the Probability Distribution of Dating a Girl November 26, 2008

Posted by keithkchan in fun stuffs.

Today, two colleagues and I had a very interesting discussion. Since none of us have a girl friend, we wanted to quantify the difficulty in dating a girl. Let me first make our problem clear. For some girl you meet, what is the probability that you will successfully date her?

We want to incorporate two important considerations. First, the more beautiful the girl is, the probability that you can date her should be more suppressed. Secondly, if the girl is ugly, you certainly are not so willing to date her, so the probability should also be suppressed. The probability distribution I come up with is Gaussianly distributed

$P(beauty)=\exp[ - ( beauty / )^2 ]$. Let’s not to bother about the normalization. I have to define the beauty parameter. I define 0 as the girl with “normal beauty” that I find it OK, and so I am willing to date her. Since she is not very beautiful, I expect the chance that I successfully date her is maximum. Beyond 0, the girl’s beauty increases, my chance of dating her is exponentially suppressed. I define the the girls with negative beauty as those less beautiful than 0, so I am not so willing to date her, and hence the chance of eventually dating her also reduces. The reason that I model it with a symmetric distribution is that I believe that the level of beauty of girls are symmetric from my view point, the zero. <beauty> is a measure of the spread of the distribution, and it is a reflection the personal definition of beauty. That is, it depends on what you mean by one unit of beauty.

The other colleague believed that the definition of beauty should be $P(0)=0$, and he proposed

$P(beauty) = beauty^2 \exp[ -(beauty/ < beauty> )^2]$. Again, neglect the normalization constant. You may notice that this is a Maxwellian distribution. I don’t like his proposal because I think the ugliness should not be bounded below. That is I believe for any ugly person you see, there exists a person who is uglier than that one. Of course when the mean beauty in his distribution is much larger than the spread <beauty>, Maxwellian distribution is essentially symmetric within the range we are interested in.

We can’t agree with each other which one is better. So let us have a poll, and your comments are important for us to decide which one is better. On the other hand, we hope that these kind of studies can facilitate people like us to find a date as many colleagues in our community have difficulty in finding a date.

P.S. Technically speaking, according to our definition of P(x), it is not a probability distribution since if we integrate over beauty it may not be 1. It should be called likelihood.
One can also generalize the beauty to some “like” parameter, which is a function of beauty, charm, and so on. It reflects how much you like her due to various factors. Of course this complicates its definition.

1. David - November 27, 2008

Right now i have a delta function distribution Mr. Chan : ))) so I think neither of your formulas works in my case 😛

2. keithkchan - November 27, 2008

Well, one of the representation of the delta function is the limit of Gaussian distribution as as the width goes to zero. I don’t know if my colleague Mr Baruski’s proposal has such a nice limit or not.
BTW, it is CHAN, rather than CHEN, Mr Pirtskhalava 😛

3. davidp1234 - November 28, 2008

Mr. Chan can’t you distinguish a from e? : ))))

4. Payam - December 8, 2008

So I prefer Mr Keith’s probability function, but I think the whole problem is not formulated well. Finding a date is not like a system in equilibrium which is totally described by a probability function, but it is more similar to a scattering process in which the effective cross section of people becomes very important. This will be the real answer to the question why people like Mr Keith can’t find a date, because whatever probability function he wants to assume, his cross section is so small (he is non interactive) that he can not find a date.

5. Irakli - December 11, 2008

6. Irakli - December 11, 2008

for yopurself. 😀

7. keithkchan - December 12, 2008

Payam
I don’t agree that the probability distribution formalism is not applicable. Think about the molecules in the gas. There may be several types of molecule in the gas, each molecule may be in different states. If you try to trace the path of an individual molecule, the path is crazy and unpredictable. But you can still describe the whole gas using some distribution function.
I agree with that cross-section is very important in this problem, but that has been taken into account in the likelihood function. I am regarding all the other girls as a heat bath. Their distribution should not rapidly time varying. Since my crosse-section is small, my likelihood function is also small relative to Mr Payam.

8. keithkchan - December 12, 2008

Irakli
I absolutely agree with you. But theory and experiment are completely different. Maybe if I devote my time on blogging to find a date, my chance of success will be higher. :=)

9. sjoert van velzen - December 19, 2008

I we want to answer the question: “For some girl you meet, what is the probability that you will successfully date her?” I think we still have to convolve the proposed distributions with the probability distribution that a girl will date *you*. This will be a function of the ratio of your beauty to the beauty of the girl in question, making the problem slightly more hard.

10. keithkchan - December 20, 2008

Mr sjoert
First of all, our description of the likelihood function is a so-called mean field approximation. We regard all the girls form a constant potential. As a first approximation, we don’t need to consider the complication you introduced. However, when you consider detailed dynamics, I think you may take the response of a girl into account. This is reminiscent of molecular dynamics to me.
In passing, enjoy your trip to Holland.