A model illustrating the exponential relationship between honesty (or trust) and growth in a society

A few words on the model

The visualization illustrates a model revealing an exponential relationship of value creation versus trust/honesty.

It works in the following way: a population consisting of a number of individuals undergo a number of transactions (iterations). Each individual is described by its capital, honesty and its trust to each of the other individuals. Each transaction occurs between two individuals A and B in the following way:

Displaying the result in a graph shows that growth depends exponentially on the honesty and trust of a population.

It quite clearly illustrates that for a group of individuals, adopting an honest and trustful culture is a winning strategy.

Try and move the iterations slider, say double the number of iterations. The slope of the point cloud doubles as well. That would indicate that the growth is also an exponential function of the number of transactions. In consequence it would be a winning strategy to process as many transactions as possible (per time unit), i.e. adopting an open and engaging attitude.

Check out the code here

Trust diagrams

The graphs below show the strengths of the trust relations in the last simulation in four different categories - low, low-medium, medium-high and high levels of honesty.

The stories of each individual

The graphs below show the evolution of each of the individuals in the population. Note: in order to study a graph more closely, set the simulation speed to 0.
The concept can be expressed as a stochastic differential equation

$$ \left\{ \begin{aligned} \frac{dv_i}{dt} &= \sum_j (1+\frac{1}{2}\gamma)v_iT_{ij}x_{ij} + \frac{1}{2}\gamma v_jT_{ji}x_{ji} + (1+\gamma)v_jT_{ji}(1-x_{ji}) \\ \frac{dT_{ij}}{dt} &= T_{ij}\left(\frac{1+\alpha}{1+\alpha T_{ij}}\right)^{2(x_{ij}-\frac{1}{2})} + T_{ji}\left(\frac{1+\alpha}{1+\alpha T_{ji}}\right)^{2(x_{ji}-\frac{1}{2})}\\ x_{ij} &= \left\{ \begin{aligned} 0,& \text{ with probability } 1-h_j\\ 1,& \text{ with probability } h_j \end{aligned} \right. \end{aligned} \right. $$ where \(x_{ij} \in \{0,1\}\) is a random variable expressing whether a transaction at time \(t\) from individual \(i\) to individual \(j\) is successful. \(v_i\) is the value (capital) of individual \(i\), \(h_i \in [0,1]\) its honesty, \(T_{ij} \in ]0,1[\) is the trust from individual \(i\) to individual \(j\) (it is kept symmetrical, i.e. \(T_{ij} = T_{ji}\) ). The constant \(\gamma\) (gain) expresses the value created in each transaction relative to the investment. The constant \(\alpha\) expresses how much the trust increases or decreases during a successful, respectively unsuccessful transaction.

Key take-aways: