Before revision:  We give novel formulas based on Markov Chain analysis to compute the distribution of opinions at any time and speed of convergence to stationary equilibrium  .
After revision:  We give novel formulas based on Markov Chain analysis to compute the distribution of opinions at any time and speed of convergence to stationary equilibrium . As an example of application we discuss a strategy to mitigate the polarisation of opinions in the presence of a backfire effect. Theoretical results are supported by numerical experiments on synthetic data .