Entropy and Intelligent System Control

A fascinating paper, by Alexander Wissner-Gross, suggests that increasing the entropy of a system, under your control, is an optimal path. This path will preserve most possible future states (and paths) of the system. So that, in some future time, when we need to again control the system, we will have more options (or system paths) from which to choose. Further, that when closed systems exhibit higher entropy this is a sign of intelligence. Or that Artificial Intelligence follows when a ‘controller’, following this principle, acts on a system.

Walking upright is an example. A body laying on the ground has lower entropy than the body standing on two legs. Likewise, his model of a cart attached to a stick with a ball on the end has the lowest state of entropy is when the ball hangs directly below the cart. A higher entropy state is when the ball is balanced on top of the cart (a very unstable system state). So now we want to ‘control’ the ball and move it somewhere else. Which state is best for this? The state with highest entropy!

His theory seems to be that it is easier for the system to move to any new state, if more paths are emerging from the current state. So if one seeks to make an intelligent automated controller then it should take actions that increase the system’s entropy along with actions that produce utility. The energy needed to move the system to a higher entropy state must be considered. Getting up and standing expends energy. Yet, while I stand, I can move to another location easier than if I am laying down.

A real world application of this principle might be the lead generation (lead gen) business. Lead gen companies sell inquiries from consumers to producing companies. An automated lead allocation controller distributes leads to clients. Imagine the home mortgage business where consumers want to refinance their home and lenders who want leads for their sales staff. The lead gen company produces marketing activities (costs) that drive consumers to a web site where the consumer can complete a qualification form. The information in the completed form is a lead. The lead gen company sells these leads to lenders for a fee. I call this collection of lead orders a Book of Orders.

Each individual Order in the Book has varying degrees of freedom (varying entropy). Some clients will accept leads from consumers who have excellent, good and poor credit ratings. Lower entropy Orders may only accept consumers with excellent credit ratings. Orders extensive qualifications are low entropy, low degrees of freedom while those with  few qualifications are higher entropy, high degrees of freedom. If two individual Orders overlap in the qualification space, then entropy increases. Much to the delight of the lead gen company, this overlap allows some inquiries to be sold to more than one client increasing revenue.

Profit is the ultimate measure of utility (success) for lead gen companies. For a given time period, the lead gen company that makes the most Profit is deemed most Intelligent. So it is natural for lead allocation controllers to focus on producing the maximum profit from each lead produced. From my limited experience, this greedy allocation policy can cause havoc to a lead gen business. One problem is that high revenue Orders are filled first, and often can overwhelm the client with quick spurts of leads and the beginning of the period and sometimes Orders are filled leaving no leads for the client at the end of the time period. As the Book of Orders is depleted over the time period, matches of leads with Orders becomes less probable. This means less revenue to cover media costs of driving consumers to the form. End of period dynamics are very difficult to control.

A lead allocation algorithm that always sought to leave the system in its highest state of entropy would NEVER choose to match an inquiry multiple times since each match adds to the loss of entropy in the Book of Orders. This would be a non-starter in the lead gen business. Multiple matches mean multiple sales and always mean higher revenue.

A simple model of the lead gen business and entropy H.

A simple greedy matching algorithm will simply look for those matches that produce greatest revenue. Matches occur when a lead satisfies an order.

I will need to think further on this. Can entropy play a role in an optimized lead allocation algorithm? Seems like it is possible, yet also possibly beyond my grasp.

Maybe the answer lies in the Cost of entropy and revenue per entropy expended. Surely these efficiencies matter.