On Learning At Home

Recently, India has enacted this Right To Education Law, one of whose provisions dictates that schools must reserve at least 25% of seats for kids from economically backward communities. This post will be tangential and will not be trying to examine the merits and demerits of the law.

So earlier this week, the Wall Street Journal published a long (and pretty good) analysis of the impact of the law (it was published in India in Mint). While I might discuss the rest of the article in another post, the paragraph that caught my eye was this one:

Sumit’s father and many of the poorer parents are troubled by the fact that their own limited literacy prevents them from helping. Some wealthy parents, meanwhile, chafe at the slowed pace of learning. They have suggested segregating the poor kids.

Made me wonder how much primary learning actually happens in school, and how much happens at home. Looking back at my own childhood, I learnt most of my “concepts” at home, and before any subject was taught in school I was well prepared for it. In fact, I would be so ahead of my class that I’d frequently get bored, and would think that my classmates were dumb because they weren’t able to keep pace with me.

My parents were no “tiger parents“. And I wasn’t a particularly industrious child. Of course, there would be times when my parents would make me recite tables of two-digit numbers as I traveled wedged between them on our Bajaj Priya, but never forced me to study (until maybe till there were a few months left for the IIT-JEE). And still, somehow, they managed to teach me everything at home. And that proved to be a massive advantage over kids that were encountering the concepts for the first time in school.

Of course, as I went to advanced classes, there was only so much they could teach me at home (since we were going beyond the basic fundamentals here, and there was only so much they could remember), but the head start that I got in primary school was, I think, really useful in my being a topper for most of my schooling, with there being a significant positive feedback.

So what do you think? How much do you think parents actually contribute to their kids’ learning in early age? Is there a positive correlation of kids doing well in school with whether their parents are well-informed, have time for kids and can teach well? If there does exist significant correlation, what are the policy implications of it? Does it defeat the purpose of reservations in school?

Diminishing Value of a Red Card

Often when we see players being sent off AND penalty kick being awarded in the event of an illegal stop of a goal-bound ball, Baada and I have thought that the punishment is too harsh. That for stopping one goal, the team effectively gives away the goal (conversion rate of penalties is high) and also loses a player (sometimes the goalie) for the rest of the game.

Now, after last night’s strategic hand ball by Luis Suarez, people are complaining that the punishment is not enough. Though it was a split-second instinctive decision by Suarez to handball, even if he were to replay the incident in his head and analyze the costs and benefits, I’m sure he would’ve done what he did. This clearly contradicts what I mentioned in the first paragraph.

The main issue here is with the value of a red card ¬†at various stages of a game. The red card has intrinsic value – of being suspended for the next game. In addition to this, the red card leaves the team one short for the rest of the game, and so it is clear that the later a red card is given out, the lesser the disadvantage it causes the team because they’ve to play for lesser time with a man short.

What makes Suarez’s decision more logical is the time value of a one-goal lead. The lesser the time left in the game, the more the value of the one-goal lead since there is lesser time for which it needs to be protected. And in this case, the handball occurred on what might have been the last “kick” in the game, and so the value of the one-goal lead was really high.

The earlier this incident had occurred in the match, the less would’ve been Suarez’s incentive to handball – more time to win back the conceded goal and more time to play a man short if redcarded. At the time when it actually occurred, Suarez would’ve been a fool to NOT handball. The payoffs were heavily loaded in favour of handballing and he did it.

People on twitter are suggesting that rules be changed, that the goal should’ve been awarded anyway instead of the penalty and stuff, but considering that the same punishment costs much more if given out earlier in the game, I think the current punishment is appropriate. The excess of this punishment in earlier stages of the game is compensated by the punishment being too little in the latter stages, and on an average I think it is appropriate.

Let’s continue to keep football simple and not clutter it with Duckworth-Lewis kind of rules. And congrats to Suarez for taking the most logical decision at the moment. It is indeed as great a “sacrifice” as Ballack’s tactical yellow card against Korea in the 2002 semis.

And I feel sad for Asamoah Gyan. But then again, with Ghana being in the knockout stages solely on the merit of two Gyan penalties, it is only appropriate that they are going out nowon the demerit of Gyan’s missed penalty.

Relationship Stimulus

This post doesn’t necessarily restrict its scope to romantic relationships, though I will probably use an example like that in order to illustrate the concept. The concept that I’m going to talk about any kind of bilateral relationship, be it romantic or non-romantic, or between any two people or between man and beast or between two nations.

Let us suppose Alice’s liking for Bob is a continuous variable between 0 and 1. However, Alice never directly states to Bob how much she likes him. Instead, Bob will have to infer this based on Alice’s actions. Based on a current state of the relationship (also defined as a continuous variable between 0 and 1) and on Alice’s latest action, Bob infers how much Alice likes him. There are a variety of reasons why Bob might want to use this information, but let us not go into that now. I’m sure you can come up with quite a few yourself.

Now, my hypothesis is that the relationship state (which takes into account all past information regarding Alice’s and Bob’s actions towards each other) can be modelled as an exponentially-smoothed variable of the time series of Alice’s historical liking for Bob. To restate in English, consider the last few occasions when Alice and Bob have interacted, and consider the data of how much Alice actually liked Bob during each of these rounds. What I say is that the “current level” that I defined in the earlier paragraph can be estimated using this data on how much Alice liked Bob in the last few interactions. By exponentially smoothed, I mean that the last interaction has greater weight than the one prior to that which has more weight than the interaction three steps back, and so on.

So essentially Alice’s liking for Bob cannot be determined by her latest action alone. You use the latest action in conjunction with her last few actions in order to determine how much she likes Bob. If you think of inter-personal romantic relationships, I suppose you can appreciate this better.

Now that you’ve taken a moment to think about how my above hypotheses work in the context of human romantic relationships, and having convinced yourself that this is the right model, we can move on. To simplify all that I’ve said so far, the same action by Alice towards Bob can indicate several different things about how much she now likes him. For example, Alice putting her arm around Bob’s waist when they hardly knew each other meant a completely different thing from her putting her arm around his waist now that they have been married for six months. I suppose you get the drift.

So what I’m trying to imply here is that if you are going through a rough patch, you will need to try harder and send stronger signals. When the last few interactions haven’t gone well, the “state function of the relationship” (defined a few paragraphs above) will be at a generally low level, and the other party will have a tendency to under-guess your liking for them based on your greatest actions. What might normally be seen as a statement of immense love might be seen as an apology of an apology when things aren’t so good.

It is just like an economy in depression. If the government sits back claiming business-as-usual it is likely that the economy might just get worse. What the economy needs in terms of depression is a strong Keynesian stimulus. It is similar with bilateral relationships. When the value function is low, and the relationship is effectively going through a depression, you need to give it a strong stimulus. When Alice and Bob’s state function is low, Alice will have to do something really really extraordinary to Bob in order to send out a message that she really likes him.

And just one round of Keynesian stimulus is unlikely to save the economy. There is a danger that given the low state function, the economy might fall back into depression. Similarly when you are trying to get a relationship out of a “depressed” state, you will need to do something awesome in the next few rounds of interaction in order to make an impact. If you, like Little Bo Peep, decide that “leave ’em alone, they will come home”, you are in danger of becoming like Japan in the 90s when absolute stagnation happened.

The Eighty-Twenty Rule

I first got this idea during some assignment submission at IIT. One guy in our class, known to be a perfectionist is supposed to have put in 250 hours of effort into a certain course project. He is known to have got 20 out of 20 in this project. I put in about 25 hours of effort into the same project and got 17. Reasonable value for effort, I thought. And that was when I realized the law of diminishing returns to effort. And that was the philosophy I carried along for the rest of my academic life (the following four years).

The problem with working life as opposed to academic life is that the eighty-twenty formula doesn’t work. The biggest problem here is that you are working for someone else, while you were essentially working for yourself while you wree a student. Eighty was acceptable back then, it is not acceptable now. Even if you are working for yourself, the problem is that the completion-rewards curve is completely diffferent now.

Imagine a curve with the percentage of work done the X axis and the “reward” on the Y axis. In an academic setting, it is usually linear. Doing 80% of the work means that you are likely to get 80%. Fantastic. The problem wiht work is that the straight line gets replaced by a convex curve. So even to get an 80% reward, you will need to maybe do 99% of the work. The curve moves up sharply towards the end so as to give 100% reward for 100% work (note that I’m talking about work done here, not effort. Effort is irrelevant)

Now, why did I cap reward at 100% in the previous paragraph? Why did I assume that there is a “maximum” amount of wokr that can be done? Note that if there is a ceiling to the amount of work to be done, and to the reward, then you are looking at a payoff like a bond – the upside is limited – 100% but the downside is unlimited (yeah I know it’s limited at 0, but it is so far away from 100% that it can be assumed to be infinitely far away). Trying hard, doing your best each time, the best you do is 100%. But slip up a bit, and you will get big deficits. It is like the issuer of the bond defaulting.

Almost thirty years back, Michael Milken noticed this skewed payoff structure for bonds, and this led him to invent “junk bonds”, which are now more politely known as “high yield debt”. Now, these bonds were structured (basically high leverage) such that a reasonably high rate of default was built in. In an ordinary bond the “default expectation” is that the bond won’t default at all. For a high-yield bond, the “default expectation of default” is much higher than 0 – so there is a definite upside if the bond doesn’t default. So that balances the payoffs.

So how does that translate to work situations? You need to basically get yourself a job where there is significant scope for doing “something extra”. So that if you take into account the “something extra”, the “expectation” will be say something like 90% of the work. So by doing only a bit more than your old 80-20 rule from college, you can fulfil expectations. And occasionally even beat them, resulting in a major positive payoff (either in terms of money or reputation or power etc.).

The deal is that when the expectation is lower than 100%, the reward-work curve changes. It remains heavily convex for the duration within the expectation (so if expectation is 90% of work for 80% of profit, the curve will be highly convex in the {(0,90),(0,80)} area). And beyond this, it gets less convex and closer to linearity, and so gives you a bit more freedom.

I’m too lazy to draw the curves so you’ll have to imagine them in your heads. And you can find some info on convex curves here: http://en.wikipedia.org/wiki/Convex_function