Hey everyone! My name is Jordan Arel. I have always hoped for a romantic relationship with a woman who shares, or at least supports me in, my impact goals.

It is also very important that we are mutually attracted to each other, share values and goals, and have a happy relationship.

Here is a Fermi estimate for myself (maybe it will also help others) of the likelihood of finding such a woman and what it might take to do so.

From past experience I estimate that, in terms of personality, I am extremely attracted (marriage-level attraction) to about 1/300 women I meet.

Of the few such women I have met, only about 1/2 have been attracted to me a mild to moderate amount in return. I suspect if I had met 10 times as many such women, perhaps 1 would have liked me enough to consider me marriage-material; so I estimate ~1/20 women I am highly attracted to will be mutually attracted to me.

1/300 * 1/20 gives an estimate that I will share mutual attraction with 1/6,000 women I meet.

Now from this it is important to exclude women who are not a values or lifestyle match. I have found compatible values and lifestyle actually have a quite-high correlation with compatible personality; however, I suspect something like only 1/3 of those with mutual attraction will share or at least appreciate my extreme obsession with impact, allowing me to feel supported by mission kinship/empathy (In my last long-term relationship I was told it’s not going to work because “I’m too obsessed with saving the world.” Which was accurate.)

There are other lifestyle factors of which I am somewhat uncertain, so I will give another 1/2 penalty that, for some reason or another, it won’t work out despite everything else.

1/6,000 * 1/3 * 1/2 brings the estimate down to 1/36,000 women being an ideal match. This means that if I chose women at random I would have to date one woman every day for ~100 years to find a woman that is a good match. My timelines aren't that long, so seems like I need a better selection process.

There are several selection criteria which I have noticed occur in unusually high proportions in women I am most attracted to, for example, (including approximate rareness of characteristic):

  • High intelligence .1 (120 IQ or higher) 
  • Altruistically Motivated .01 (top 1 percentile) 
  • Overachiever/highly ambitious .05 (top 5th percentile) 
  • Unusually Playful .05 (top 5th percentile) 
  • Red hair ~.04 (in the United States) 
  • High sex drive .15 (top 15th percentile) 
  • “Spiritual” .15 (percent of people who meditate) 
  • Musicality .1 (moderately to highly skilled) 
  • Caring .15 (top 15th percentile) 
  • Theatrical .15 (guess)

If I simply required all of these characteristics, naively assuming there is no correlation/anti-correlation between characteristics, this would mean I would have to go through more than 10^11th women to find one match

Non-coincidentally, none of the women I have liked have actually had 100% of these characteristics.

While the full combinatorial math is too hard or at least annoying for me, if I hypothetically took the top five most important characteristics and said she has to be in the top 10th percentile in at least three of those characteristics, if GPT-4 did the math right (I double-checked and pretty sure it is correct), this would select only .856% of women.

This is good enough for a Fermi estimate. I can narrow the pool of women down significantly based on such characteristics; I just have to find a way to screen for those characteristics and perhaps iteratively seek even better screening criteria, algorithms, and screening methods.

To finish up on the math aspect of this, while this screening process would leave me with only ~1% of women, I suspect it would initially have something like a 90% false positive rate;

So instead of reducing the search from 36,000 to 360 women, I expect it would really only get me down to needing to search through 3,600 women. I could get through them all if I dated five women per day, for one hour each, over two years, this wouldn’t be completely impossible, but I suspect that through other screening processes like screening at various levels of depth, utilizing machine learning, hired help, and a lot of iteration, I could probably eventually get this number down a lot further and find more efficient processes that give less false positives and false negatives. The rest of this post will speculate on a few such techniques.

A few possible techniques: 

  • Using bots to search through and screen dating profiles
  • Using machine learning, especially on hard to quantify qualities, trained on data from interactions with women and profiles I like
  • Maybe hiring some data scientists to help me do this better
  • Rapid iteration to improve this process
  • Maybe signal-boosting to quickly reach a large number of women by becoming more famous in my field of altruistic interest, dropping a few $1000 on a rapidly tested and iterated dating profile, or other ways of reaching a large number of potential women faster

Another thought, maybe I just need to find the right spaces, for example highly involved & high performing EAs or Social Entrepreneurs, hanging out at Irish music festivals may be wise (the top two women I have liked had red hair which is a 1/625 probability by pure chance (and both were also talented musicians)), hang out at the Mega Society, etc.

Something I have been thinking about a lot lately is being the type of person who would attract the type of woman I would want to date, which would mean myself being in the top 10% or so of certain characteristics I hope she will share, plus other generally attractive characteristics.

I hope this was helpful or entertaining, would love to hear feedback and ideas. If you are interested, here’s my dating doc I just created.

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9 comments, sorted by Click to highlight new comments since: Today at 11:12 PM

Your Fermi estimate starts from the women you’ve met but your conclusion is on women in general, who might present widely different characteristics.


According to Gallup polls, about 46% of Americans are creationists. (…) That’s half the country. And I don’t have a single one of those people in my social circle.

A lot of sympathy for the challenge you describe. My possibly bit half-baked views on this:

  1. If you take your criteria seriously, dating sites where you can answer questions and filter according to answers might help
  2. Knowing that for a marriage to work you anyway need something rather close to radical acceptance, you might simply try to put your abstract criteria a bit into perspective, and focus more on finding a partner that accepts your ways very happily rather than sharing so much of them (there is also some danger in this; maybe the truth 'lies in the middle': do that partly, but of course also not too generously; I guess what I mean to say is, reading your text, I get the feeling you might be erring too much on the side of strict requirements, though it's only a spontaneous guess)
  3. 'Red hair as a serious criterion - really?': I think the 1/625 sounds like a reasonable candidate for spurious correlation: there is such a large number of characteristics that persons have, that two of your favorite dates sharing one of them does not say much about the relevance of that individual characteristic, statistically speaking. That said, I can believe you simply have a sort of red-hair fetish/preference, but then, I'd for sure think if things fit more generally with a person, her having the 'right' hair color as well seems very unlikely to be a major relevant factors for long-term happiness with her.

And good luck!!

Don't underestimate the value of a red-headed woman...

This was interesting right up until "if GPT4 did the math right". I believe GPT4 is terrible with story problems like that, and with math like that story problem describes. Unless it used a plugin and described its solution in a way you can include for checking. Bite the bullet and do the math. You can't do fermi estimates without a little math.

Ah dang sorry, was not aware of this. Brute force re-taught myself how to do this quick 10^5 / (5-2)! = 100,000 / 6 = 1/16,666. You are right, that was off by more than a factor of ten! Thanks for the tip.

Edit: agghh I hate combinatorials. This seemed way off to me, I thought the original seemed correct. GPT had originally explained the math but I didn’t understand the notation, after working on the problem again for a while I had it explain it’s method to me in easier to understand language and I’m actually pretty sure it was correct.

If you explained the math in a footnote or something, you'd probably get some math collaboration from readers. I don't know how to do that one off the top of my head, but it's interesting.

My sense is that GPT isn't trustworthy on that, and it could be off by a lot, so it's necessary to include your (or its) math if you're not sure about it yourself.

I’m quite sure now, I came to the same conclusion independently of GPT after getting a hint from it, which itself I had already almost guessed.

A woman having the top 10% of any characteristic is almost the same as rolling a 10 sided die and coming up with a 1 (this was the actual problem I presented GPT with, and when it answered it did so in what looked like a hybrid of code and text so I’m quite sure it is computing this somehow).

What was clearly wrong with the first math was that if I roll just three die, there would already be1*10^3 or1/1000 chance of getting all 1’s. And if I roll five die, there would be a much higher, not lower chance that I get at least three 1’s.

When rolling five die, there are 10 different possible combinations of those five die that have exactly three out of five 1’s, and it’s a little bit more complicated than this, but almost all of the probability mass comes from rolling three 1’s, since rolling four or five 1’s is far less likely. So you get very close (much closer than needed for a Fermi estimate) to the answer by simply multiplying the 10 possible combinations by 1/1000 chance that each of those combinations will be all 1’s, for a total of about 1/100 or ~1%. Pretty basic once you see it, I would be surprised if this is incorrect.

I definitely like the estimation method. I'm totally convinced that the answer is higher than 1/1000 as you describe. The bit about dividing that by the number of ways you can roll three ones on five dice sounds sketchy - I can't tell for sure that that's sensible. But it does sound intuitively right. There are five ways to roll 4 1's (simplifying it to ten sided dice is a great move for my intuition), ten ways to roll 3 1s, and 1 way to roll 5 ones; so that's 16. That would be 1.6%, which is different than GPT4's .86%. So I think that does get into the ballpark, like you said, but it's not exactly right. Anyway, we're into the details. I think you're right about the order of magnitude, and that's good enough for a Fermi estimate.

Yes, that’s the main place I’m still uncertain, the ten combinations of three 1’s have to be statistically independent which I’m having trouble visualizing; if you rolled six die, the chance that either three pre-selected specific die would be 1’s or the other three die would all be 1’s could just be added together.

But since you have five die, and you are asking whether three of them will be 1’s, or another overlapping set will be 1’s, you have to somehow get these to be statistically independent. Part of that is actually what I left out (that GPT told me, so not sure but sounds sensible), you take the chance that the other two leftover die will both not be 1’s; there’s a 9/10 chance that each will not be a 1, so .81 chance that both will not be ones, and you actually have to multiply this .81 by the 1/1000 for each set of three 1’s. So that slightly lowes that part of the estimate to (1/100010).81=.81%

So you have excluded the extra 1’s from the sets of three 1’s but then you have to do the same calculation for the sets of four 1’s and the one set of five 1’s. The set a five 1’s is actually very easy, there’s a 1/10 chance that each will land on one, so all of them together is 10^5=1/100,000, adding only .001% to the final calculation, and the four 1’s are also about a factor of 5 less likely then three 1’s because you have to roll another 1 to get four 1’s. So you have to roll four 1’s and one not-1, or (1/10,000).95=.045%


Still not 100% sure because I suck at combinatorials but this seems pretty likely to be correct. Mainly going off that 1/1,000 intuition for any three sets of 1’s and that being repeated ~10 times because there are five die, and the rest sounds sensible