What should be the punishment for rape?

Using back-of-the-envelope calculations, I will try and understand whether the magnitude of punishment for rape really matters? Usually in the aftermath of a rape we hear a range of pronouncements for the punishment of rapists that range from 20 years imprisonment; life imprisonment; death sentence to even castration. Even Vir Sanghvi indulges in this rhetoric like here. Is the magnitude of punishment really effective in conveying to the rapist the consequence of his action?

The numbers I use are taken from the very informative paper Rape victims in Kerala.

In 1999, about 487 women were raped in Kerala. Since about 60-70% of rapes go unreported (ballpark figues obtained from the internet, there are groups who argue it is much higher) the actual number of rapes in Kerala is (let us say with a 60% average) about (487*100/40). In the same year the number of convictions for rape were 36. That gives rise to an approximate conviction rate of 3%. Keep this figure in mind.

Now suppose you raise the sentence from the minimum seven year imprisonment to a twenty years. Let the rapist be earning Rs 1.5 lacs in a year. (If you consider that low, any increase of salary will have a lower conviction rate because of better quality of legal support in favor of the rapist.) His total earning in 20 years is Rs 30 lacs.

Now consider his situation.

He stands a 3% chance of losing the Rs 30 lacs and additional money, in total Rs 50 lac (let us say) IF he is caught and goes to prison. On the other hand, he has a 97% chance of gaining Rs 30 lacs if he goes scot-free. Work out his expected value and you will find it comes down to (29.1 - 1.5) = 27.6 lacs.

This number basically tells us that because of the low probability of conviction he doesn't stand to lose much even if you increase the sentence. You can make a complex model from this but this gives us a rough idea of the economics of crime!

It is the guarantee of punishment that works much better than the increase of severity for the punishment of a crime! Speedy and guaranteed punishment are the best deterrence against crime.