or even if the interviewer was using the strategy, but it might inform your interview scheduling. Of course, if you wait too long, the position may be filled before you arrive.
posted by notyou at 8:56 AM on February 28, 2016


My wife has just assured me - again - that I am not.
posted by nubs at 8:53 AM on February 28


I'd favorite that nubs, but it just seems mean.
posted by BigHeartedGuy at 8:58 AM on February 28, 2016 [3 favorites]


Favorites are the consolation for not being George Clooney.
posted by nubs at 9:00 AM on February 28, 2016 [45 favorites]


Yeah, the original exposition I got of this from probability class was assuming people came in with a Poisson distribution, which is as faulty on the tail measures as assuming web traffic comes in in a Poisson distribution (with that Poisson distributional ansatz, you basically state that slashdotting doesn't exist. I mean, usually there is a structure of causation associated with getting slashdotted, but just because there is such a structure does not mean that you cannot shove it in there in the model - so you use a fractional brownian model or FARIMA or something)
posted by hleehowon at 9:08 AM on February 28, 2016 [2 favorites]


a Poisson distribution

That's the that's shaped like a fish, right? Pointy at one end, thicker in the middle, starts narrowing again but suddenly a wide tail before abruptly terminating? And usually quite damp? I always get it mixed up with the normal curve.
posted by five fresh fish at 9:22 AM on February 28, 2016 [8 favorites]


MetaFilter: the consolation for not being George Clooney.
posted by Fizz at 9:27 AM on February 28, 2016 [2 favorites]


I married my first love. Apparently I did it wrong and just got lucky.
posted by COD at 9:29 AM on February 28, 2016 [3 favorites]


When to stop dating and settle down...

A dimly-remembered quote from M*A*S*H, 37 years ago (Season 8, Episode 14 apparently, found in 0.56 seconds via a web browser): “Hawkeye (to Margaret): Maybe you and I are just too choosy. We're both looking for a custom fit in an off-the-rack world.”
posted by LeLiLo at 9:30 AM on February 28, 2016 [4 favorites]


hleehowon: Yeah, the original exposition I got of this from probability class was assuming people came in with a Poisson distribution

What followed a Poisson distribution?

In the classical secretary problem it is assumed that the number of candidates is known in advance (so the time at which they arrive is irrelevant), and no assumption is made about how the fitness of the candidates is distributed: it is just assumed that they can be ordered.

"What I shall call the standard secretary problem is as follows. A known number of items is to be presented one by one in random order, all n! possible orders being equally likely. The observer is able at any time to rank the items that have so far been presented in order of desirability. As each item is presented he must either accept it, in which case the process stops, or reject it, when the next item in the sequence is presented and the observer faces the same choice as before. If the last item is presented it must be accepted. The observer's aim is to maximize the probability that the item he chooses is, in fact, the best of the n items available. We shall abbreviate this outcome to the single word 'win'" - The Secretary Problem and its Extensions: A Review
posted by James Scott-Brown at 9:31 AM on February 28, 2016 [5 favorites]


And what about the other person? You sit down and do maths together, or they are beholden to your 'hire'?
posted by standardasparagus at 9:34 AM on February 28, 2016 [4 favorites]


Yes, what happens if both parties believe they are the boss choosing a secretary?
There are two people making a choice in this scenario.
posted by chapps at 9:44 AM on February 28, 2016 [2 favorites]


Ah, I see there is a variant of the problem in which n is unknown, but the candidates "are presented at the time point of a Poisson process of known rate lambda and the observer must make his choice betfore some fixed time T", discussed in section 5.3 of the PDF I linked.

Despite how often it is discussed, I think it would be more accurate to say "In the real world, it is often almost never applied to help decide when to stop dating and get married." A better example of actual real world use would be American option pricing.
posted by James Scott-Brown at 9:50 AM on February 28, 2016




Yes, what happens if both parties believe they are the boss choosing a secretary?

That's the classic romantic comedy plot where both are marrying for wealth and social status but both are fakes, then they fall in love and live happily in poverty in a five flight walkup with high ceilings in the middle of Greenwich Village.
posted by sammyo at 9:58 AM on February 28, 2016 [16 favorites]


don't plan on living the romantic comedy life
posted by sammyo at 9:59 AM on February 28, 2016 [3 favorites]


you don't get to know if you're George Clooney until you learn that you're George Clooney

There are the known not-George Clooneys, and then there are the unknown not-George Clooneys.
posted by AndrewInDC at 10:05 AM on February 28, 2016 [2 favorites]


I was going to say that I have my doubts about how much you are going to learn about yourself and your partners if you go into your first three serious relationships planning to dump them no matter what.

But the more I think about it, the more it might actually be emotionally healthy to go into high school and even early college relationships with the mindset of "this is definitely not forever."
posted by 256 at 10:12 AM on February 28, 2016 [15 favorites]


These are fun pure math explorations, but they assume the challenge of finding a partner is when to stop searching, with no evaluation of whether "settling down" is actually a possible outcome with a given partner. Which is quite a shitty lens to view potential partners, no agency and willing to accept you forever if only you'll truly commit.

Has anyone built a simulation in which both sides are independent actors? Or one which includes the possibility that "choosing" isn't sufficient? A model with a "80% chance they say yes" might make the observed reality (willing to settle down after only a 2-3 serious partners) closer to an optimal solution.
posted by notpeter at 10:15 AM on February 28, 2016 [1 favorite]


I married the third woman with whom I had a long(er) term relationship. That marriage lasted approximately 20 years before collapsing. I guess I should have waited until the fourth relationship.

(I am not George Clooney, but I am not Mickey Rooney either who seemed to use the algorithm that if she is willing to say yes, she should be married.)
posted by AugustWest at 10:18 AM on February 28, 2016 [1 favorite]


While this is neat, I always notice how contemptuously framed a lot of these thought problems are - there's the one where you kill/not kill a fat person to save a trolley of children, for instance; and of course, there's this one - the "secretary problem". It makes me - a secretary! - realize that I'm not actually the intended audience, as I will never be a man hiring a secretary, and my hope will always be for steady employment working for a non-asshole, instead of hoping that in my immense privilege I can extract the maximum labor possible from some pink collar serf....so I'm already othered when I start reading.
posted by Frowner at 10:18 AM on February 28, 2016 [20 favorites]


Yes! What if these problems were written from another perspective, would it change the math calculations that emerge?
posted by chapps at 10:36 AM on February 28, 2016


This all seems overly complicated. I just selected thirty of the people I was dating by lot and then reduced that number, also by lot, to nine, and those nine chose forty, after which the forty were reduced by lot to twelve, who chose twenty-five, who were then again reduced by lot to nine and then those nine elected forty-five, who were reduced by lot to eleven, and those eleven chose the forty-one who actually selected my spouse.
posted by kyrademon at 10:38 AM on February 28, 2016 [11 favorites]


The Times just published a piece about how how people are increasingly marrying within their class: "With more marriages of equals, reflecting deep changes in American families and society at large, the country is becoming more segregated by class."

So the "n" of available partners is going to vary based on your wealth -- the lucky poor will have lots of people to choose from, but the unfortunate elites are going to be sadly limited in their options. (Yes, that was meant sarcastically.) More seriously, the increase in assortive marriage and the rise in inequality more generally does change this problem, giving some people much better selection options and access to information, and leaving others with constrained choices and very limited information.
posted by Dip Flash at 10:49 AM on February 28, 2016 [2 favorites]


George Clooney is not all that, y'all.
posted by jfwlucy at 10:50 AM on February 28, 2016 [4 favorites]


"I always notice how contemptuously framed a lot of these thought problems are"

You can bring it into even sharper relief by prefacing each one with "I say, chaps!"
posted by i_am_joe's_spleen at 10:51 AM on February 28, 2016 [8 favorites]


Dip Flash: The Times just published a piece about how how people are increasingly marrying within their class: "With more marriages of equals, reflecting deep changes in American families and society at large, the country is becoming more segregated by class."

Is that because an overwhelming amount of people born into their class never make it out?
posted by gucci mane at 10:57 AM on February 28, 2016


My father, an astrophysicist who loved making us figure out logic problems, used to have his children apply stopping theory to restaurant selection when our family was travelling through an unfamiliar town. First we had to solve for n, of course, by estimating population/market size and what that portended for the number of restaurants. And I, um, became a land use economist with a behavioral bent and a practice that encompasses city planning, real estate development and cultural facilities. Far from the tree indeed.
posted by carmicha at 11:07 AM on February 28, 2016 [55 favorites]


What if you just marry the person you fall in love with? What does that do your maths?
posted by valkane at 11:52 AM on February 28, 2016 [2 favorites]


carmicha, I logged in just to favorite that. Awesome. Going to do that with my kid.
posted by emkelley at 11:59 AM on February 28, 2016 [3 favorites]


What if you start with cats, and add cats until you find the perfect cat? How many cats do I get before I find the perfect one?

(That's a trick question. Every cat is perfect in their own unique way.)
posted by schroedinger at 12:11 PM on February 28, 2016 [15 favorites]


It's propinquity.
posted by Bringer Tom at 12:16 PM on February 28, 2016


I knew my wife was the one when she loudly proclaimed her love for public transportation and timeliness.

That sounds like a hard life. "I love Florida and skiing." "I love social media and getting work done."
posted by officer_fred at 12:24 PM on February 28, 2016 [7 favorites]


Every cat is perfect in their own unique way.
posted by schroedinger

At least, it is until you observe it.
posted by Greg_Ace at 12:31 PM on February 28, 2016 [16 favorites]


I just selected thirty of the people I was dating by lot and then reduced that number, also by lot, to nine, and those nine chose forty, after which the forty were reduced by lot to twelve, who chose twenty-five, who were then again reduced by lot to nine and then those nine elected forty-five, who were reduced by lot to eleven, and those eleven chose the forty-one who actually selected my spouse.

Dating can be pretty doge-eat-doge
posted by Greg Nog at 1:10 PM on February 28, 2016 [11 favorites]


Is that because an overwhelming amount of people born into their class never make it out?

In my understanding, it is the reverse: people marrying within their class prevents people from making it out. A stockbroker marrying a minimum wage worker raises that minimum wage person much more than it lowers the stockbroker, economically speaking. It's one more way that the post-war boom years stand out as unusual in terms of class mobility and opportunity, in contrast to the periods before and since.
posted by Dip Flash at 1:26 PM on February 28, 2016


AndrewInDC: " you don't get to know if you're George Clooney until you learn that you're George Clooney

There are the known not-George Clooneys, and then there are the unknown not-George Clooneys.
"

Man, set theory? What about the hypothesis that I know my eyebrows are inadequate, and by that I can theorize I am part of not(George Clooney)? Do I then prove black is white and go on to die at the next zebra crossing?
posted by Samizdata at 1:34 PM on February 28, 2016 [1 favorite]


schroedinger: "What if you start with cats, and add cats until you find the perfect cat? How many cats do I get before I find the perfect one?

(That's a trick question. Every cat is perfect in their own unique way.)
"

You ended up with enough cats you never get a date. QED! Problem solved!
posted by Samizdata at 1:36 PM on February 28, 2016


What if these problems were written from another perspective, would it change the math calculations that emerge?

Depends on what that perspective is. From the employee side of things, you just need to stipulate that you're after multiple offers, and it's pretty much the same.

Of course, employers have thought about this much more rigorously, and do their damnedest to avoid putting an offer in the hand of someone who will get another offer soon. "Here's our offer, we need your acceptance by 5pm Wednesday." And your interview on Thursday? Surely you'll just cancel that.
posted by pwnguin at 1:37 PM on February 28, 2016 [3 favorites]


the dumbest-thing-that-could-work heuristic

Some of my coworkers contend this is how we hire our secretaries.

Others, our executives.
posted by oheso at 1:47 PM on February 28, 2016 [3 favorites]


don't plan on living the romantic comedy life

I didn't choose the romantic comedy life. The romantic comedy life chose me.
posted by oheso at 1:53 PM on February 28, 2016 [2 favorites]


The Times just published a piece about how how people are increasingly marrying within their class:

Well, like 40 years ago, everyone was all about Fighters getting together with Mages and so on, but that led to a whole lot of confused multi-class children, now a young Mage just wants to find someone else who can appreciate a good Fireball spell without all that fuss of THAC0, and is that so wrong?
posted by GenjiandProust at 2:24 PM on February 28, 2016 [10 favorites]


PS, don't come at me with your new-fangled "classless" skill systems. You still end up with class-like packages. Same difference, guys.
posted by GenjiandProust at 2:25 PM on February 28, 2016 [3 favorites]


The point at which to marry is when you are at your peak attractiveness, and those marry well (by their own prospects) are those who have good insight into how attractive they can be.

The NYT piece was silly. People never married much out of their class. What's different is people often married out of their income because before equal rights and birth control, women married very young while holding very low paid jobs or no job at all, regardless of their education or their parents' income and education level.
posted by MattD at 2:58 PM on February 28, 2016


Y'all, I am a spinster so as to increase your chances of getting married. You're welcome.
posted by mollymillions at 3:09 PM on February 28, 2016 [5 favorites]


mollymillions: "Y'all, I am a spinster so as to increase your chances of getting married. You're welcome."

Sorry, in a potential partner, I like

A] Eyes I can see. Embedded lenses a definite turn off.
B] No razor knives under fingernails. Passionate moments can be overly painful. Don't ask me how I know this.
posted by Samizdata at 3:16 PM on February 28, 2016 [4 favorites]


You ended up with enough cats you never get a date. QED! Problem solved!

If you can't handle me with all cats, you don't deserve me with no cats.
posted by schroedinger at 3:18 PM on February 28, 2016 [10 favorites]


And as we all know, mathematics are the most romantic of all the pure sciences
posted by Automocar at 5:27 PM on February 28, 2016 [2 favorites]


Having bootstrapped my own statistical distribution from my proximate dating pool, my optimal strategy is to remain single and begin acquiring cats.

And what about the other person? You sit down and do maths together, or they are beholden to your 'hire'?


Face it - I'm your statistically significant other.
posted by pemberkins at 5:41 PM on February 28, 2016 [1 favorite]


schroedinger: "You ended up with enough cats you never get a date. QED! Problem solved!

If you can't handle me with all cats, you don't deserve me with no cats.
"

And there goes my PTSD trigger with my last ex-girlfriend. Except it wasn't just cats. She wanted ALL THE ANIMALS!
posted by Samizdata at 6:48 PM on February 28, 2016 [1 favorite]


So people who are risk-averse end up causing divorce by acting on their insecurities while young daters are incentivized to be selfish and insensitive. Is math really necessary here?
posted by onesidys at 8:18 PM on February 28, 2016 [1 favorite]


No, what you do is, you date a series of people, and then ask all of your friends and acquaintances to vote on which one of the people was the best.

Except that your friends don't actually vote for your prospective romantic partners directly; they vote for a set of "electors," usually the twenty or so friends you like the best, who pledge to vote for one partner or another. Then there are also the "superdelegates," generally the people who are already in positions of power in your life (your mom, your high school principal, your first and most recent bosses, etc.), who get to vote for whomever they like. Both electors and superdelegates will sometimes say they're going to vote for one person but change their mind at the last minute; this is a normal and expected part of the process.

In the event of a two-way tie, the person with whom you will have a long-term relationship is decided by coin flip or the drawing of cards from a deck. (For three-way or higher ties, the determination is made by what is called a "brokered convention," where all your family, friends, acquaintances, employers, etc. all get together and fight it out on their own behind closed doors, then the survivors come and tell you their decision.)

And this is the best way to determine who you should marry.
posted by Spathe Cadet at 10:32 PM on February 28, 2016 [5 favorites]


And as we all know, mathematics are the most romantic of all the pure sciences

Well, since all sciences are derived from mathematics, logically all romantic sciences must be derived from mathematics. Meaning that mathematics must therefore be the most romantic science.

I have a truly marvelous proof of this, which the comment window is too narrow to contain...
posted by happyroach at 1:59 AM on February 29, 2016


I'm pretty sure I'm not George Clooney.

I used to be sure I wasn't George Clooney but since then I have shit in a cat box and married a woman who is more traditionally successful than myself so now I am not sure.
posted by phearlez at 12:42 PM on February 29, 2016


Spathe Cadet: And this is the best way to determine who you should marry.

That only works for people you're planning to marry for 4-8 years at the most.
posted by Greg_Ace at 4:06 PM on February 29, 2016


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