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14 May 2018

Modelling Behavioral Economics with Entropic Brain

The Hypothesis

Ever since I first read about Shannon’s Entropy twenty years ago, I believed that in all likelihood human brain is Entropic-Bayesian-Electrochemical device. Now, in last four years neurobiological evidence is emerging for initial confirmation of Entropic brain hypothesis1.

Human brain, like any other living thing, is a play on the entropy-energy cost curve. The objective of life is to efficiently create and consume energy to manage the entropy of its surrounding system. As a natural extension of the same, it is now proposed that human learning is entropy efficient2. In this initial document, I will propose that human memory is entropy cost efficient, and entropy cost efficiency leads to bias in human memory leading to biased human behavior.

The current state of behavioral economics is akin to the medieval alchemy – a collection of diffused actionable observations without any unifying structure.

In this document, I attempt, for the first time to create a path towards a unifying structure for behavioral economics using Shannon’s Entropy as a modelling technique.

The Toy Example

For this I start with a toy example of human bias. In India, wherever people gather for social events, discussion eventually veers towards how the Bollywood songs of yesteryears of exemplary quality and how the new songs cannot hold light in front of old songs.

Now, let us assume, in this example, that every year songs produced are of uniform quantity as compared to any other year. We assume that every year 10,000 songs are produced following a Pareto distribution across quality curve. For simplicity we assume that songs are classified into 10 bins of quality with Bin#1 containing the least quality songs and Bin#10 containing masterpieces.

Now, we assume that entropy cost curve function of how long any human being will remember a song is driven by a function which closely resembles Shannon’s entropy function.


Years is how many years one will remember any song in a particular quality bin
P is probability of that particular quality bin.
Int is integer function.

The above assumptions lead to a Pareto function and Entropy cost function as defined in the Table 1 below

Table 1: How long a song will be remembered

Based on Table 1, if we consider the songs in the last 15 years as the total universe, we arrive the memorable songs cohort distribution as given in Table 2.

Table 2: Memorable Songs Cohorts

The numbers which are in light font indicate the number of songs produced in that year which humans have forgotten at the end of Year 15 as a result of entropy cost function. Conversely, the numbers which are in dark font indicate the number of songs produced in that year, which humans still remember at the end of Year 15.

Out of total of 150,000 songs produced in the 15 year period, humans are remembering only 1421 songs, henceforth called memorable songs. Table 3 below shows the analysis of memorable songs into old songs and new songs. Songs produced before year 5 are defined as old songs. Other songs are defined as new songs.

Table 3: Bayesian Analysis of Memorable Songs

While the probability of any song being produced will appear in Bin#10 is 0.01% in any given year, the probability that an old memorable song will be in Bin#10 is 25.0%. This massive transformation of perceived probability has happened due to the operation of entropic cost function.

The Conclusion

The toy example shows that irrational human behavior can be potentially modelled using Entropy Cost Function.

The field of economics has suffered enormous ignominy and failure due to assumption of rational person hypothesis.

While behavioral economics attempts to remedy the situation, there is currently no unifying mechanism which can bind together all the irrational behaviors gleaned from myriad surveys, hence potentially limiting their usefulness.

Using entropic brain hypothesis for learning and memory can potentially remedy the situation and show future pathways for development of economics exactly the same way as understanding of atomic bonds lead to unification of common understanding of chemistry across along elements.

Significantly more research is required to be conducted in this path, and the author is looking to collaborate with like-minded persons to further research this area for completely proving the hypothesis.

Further, post the proof, there are multiple implications of this hypothesis for further study, for example, direct AI linkage to human brain will change the entropy cost function of the brain and can lead to reduction in irrational behavior; similarly, the hypothesis will help model behavior of groups of humans interacting with each other, hence when this hypothesis is married with phase transition structure of dynamical systems, it may lead to better prediction and management of economic cycles.



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