Where's my twin ?

Where's My Virtual Twin ?

Consider a user A. Say I know everything about A - i.e. I know all the situations (s) that A has faced and what choices A made in each situation (links clicked, job applied, items bought, etc. ). This past behaviour of A can be called - P(a,s). Say I have similar information about a large set (N) of users. The set of users is Un and their past behaviour is modeled as a matrix P(n,s).

Now, can I use this past information P to predict A's behaviour in a new situation x ?

This requires a function f, such that F(a,x) = f ( P )

The existence of such a function, assumes :
(1) that user's behaviours are correlated - see Arrow's Impossibity Theorem and Social Choice theory.
(2) that a LOT about user A is known - i.e. the user A's row in matrix P is well populate and that a lot is known about situation s. Many other users have faced situation s, so the column s in P is also well populated.
(3) that f is practically computable.

How big does N need to be and how densely does the P matrix needs to be populated to make good predictions ?

The online portals, search-engines and purchase sites already know a lot about P. How much P does they really keep, analyse and use ? Does any one of them already have a useful subsection of P ? If not, can they share the parts of P that they each know without revealing identities ? Is P valuable enough to drive consolidation in the industry ?

If there is such a computable function f (and there may well not be), it leads to interesting possibilities.

1. You have a virtual twin. Your twin can predict what choices you will make in each situation. It might even tell you how you are going to feel if you click on a particular news story.

2. You can model macro-behaviours - If you can model everybody's behaviour and their reactions to each other's behaviour, then you can predict what the best marketing strategy should be for a given situation or what the reaction of the population will be to a given story.