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How To Find True Love: The Marriage Problem

MEB + ARK, a.k.a. the Haystack Hunters, wrote the following:

As fans of your work in real life probability and breaking the law of averages, we were hoping you could apply your theories to the most perplexing problem of all: true love. According to some recent articles, the pool of eligible, educated, single males aged 27-37 is dwindling, while the number of equally eligible women is climbing so with the odds stacked against us how to we go about finding our “One.” Is there any way to fix the numbers in our favor? As writers we can barely balance a check book, let alone weigh the odds of finding our perfect mate particularly since he’s one in a million (read: above average) and we’re both one of a kind. So how do we solve life’s most essential equation: i + u = xoxoxo? We’re quite serious about our search and would so appreciate any statistically proven insights.

Statisticians are, as everybody knows, the best people to ask about matters of the heart. And if statisticians in general aren’t, I am. After all, everybody loves me. When you think of me, you think of amour; or is it amour-propre?

Anyway, there is in probability a classic conundrum called the Marriage Problem, which is applicable to your request. Sort of. By which I mean the Marriage Problem gives an approximation about how many men you should go through before stopping at the one you have in your hands and latching onto him permanently.

Assume you know you have N date-worthy men swimming before you. You can date one at a time. You can keep the current one, or discard him forever hoping to find a better one later. You also must know all there is to know about all the men such that you could rate their marriageability unambiguously. That is, you must be able to rate them, from least to best.

If you know there’s only one guy whom you can date, then the solution is obvious: marry him. If there are two, then if you don’t like the first guy you must marry the second. The chance number-two is better (or worse) is 50%, which is thus the chance that you make the best marriage.

Surprisingly, this same strategy—dumping all suitors hoping to find a better later—gives a 50% chance of finding the best mate if there are three dateable men. And it gives about a 40% chance of finding the best mate if there are as many as ten men. Pretty good!

How many men should you consider before stopping? Well, it’s all been worked out (a good explanation is here: pdf)

For every value of N—which you assume you know without error—here are the optimal number of men at which you must stop. Also shown in the probability (rounded to the nearest hundredth) for each stopping value. After N is larger than 3, this probability varies little from 40%—as N increases to very large numbers it levels off at 37%. Meaning you have a pretty good shot at finding your optimal mate if you follow these rules.

 

N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Stop 1 1 1 1 2 2 2 3 3 3 4 4 5 5 5 6 6 6 7 7
Prob 1 0.5 0.5 0.46 0.43 0.43 0.41 0.41 0.41 0.40 0.40 0.40 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.38

 

For example, assuming you know that you can date as many as N = 7 men in your lifetime, you should date the first man then drop him (abruptly, if he doesn’t call), but you should keep the next guy that is better than the first, and also drop the others after the first who weren’t as good as the first. If you do this, you have a 41% of finding True Love.

Of course, it could have been that the first guy was the best. What happens then is you end up going trough the other 6, one by one, your despair increasing with each new suitor. Finally, you’ll land on number 7 with whom you’re stuck—unless you choose spinsterhood and consider a houseful of cats an appealing alternative. All you can do is pray that the seventh guy wasn’t the worst in the bunch.

The problem with this table is that it assumes you know the value of N, which most people living outside a prison or desert island don’t. N could be large or small, depending on life’s vicissitudes and the number of marriageable men who live within easy reach.

The following pictures help account for the uncertainty you have in N.

Marriage problem

I still assume (for illustration) that the maximum number of men is 20, but that you don’t know you’ll have as many as that. If could be that you believe that you will only meet about one to five dateable guys. More are possible, but not probable, especially above 10. Call this the San Francisco, or Sparse scenario. This is pictured in green.

This scenario says that you think there is about a 15% chance you will see only N = 1 dateable man, but there is also 23% chance you will see N = 2 dateable men, and so on. If this picture represents your uncertainty in N, then your optimal stopping point is 1. Marry the first guy, whether he agrees to meet your mother or not.

The second scenario is the Midwest or Average view. You believe there will be a maximum of 20 men, but the most likely course is that you will know N = 9 or N = 10 dateable men (about 13% chance each). It’s possible, you think, that will only know just 1 dateable man, or even 20 men, but each possibility is remote (less than 1% chance for either). In this case, you should stop at 3.

That is, reject the first guy, then all the others that are worse than him, but then also drop the very next guy better than him. Tease this improved-over-number-one guy for while if you like, but move on. Reject all other suitors that are worse than all that came before, but keep the very next one that is better.

The last view is the New York or Thick scenario. This is where you believe that there are as many as 20 dateable men, and where you also think that the chance you can see them all (if you wanted) was high (about 16% chance for 19 or 20). Seeing just 1 dateable man is possible, but unlikely. Here you should date a lot, and drop most of them like last year’s handbag, until the sixth guy who was better than all who came before. Keep him. He will be Mr Right.

But only if this model truly represents reality. Which it probably doesn’t.

For one, it assumes that you can’t reconsider those who you have previously dumped, that men are constant in their behavior and their rankings fixed. As you date you age, so it’s likely that future men you date will begin to look better than they looked when you were younger. The model also assumes you don’t change, and that the man isn’t using the same strategy as you are.

How to account for all these (and other) contingencies is unknown, so it appears that the safest bet is not to be too picky.

15 thoughts on “How To Find True Love: The Marriage Problem Leave a comment

  1. ….”…..so it appears that the safest bet is not to be too picky.”

    Alcohol has also proven its value from time immemorial.

  2. Then there is the old fashion approach: find one that is good enough and work very hard at making it work. Adding to the mix is the modern approach: if it doesn’t work out, try and try again until you run out of time, money, and/or life.

    There are too many degrees of freedom in the equation to compute the one correct result in the beginning. Life is too short to measure the values of all the unknowns for your equation so you can solve it. Actually, you are hard pressed to be able to identify all the unknowns. Perhaps giving it your best shot is as good as you can do.

    The only sure thing is no one gets out of life alive so the best thing might be to live your life to the fullest while you are alive. The trick is to discover what “the fullest” means soon enough to do you some good.

    Sorry, I can’t help with that because I am too busy giving my life my best shot.

  3. Can you change my post above so my last name doesn’t show? Or just remove it entirely and replace it with this one? Please?

    Great. Now on top of being single during Christmas, I have a statistician basically telling me to lower my standards.

    “Statisticians are, as everybody knows, the best people to ask about
    matters of the heart. And if statisticians in general aren’t, I am. After all,
    everybody loves me. When you think of me, you think of amour; or is it
    amour-propre?”

    Maybe everyone used to love you. Until you killed cupid, and along with him, our romantic dreams.

    such a downer…

  4. Christine,

    (I’ve removed your name.)

    The solution is to just increase your N! Try winning the lottery. Men will swarm.

  5. Heh, the gals have a very cute and even profound website.

    A couple of points that I can shed some light on. Your numbers and graphs are, I have no doubt, statistically sound. The only number the women provide is “eligible, educated, single males aged 27-37” which is said to be “dwindling.”

    It it be dwindling it’s not because of a lack of males of that age–one assumes that there are about as many males as females in America aged that. To be clear, the women are (I am guessing here) substituting “educated” for “successful” in terms of controlling resources. And of course, almost all women want a man who is more successful than they are in income, power and dominance. Female hypergamy is a fact not to be wished away. In turn, most men (in their heart of hearts) prefer women with the qualities of beauty, fidelity, cheerful disposition and potential as mother and helpmeet.

    Now, back to the statistics. If you are a woman, say 30 years of age, living in a large American city and grossing $100,000+ per year, single, tough-minded in the workplace and have slept with 50-60 men (that’s only 4-5 per year since college) are you really presenting a picture that is going to make a 35 year-old, handsome, single bachelor who makes $150,000+ per year want to marry you. Let’s be honest.

    Feminism has caused the number of “eligible” men to “dwindle.” If you are a young, successful professional man why would you want to get married when all the tail you can handle is only one date away? When the mother of your children is going to compete with you for dominance on a daily basis? When the family courts will likely screw you when you get tired of it? I mean, REALLY.

    Okay ladies, you want to maximize your chances of finding Mr. Right? Get a BA and don’t take on a lot of debt. Sleep with ery few men at college. Work very, very hard to be at your ideal weight–you’ll really stand out from the crowd. Get a position as an admin assistant in a fairly large organization, business or government. Dress well, but very slightly demurely, and take great care with your appearance. Do you job extremely well, without appearing that your are competeing very hard to get promotions as fast as possible. Be slightly standoffish and formal with the men at work. Go to bars in the neighborhood with friends and have 1-2 drinks then go home. Don’t sleep with anybody. Attend charitable events where professional men gather. Attend the churches where the best families in the city also attend.

    My informal, educated guess is that you will have a choice, indeed a field of candidates asking for you. Probably at least N=6-10 over the course of a few years. Then, merely follow Briggs’ statistical advice!

    If you are already a feminist professional woman over 30 you could try a modified version of the above. Expand your age range upward and soften the hard edges a bit. There are a lot of successful older men who you have a chance of happiness with, but it is doubtful they are going to fit all the criteria of your value system.

  6. Addendum: Briggs, you as an amour-propre type was good for a hearty laugh. Yeah, anyone who reads your site can see how concerned you are with the approval of society in the Rousseauean sense.

  7. Dear Mr. Briggs (and company)

    Thank you very much for the advice. We’re very serious in our quest and only medium picky. So if you have any thoughts on love or a single cousin (aged 27-37) feel free to email us, we need all the help we can get. And Christine instead of being discouraged (or winning the lottery) we suggest C) checking out our project — which is jam packed with nuggets of information about finding your needle in the haystack. From hoodoo magicians to Michael Bolton, we’re not stopping until we’ve beat the odds.

    xo MEB + ARK
    Needleinthehaystack1@gmail.com

  8. @ Robert has pretty well nailed it. Our distaff inquirers are tackling their quandary backwards, as evidenced by their narrow and restrictive range of potential N’s. One suspects they’ve bought in too intensely to the “I am woman; hear me roar” meme and are now discovering one of it’s major shortcomings; ie. lack of opportunity for achieving long-term fulfilling intimacy. They can search and search and search, but until they place themselves in the position of being sought not much activity in the marital sphere will be taking place.

  9. Emigrate to a country where an American woman is an exotic novelty. And, if you can, develop an attractive voice without that unpleasant quacking/honking quality that is so common in the US but which, mysteriously, American men are much less subject to.

  10. I would not put the supply of eligible men as something small. However, it may be work to separate the wheat from the chaff.

    Assuming you have a man, the question is “should I stay or should I go”? What is the expectation that the next man will be better than the current one? and what are the costs involved.

      t|
      r|               xx
     o|               xx
     u|               xx
     b|    xx        xx
      l|    xx        xx  
     e|__xx____xx____
            go       stay
    
  11. And what if the man you choose just doesn’t want to marry you? What if none of them want to marry you? How far down the scale of acceptable men would you go to find a man who is willing to marry you?

    What criteria would you compromise? No drugs. No smoking. No dumbbells. No progressives. No Lotharios. No casual lawbreakers (e.g. illegal parking, littering — bad example for the children). No money management problems. No type A’s who don’t really have time for you.

  12. I find this post and all comments funny. Since they are from ‘older’ men, women seeking men for love and marriage probably should take them seriously. ^_^

    I don’t know much about modern dating or what true love means to other people, so I don’t have any strategic suggestions. Simply get a life and enjoy it, single or not!

  13. JH–simply “get[tting] a life” is, it seems to me, something like “just be[ing] yourself.” Everyone reading has, and is, without any effort at all!

    When speaking of the quality of getting and being, well, your mileage may vary. 🙂

  14. I thought, in America, “getting a life” means finding something interesting or more worthwhile to do. I am not sure that looking for a spouse or the love their life is a worthy goal. If love happens, it happens.

    (oo..oh.. I wasn’t saying that you guys should find better things to do than giving mate-finding advises. ^_^)

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