The Mathematics of Marriage
Image by George Eastman House via Flickr
UPDATE (8/19/09): Vote in the poll: Would you use an equation to choose a mate?
Following up on the mathematics of a zombie attack, here’s some analysis of the mathematics of choosing a mate, toward the end of this article on gambling. Leave it to mathematicians to be this romantic:
Suppose you are told you must marry, and that you must choose your spouse out of 100 applicants. You may interview each applicant once. After each interview you must decide whether to marry that person. If you decline, you lose the opportunity forever. If you work your way through 99 applicants without choosing one, you must marry the 100th. You may think you have 1 in 100 chance of marrying your ideal partner, but the truth is that you can do a lot better than that.
If you interview half the potential partners then stop at the next best one – that is, the first one better than the best person you’ve already interviewed – you will marry the very best candidate about 25 per cent of the time. Once again, probability explains why. A quarter of the time, the second best partner will be in the first 50 people and the very best in the second. So 25 per cent of the time, the rule “stop at the next best one” will see you marrying the best candidate. Much of the rest of the time, you will end up marrying the 100th person, who has a 1 in 100 chance of being the worst, but hey, this is probability, not certainty.
You can do even better than 25 per cent, however. John Gilbert and Frederick Mosteller of Harvard University proved that you could raise your odds to 37 per cent by interviewing 37 people then stopping at the next best. The number 37 comes from dividing 100 by e, the base of the natural logarithms, which is roughly equal to 2.72. Gilbert and Mosteller’s law works no matter how many candidates there are – you simply divide the number of options by e.
So, got that? Figure out your potential pool of mates (X). Divide X by 2.72. Then marry the next best one, after you’ve dated X/2.72 people. Let’s say you determine your mate pool is 500. Date 184 people. Then marry the first person who is better than the 184+ people you’ve interviewed.
Is this advice in any way practical? The first thing that might strike most people as impractical is the idea of determining your mate pool. There are billions of people in the world, hundreds of millions in America, millions in many cities in America. How the hell would you determine your mate pool? I guess I’d go about it as follows…
How many single people did you meet last year, people you can recall, who could be considered plausible mates? People, that is, it’s reasonable to imagine might have dated you — be honest, you can’t count that 10 at your office if you’re a 4 — and that you might have possibly wanted to marry yourself. Take that number, take the years since you were 18 until the last year you’d want to get married — say, hypothetically, 18-34, 16 years — and multiply. Are you picky? Say the number of potential mates you meet in a year is 5. Multiply 16 X 5. You’ve got 8o potential mates you’re likely to meet between the ages of 18-34. (This works whether you’re 19 or 33 at the time you’re making the calculation — you’ve presumably already dated some number of potential mates.)
While it may sound limiting, the fact is that despite how large the world is, we tend to meet very few people in our routine lives — unless we engage in aggressive singles activities, online dating, etc. And even with aggressive dating, I think most people would still be limited to, at best, low double digits as to people they could actually marry and might actually marry them.
So, I think defining the universe of potential mates — at least in a back-of-the-envelope sense — is quite doable.
What’s harder? Actually pulling the trigger based on the idea that you’re statistically likely or not to do better. Say you’re in that universe of 80 potential mates. Under the model, you’re supposed to date 29 people, then choose the best one after that. First of all, it would take a pretty cold person to toss guy or gal #27 because you haven’t gotten to #29 yet. And what exactly as you supposed to think during “interviews” #1-#29? That you’re dating someone with no chance of marrying them, just to set up a baseline for your statistical model? Obviously, this is silly.
Furthermore, probably the biggest thing that influences a lot of people’s decisions to marry is sunk costs. You’ve been with someone X number of years. The higher X is, the harder it is to make the calculation to toss aside those years and start over. Humans are notoriously loss averse — and that’s a big loss to take. What’s more, women at least see their mate choices getting worse as the years go by (the “all the good ones are taken or gay” effect). Yet another finger on the scale urging someone in a relationship to pull the marriage trigger.
It strikes me that the limited usefulness of this exercise is a fairly depressing one: helping people calculate when it’s reasonable to settle. You’re a 33-year-old woman. You figure you’ve dated 30 of your 80 potential mates. You’re starting to feel anxious about all the usual reproductive stresses women feel at such an age. This lets you know that it’s reasonable to assume, if guy #35 is better than the rest of the ones you’ve dated, that — statistically — you’re taking a pretty safe bet that it makes sense to settle down with him, rather than “interview” the other 45 candidates.
It could hardly be used scientifically. But perhaps it provides a useful exercise to rationally evaluate your options.
HT: Geek Press
Post Your Comment
You must be logged in to post a comment
T/S Members
Log in with your True/Slant account.
Sexist much? Only women see their marital choices narrowing with age? Take a look at most guys as they age, not nearly as permanently attractive as they might think.
“Settle” as in settle down or settle for something less than your ideal as you’re just too pooped to keep flipping through the racks? I think women settle/down, if and when they do, when they realize every guy they date has some flaws (just as she does) but it’s the one whose flaws are most bearable who finally gets the marital vote. It’s the fatigue/burnout factor as much as the coup de foudre.
Dating is like shopping at Loehmann’s. You enter the marketplace fresh and optimistic, your heart pounding, certain there’s some stunning little number lurking amid all that lurid polyester. After years of looking, you get better at spotting cashmere and grabbing it. It’s the paucity of cashmere, so to speak, that makes it such a challenge.
Yup, that was a sexist thing to say.
Sexist? Maybe insomuchas the world is…
The fact is women feel societal/biological pressure to marry/reproduce at a younger age than men do. And as men age, their dating pool grows (most guys will date women significantly younger than them, of course, and plenty of them will consider a woman 15 or more years younger a perfectly acceptable — if not perfectly awesome — mate). Few women, meanwhile, as they get older truly consider a much younger man an acceptable mate — Demi Moore aside.
A man at 40 may start to get lonely and want to marry — even if it means settling. But he’s much more likely than a woman of the same age to decide he’s still got plenty of time to play the field and be selective.
Not all guys are going to age like George Clooney, of course. But plenty of women aren’t judging just based on loooks. With men… that just ain’t the case.
In response to another comment. See in context »The article you quote from glosses over a very important part of the model, which is more commonly called the secretary problem. The 1/e strategy is only optimal if you must have the very best candidate, and otherwise have no preferences between candidates. So while this strategy maximizes the chances of picking the best one, there is also a 37% chance you pass by the best and go through the entire pool only to settle on the last candidate available.
A more realistic model is that you don’t have to have the single best one, but want to maximize the expected value of the candidate you do end up selecting. In that case, the optimal strategy for n candidates is to look at the first squareroot(n) and select the first one better than all of those. Half of the time, you will select a candidate after examining the next squareroot(n), and the probability of settling on the last candidate is 1/squareroot(n). Even this model ignores search costs though.
Using your dating pool size of 80 people, you should date ~9 before proposing. 50% of the time you’ll date less than 18 people total, and 75% of the time you’ll date less than 36. The probability of dating all 80 is ~0.11.
I think the thing that might screw up the math even more is the idea that once you’ve dated someone, they’re out of the picture forever. Given that people get back together with exes all the time, there’s much less of a penalty for passing by “the one” in real life than in the model. If you dated and broke up with “the best,” there’s a non-zero chance of simply going back and correcting the mistake.
In response to another comment. See in context »[...] On: The Mathematics of Marriage [...]
A more interesting problem is the optimal policy when the field of potential mates is not randomly distributed. What if the pool of mates is hump-shaped, with the best most likely to appear in the middle? What if it declines over time? A truly random distribution is far from likely.
Lol – only in New York
You talk this way on dates don’t you Ryan?
Animals have been coupling for hundreds of millions of years… it’s a process whose complexity defies natural logarithms and will be most successfully achieved by application of one’s heart and not brain… Daniel-San.
Now I know why marriage is so much work… it’s statistically impossible to choose well….
It’s a fascinating-if-arrogant/unrealistic assumption you’ll get a do-over for the great gal/guy you passed over a while back in search of a better option. Maybe they’ve actually found someone not only better but, crucially, able to make a commitment to them. However quaint the notion, there are still men and women who believe marriage is a thoughtful choice made, ideally, for life — not some amusing interlude before you head out again on the hunt for all the ones you left behind, the best of which are awaiting their second chance with you. Oy.
As some of us know, we didn’t choose to stay with one guy or marry another for very good reasons, which hindsight only makes even clearer.
Well, I’ve never done the on-again, off-again thing myself. Can’t really get my head around it, I think the same as you.
But people seem to do it all the time — especially young people who probably have a better excuse for messing up.
And not 100% of people have to be willing to backslide to effect these numbers, I would guess.
In response to another comment. See in context »How do young people have a better excuse for messing up?
How do younger people have a better excuse for making stupid relationship decisions? Because they’re younger and stupider and less experienced and have no idea what they want, maybe.
Also, a good reason people ought not get married at 21. (not that it can’t work — but looking back at myself at that age, i don’t think i had much idea what would have made a good marriage versus a bad one)
In response to another comment. See in context »Oh my goodness! It seems to me that this mathematically interesting exercise in game theory has no (none, zero, zilch) application to real world decisions about marriage for the simple reason that good marriages are made, not found. And marriage-interaction researchers like John Gottman (see The Marriage Clinic) have actually been crafting interesting mathematical models for predicting what works and what won’t in a marriage. One finding is that contempt is like relationship kryptonite–it can destroy whatever is good and strong in a relationship. So, the mathematics of actual marriage suggests that someone who feels their marriage would be settling for less than what they deserve would perhaps be better served by avoiding the institution altogether. Doubt is fine (even inevitable), but the contempt of settling for less because that choice is your statistical best chance is just not workable.
[...] For those who have no idea what this is about, go back and check out The Mathematics of Marriage. [...]
[...] http://trueslant.com/ryansager/2009/08/17/the-mathematics-of-marriage/ [...]
[...] http://trueslant.com/ryansager/2009/08/17/the-mathematics-of-marriage/ Leave a Comment No Comments Yet so far Leave a comment RSS feed for comments on this post. [...]