Friday, January 29, 2010

On the Misjudgment of Probabilities

A somewhat rambling, indulgent post. I'm writing a blogpost after quite a while which may account for the rather stodgy turns of phrase.

Finished reading Nassim Taleb's bestsellers Fooled by Randomness and Black Swan lately. One among the several insights in the books is that in the real world, it is difficult to assess the degree of uncertainty as risks are not easily computable. The tools of Probability theory come in mighty handy to help compute odds in controlled environments like a casino. But they are of little use once we step out of such regulated environs.

Also, even when we are in a position to reliably compute the odds, we do not consciously use the odds while taking decisions.

Suppose an insurance salesman presents you with two policies.

- Death on account of a terrorist strike
Covered Amount: $50,000
Annual Premium: $50(for 5 years)

- Death on account of any cause
Covered Amount: $50,000
Annual Premium: $2500(for 5 years)

Now, I find Policy A just as attractive as Policy B if not even better. Yes, we would all expect the premium on a special-case death policy to be a lot lower than a "normal" life insurance policy.
A premium of $50 as opposed to $2500 seems fair enough as it appears to account for the relative rarity of a death on account of a terrorist strike.

However, though a ratio of 1/50 ($50/$2500) sounds very good, Policy A is terribly overpriced! (I'm assuming ofcourse that Policy B is reasonably priced)

Death on account of a terrorist strike is an extremely rare event. Surely, fewer than one in fifty deaths is caused due to a terrorist strike. Even if Policy A were priced at $10, I'd still regard it as overpriced!

This reminded me of the law trial in the memorable Otto Preminger classic - Angel Face starring Robert Mitchum and Jean Simmons (who passed away last week) that I watched the other day on DVD. A 20 year old girl kills her step mother by tampering with the gear and break system of the latter's convertible. She succeeds quite spectacularly in her attempt as her victim hurtles to her death along with the vehicle which falls off a cliff.

In the trial that ensues, the ruins of the vehicle are examined. An automobile engineer concludes that the gear shaft was manipulated. The defence lawyer asks whether the gear shaft may have reached its present position due to the impact of the fall. The engineer replies that it is a one in a million event. The shrewd lawyer rejoins - why not one in a thousand? or even one in ten!

So now the case rests on the jury's assessment of probabilities. The higher the likelihood of the gear shaft reaching its present position during the fall, the better the chance of the step daughter getting acquitted. Here's a case where there is no way one can judge the likelihood of the event, no matter how sophisticated you are in your knowledge of statistics and probability. Juries tend to play safe in scenarios like these (i.e over-estimate the likelihood of the rare event) and let the criminal go scot-free.

PS: Jean Simmons does get acquitted in the movie, somewhat predictably.
I've seldom seen a mainstream Hollywood movie demonstrate our inability to come to terms with randomness. Angel Face is an honourable exception.

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