A Mental Model to estimate the size of the unknown from the known

Accelerated Learning Mental Models
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I was reading a book called “100 Essential Things you Didnt know you Didnt know”.

A few pages into it I read a one page chapter on a very simple way to estimate things that are yet not found which i believe classifies as a mental model - and a very practical one at that.

This mental model was used to estimate the size of unknown species and also to estimate the size of Shakespeare’s vocabulary. On a business front it seems to be used very often in oil exploration as the following line from the book suggests.

“…this type of argument can be used in many situations. Suppose different oil prospectors search independently for oil pockets: how many of them lie unfound…”

It has direct implications in investing and helping us avoid companies that should be avoided - changing this sentence a litte bit

“…this type of argument can be used in many situations. Suppose different investors search independently for discrepancies in the financial satements: how many of them lie unfound…”

The model goes like this

In the authors Phd thesis defence ( this was in the days before word processors) - two examiners went through his dissertation independently and both of them found typos.

Examiner A found 32 typos and Examiner B found 23 typos. 16 typos were common to both examiners i.e both of them had found the same ones. Hence, A found 16 unique typos and B found 7 unique typos. & 16 were common

The simple question was how many more typos remain unfound?

and and the formula for estimating it is equally simple.

(A-C)(B-C)/C

Where A = Typos found by examiner A
B = Typos found by examiner B &
C = Common typos found by both examiners.

Evaluating this gives us an estimate of the unknown of 7

(A-C)(B-C)/C

(32-16)(23-16)/16

(16)(7)/16

112/17 =7

Pretty cool huh!

This essentially means that if two bearish expert investors - A & B ( or more ) are evaluating the same company (XY Ltd) independently and lets say A finds 8 valid concerns and B finds 5 valid concerns and only 1 concern is common. Then the potential unfound problems with XY Ltd is a whopping 28

(8-1)(5-1)/1 = 28

Now lets suppose two bullish expert investors - C & D are evaulating XY Ltd and C finds 51 awesome things & D finds 60 awesome things with XY Ltd ( you see C & D are bullish and everyone loves their find! - me included ) but 50 awesome things are common to both C & D. Then the potential unfound awesomeness of XYltd is just 0.2

(51-50)(60-50)/50 = 0.2

If A,B,C & D get together then there is a strong case for NOT INVESTING in XY Ltd because the potential unfound risks (28) far exceed the potential unfound awesomness ( 0.2). There is likely to be a problem with XY Ltd going forward.

I think this is a superb mental model and gives rational decision making a new dimension.

Happy Investing!

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The following further reads may be helpful on this topic:

i) Prof. Richard Zeckhauser’s article ‘Investing in the Unknown and Unknowable’ and

ii) Prof Sanjay Bakshi’s lecture notes of a talk he had delivered on this topic.

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I tried reading Prof Z article in the past but its too cerebral for me! I like to read simple stuff

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numbers can be tweaked for bullish investors for different conclusion
C finds 25 awesome things & D finds 35 awesome things, only 1 thing in common
then awesomesome index as per formula goes to =24 x 34 /1 = 816
so i believe this model is not complete.

However, an article from Prof. Sanjay Bakshi on probability of events is more complete
e.g. pharma companies have lot of moving parts and each step has to b successful for final product to be successful - multiplying probability of success of every single step results in final probability of success to b v.low
will have to dig to find that article - as usual Prof. Bakshi is a master !!

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The more unique things people find out about something the more of them there are likely to be. That’s the central message of this model

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This assumes that the capabilities of the two individuals who are figuring these out - viz., examiners have :slight_smile:

  • similar capabilities
  • are looking at it at the same slice of time
  • and have a similar perspective
  • use similar mental models and accord similar weightages to arrive at their decision tree calculation.
  • have access to and gleaned the same information
  • are trying to assess the same things

It seldom is the case, especially in investing. That’s a caveat to be remembered - if the above is true, efficient market hypothesis too should be true. Its something to remember nevertheless.

Thanks for sharing !

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Yup the model makes many assumptions as you correctly pointed out. But I like the central point , if a bunch of investors independently dig out unique things about a business (good or bad) then the chances are high that there is more of it where it came from.

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