Sunday, July 11, 2010

Paul and Randomness

I have been a great devotee of Paul the Octopus, and cannot wait to invest in the company that buys him out and starts a predict-your-future gig. He's had 8 consecutively correct predictions, and I was sold by the time the 3rd one rolled in. I truly feel that he's got something going.

This reminds me of an anecdote Taleb relates in Fooled by Randomness. (paraphrasing) A smart scamster takes 10,000 envelopes on Dec 15th, and fills 5000 of them with this message: "Greetings! We have a fantastic new stock market predicting technique, and we think you'd be interested. But you needn't believe us. We'll send you one prediction a month, and you can call us when you get interested. We claim that by Jan 31, the stock market would have gone UP from its Jan 1 level". The other 5000 have the exact same message, except that it says the market would go DOWN by Jan 31. The envelopes are then sent out all across the country, with some simple measures to minimize chances of some of the 10000 people knowing each other.

By Jan 31, 5000 people would have received a correct 'prediction'. Our chap then writes a more confident message, and tells 2500 of them that the market would be "EVEN higher by Feb 28!". To the other 2500, he writes "BUT THIS TIME, the market's going to go down!". Come Mar 1, 2500 people would have received two consecutive correct predictions with an increasingly confident pitch.

It wouldn't take people more than 5-6 months to start believing something is seriously on. The crucial part in this, as well as with Paul, is that these planned events are intertwined with everyday life, and not perceived as clearly laid-out thought experiments. One prediction would have made someone want to "try it out", and when it worked, it would have resulted in a whole chain of events in his life. A little more confidence the next time, and even higher rewards. 

As Jean Cocteau once said, "We must believe in luck. For how else can we explain the success of those we don't like?"

:-)

9 comments:

Dileep said...

Mamu, I finally finished reading Anathem (a few days back). That fellow is using the Multiverse interpretation of Quantum Wavefunction Collapse. So in some Universe, everyone can predict right all the time!!!

shankar (shankin) said...

i am curious to see if he preferentially chooses left or the right box (it might be left-left-right tentacled). If it so happens that he choose left one most, and it happens to be Germany most of the times and Germany wins most of the matches ....then yeah he will have a high success rate. But among the matches Germany lost, it has got 2 right and 1 wrong. So it not really all that impressive.

BoFi said...

Coincidentally, just after I read your post, someone asked me a puzzle, which I managed to get because I had just read your post :D Thought I should post it here...

There are a 100 prisoners (aren't there always!). Now the authorities tell them that if they can solve a puzzle, they will be freed. The puzzle is as follows: Each prisoner will be given a cap of one of two colours (say black or white). They are then put in a room. Each one can see all but his own cap. After a while each one must write down what he thinks his cap's colour is. There is no talking/signalling of any kind (although they can plan out a strategy before the game starts), and no one knows what the others have guessed. If 50 or more people get it right, then they are freed.

Can you ensure that they are always liberated.

KVM said...

The BoFi himself! An unprecedented honor, sir!

This puzzle seems to be rapidly spreading... a friend told me a version he saw on Wilmott that poked harsher fun at the poor prisoners: instead of 2 colors, that hats could be any of 100 possible colors. In return for the increased complexity, just one prisoner needed to get it right.

His solution was that if each color was assigned a number, the sum of all colors mod 100 could only have 100 possible values, and the ith prisoner wrote it assuming the remainder was i. The same thing would work here, too: black 0, white 1, half would guess the sum was odd and half even. But I don't see any connect between Taleb's trick and this. Is there another way you solved this? Pliss to explain.

KVM said...

You dare think Paul's supreme powers are a mere tentacledness-thing? The insolence! Unspeakable blasphemy!

KVM said...

I lost you at 'finished reading Anathem'. I cannot not imagine any human being managing to finish that... that... ugh.

Out with it. What is your purpose on Earth, visitor?

Dileep said...

Well, since we don't know if the distribution of Black and White is uniform, every inmate needs to assume his colour is the same as the one the majority of all the other 99 inmates are wearing. This will only fail if the distribution is 50-50, and will work for everything else.

KVM said...

Sweet - I think that's a nice, natural way to arrive at it without generalizing. The 50-50 case can be handled like this: If anyone sees 50 caps of color A and 49 of the other, if his prisoner number is odd, he writes A, else B. It is necessary to include ordering for the prisoners here, but that's one of the first things one thinks of.

BoFi said...

No...same solution. Decide your parity and guess accordingly. Taleb's trick is also basically just an application of this pigeonhole principle argument. If you have n possible answers and m=kn guesses, then you can always ensure that k guesses are correct...