Where do all the smart girls go?

This question had initially popped up in my head about a year back when I was in the arranged scissors market and was getting frustrated about not meeting any smart girls. This was around the time when I had to indicate to some shady “marriage exchange” about my preferences in terms of the girl’s education and I gave some serious thought to it, but for some reason ended up not blogging about it.

I don’t want to get into debates regarding “better” colleges here so let’s just simplify that discussion and rank colleges by demand for admission for undergraduate courses. Again it is not going to be a precise ordering since different colleges have different admission processes but I’m sure that with some approximation and adjustment such an ordering is possible. Yeah this is also not a precise ordering butI supose this is the best we can get. As Prof Ramnath Narayanswamy says, “reality doesn’t matter. Perception does”.

Now make a table with three columns. In the first column write down the above prepared list in order, with the number one college on top. In the second column, write down the average number of boys each college typically admits per year, and in the third column the average number of girls admitted by the college.

Next, add two more columns to the table. In the fourth, make a “cumulative total” of the second column and in the fifth a “cumulative total” of the third column. So if I look at the nth row of the 4th column, I know the average number of boys admitted in a typical year by colleges ranked 1 to n. Similarly for girls and the fifth column.

My hypothesis is that at least for the first 100 rows, the number in the 4th column is at least twice as much as the number in the 5th column. Actually, I would go a step further and say that the above is true for the first 500 rows. If you look at the papers the day after CBSE announces its board exam results, you will see that girls would’ve done as well on average, if not better, than boys. So where do all the smart girls go?

One thing might be that there might be certain courses which girls show a marked preference for but most boys avoid because of which demand goes down because of which they go down in the rankings. Another could be that girls in general have preferences so niche that the best colleges in these niches don’t show that kind of admission demand. On the other hand, boys seem more homogeneous (everyone wants to do engineering) because of which demand for the best engineering colleges is really high.

There is a school of thought that a large number of girls are interested in the humanities which few boys show a liking for so a lot of smart girls are to be found in the better humanities colleges. But then, what happens in cities such as Bangalore or Madras which simply don’t have the same kind of humanities colleges as do cities such as Delhi and Bombay? Do girls who want to do humanities in these cities still go to the not-so-great humanities colleges rather than choosing better (in general) colleges in other disciplines?

Another explanation is girls only colleges where naturally demand is low since half the population can’t apply. But then I would expect the better of these to have enough demand that they rank fairly high. I’m again not satisfied by this explanation.

So the question remains. Where do all the smart girls go? Don’t tell me some of them actually choose not to go to college or something!

Search strings – last one month

It’s been a long time since I’ve done this and I’m feeling bored now so thought I should write this. It’s the same old usual thing – unusual things that people have searched for and landed up at my blog. I used to compile these stats on a daily basis earlier but nowadays due to NED have abandoned it. So here is an attempt to revise it. This time it’s not for a particular month. It’s just over hte last 30 days. Here goes:

  • travelling on general compartment on shimoga express
  • “ramnath narayanswamy” sex
  • doctor is that the coin falls the right way
  • is token system better than queue in reception of hospital
  • where is kodhi math in karnataka??
  • women in skimpy cut offs

Ok I know the list is smaller than the usual, but I think people aren’t being that crazy nowadays, or for some reason the crazy people are being repelled by my blog! Hopefully next month I’ll have better stuff.

Arranged Scissors 13 – Pruning

Q: How do you carve an elephant?
A: Take a large stone and remove from it all that doesn’t look like an elephant

– Ancient Indian proverb, as told to us by Prof C Pandu Rangan during the Design of Algorithms course

As I had explained in a post a long time ago, this whole business of louvvu and marriage and all such follows a “Monte Carlo approach“. When you ask yourself the question “Do I want a long-term gene-propagating relationship with her?” , the answer is one of “No” or “Maybe”. Irrespective of how decisive you are, or how perceptive you are, it is impossible for you to answer that question with a “Yes” with 100% confidence.

Now, in Computer Science, the way this is tackled is by running the algorithm a large number of times. If you run the algo several times, and the answer is “Maybe” in each iteration, then you can put an upper bound on the probability that the answer is “No”. And with high confidence (though not 100%) you can say “Probably yes”. This is reflected in louvvu also – you meet several times, implicitly evaluate each other on several counts, and keep asking yourselves this question. And when both of you have asked yourselves this question enough times, and both have gotten consistent maybes, you go ahead and marry (of course, there is the measurement aspect also that is involved).

Now, the deal with the arranged marriage market is that you aren’t allowed to have too many meetings. In fact, in the traditional model, the “darshan” lasts only for some 10-15 mins. In extreme cases it’s just a photo but let’s leave that out of the analysis. In modern times, people have been pushing to get more time, and to get more opportunities to run iterations of the algo. Even then, the number of iterations you are allowed is bounded, which puts an upper bound on the confidence with which you can say yes, and also gives fewer opportunity for “noes”.

Management is about finding a creative solution to a system of contradictory constraints
– Prof Ramnath Narayanswamy, IIMB

So one way to deal with this situation I’ve described is by what can be approximately called “pruning”. In each meeting, you will need to maximize the opportunity of detecting a “no”. Suppose that in a normal “louvvu date”, the probability of a “no” is 50% (random number pulled out of thin air). What you will need to do in order to maximize information out of an “arranged date” (yes, that concept exists now) is to raise this probability of a “no” to a higher number, say 60% (again pulled out of thing air).

If you can design your interaction so as to increase the probability of detecting a no, then you will be able to extract more information out of a limited number of meetings. When the a priori rejection rate per date is 50%, you will need at least 5 meetings with consistent “maybes” in order to say “yes” with a confidence of over 50% (I’m too lazy to explain the math here), and this is assuming that the information you gather in one particular iteration is independent of all information gathered in previous iterations.

(In fact, considering that the amount of incremental information gathered in each subsequent iteration is a decreasing function, the actual number of meetings required is much more)

Now, if you raise the a priori probability of rejection in one particular iteration to 60%, then you will need only 4 independent iterations in order to say “yes” with a confidence of over 95% (and this again is by assuming independence).

Ignore all the numbers I’ve put, none of them make sense. I’ve only given them to illustrate my point. The basic idea is that in an “arranged date”, you will need to design the interaction in order to “prune” as much as possible in one particular iteration. Yes, this same thing can be argued for normal louvvu also, but there I suppose the pleasure in the process compensates for larger number of iterations, and there is no external party putting constraints.