Thursday, April 22, 2010

E, Marriage, & Stock Markets

Meghan McArdle wrote her own book review on Lori Gottlieb's "Marry Him". McArdle brought up the inherent game theory aspect of the dating jungle. Indeed, the current dating system is quite inefficient at connecting people together in a long lasting way.
http://www.theatlantic.com/culture/archive/2010/04/reader-marry-him/39342/

As I've been reading Caroll Quigley's Evolution of Civilizations, I have to wonder perhaps that the Western dating scene has institutionalized. That the combination of fairy tale endings and the sexual liberation has transformed the instrument of dating, as a way to interview suitors, into an institution more concerned with dating for its own sake.

As a side note, the book is fantastic, and it has definitely transformed the way I look at history and current events.

Anyway, when I went to a math camp, I saw a population problem that has some bearing on this dating business. Readers perhaps will find this of use in their own lives:
http://en.wikipedia.org/wiki/Hampshire_College_Summer_Studies_in_Mathematics

Assume that the dating population is stochastic, meaning that you will, at random, meet dating prospects who are of random quality. The problem is that you have no pre-existing basis to judge your boy/girlfriends: Is s/he sufficiently good enough to settle with? How do you know if s/he is the best you can do?

It turns out that, given a time range when you plan to date, by time 1/e, you will have met enough of the population to know the upper and lower bounds of the population. By time 1/e, you have a good enough idea to know what "great" looks like, and to settle with the next best guy/girl that comes along. At age 22.4 [for range 18 to 30], you will have enough data history to know what is the best you can get.
http://en.wikipedia.org/wiki/E_(mathematical_constant)


So at age 21 to 23 [23 is using another age range], you need to sit down and seriously compare your internal romantic ideal versus the past boy/girlfriends you've had, just so you don't keep pining for that Disney prince/princess to come along.

This particular solution assumes that dating and pickup skills do not improve, which is not necessarily the case. But it is a good metric.

The number 1/e is applicable for other random walk problems as well. For example, assume that the stock market is a random walk, and that you need to invest $5,000 into the stock market every year [aka, your IRA contribution]. If you want to time the market, you want to know when is a great low-point to plunk your money into the market. Well, the 1/e works here, too. Assume 12 months, by April 12th, you will know what's the likely lower bound of the market. The next time the market crosses that lower bound, you know that the opportunity has arrived.

2 comments:

Tung said...

Very interesting post! But don't you have to adjust for the relevance of one's prior dating experience/pool to subsequent pools? Ages 18-22.4 (using your range) for me were pretty useless in terms of providing me with information about what was within my realistic range, because ages 18-20 were spent at Caltech, a place with a male-female ratio of 8-1, and ages 20-22 were spent teaching high school kids SAT classes, so the largest group of females I met were too young and off-limits.

It wasn't until I got to Berkeley for grad school at age 22 that you could say I was in a "normal" environment. And then I have to grant you that 4-5 years to figure things out has it about right. I didn't actually get married for another 4 years after that, but that's because 3 of those years were spent moving across the country in 1-year positions working for federal judges. When I met my now-wife within that range though, and we started dating, we moved quickly toward marriage.

So I suppose with the one friendly amendment, I'm a data point in confirmation of your theory!

Jimmy said...

assuming the dating pool is random, and that your desirability criteria stay the same, your external environment does not have much bearing on that.

Certainly your circumstances (moving around) preclude serious involvement in general, but if you had met your "upper bound" during that time moving around, you would have known she was it.

I guess you were lucky that you didn't meet your wife until you and she were both ready :)