  Political regimes have been changing throughout human history. After the
apparent triumph of liberal democracies at the end of the twentieth century,
Francis Fukuyama and others have been arguing that humankind is approaching an
`end of history' (EoH) in the form of a universality of liberal democracies.
This view has been challenged by recent developments that seem to indicate the
rise of defective democracies across the globe. There has been no attempt to
quantify the expected EoH with a statistical approach. In this study, we model
the transition between political regimes as a Markov process and -- using a
Bayesian inference approach -- we estimate the transition probabilities between
political regimes from time-series data describing the evolution of political
regimes from 1800--2018. We then compute the steady state for this Markov
process which represents a mathematical abstraction of the EoH and predicts
that approximately 46 % of countries will be full democracies. Furthermore, we
find that, under our model, the fraction of autocracies in the world is
expected to increase for the next half-century before it declines. Using
random-walk theory, we then estimate survival curves of different types of
regimes and estimate characteristic lifetimes of democracies and autocracies of
244 years and 69 years, respectively. Quantifying the expected EoH allows us to
challenge common beliefs about the nature of political equilibria.
Specifically, we find no statistical evidence that the EoH constitutes a fixed,
complete omnipresence of democratic regimes.
