22 May 2022

Modeling democratic backsliding into Authoritarianism

Posted by jofr

One of the most pressing political issue of our time is the rise of authoritarian populism and democratic backsliding in democratic societies (Norris & Inglehart, 2019). Authoritarian rulers, strongmen and self-proclaimed saviors destroy democracies (Ben-Ghiat, 2020) while populism is on the rise (Müller, 2016). Sarah Kendzior argued it can also happened in a democratic country like the USA (Kendzior, 2020). This is concerning because historically democracies have a tendency not to go to war with one another. More authoritarian systems means war becomes more likely.

On the other hand we see attempts in Eastern Europe of the people to overthrow their authoritarian goverments who fake elections and enrich themselves, especially in Ukraine and Belarus (Wilson, 2021). A political system can apparently develop in both directions: from democratic to authoritarian, as we witness in democratic backsliding, or from authoritarian to democratic. David Waldner and Ellen Lust (2018) argue that “despite a rich and diverse literature, we lack readily available theories to explain backsliding”.

So how do democracies backslide into authoritarian regimes? Can we model it? Robinson and Acemoglu argue in their book “Economic Origins of Dictatorship and Democracy” (2012) that different social groups prefer different political institutions because of the way they allocate political power and obtain resources. This aspect alone results in interesting dynamics:

In an (aspiring) autocracy demagogues, corrupt oligarchs and wannabe autocrats who care only about their clan, tribe or family and who are involved in shady or corrupt business deals have clearly an incentive to weaken political institutions, to restrict freedom of speech and to manipulate elections to remain in power, because they have to fear independent courts, investigative journalism and free elections. If they stop doing it, they risk changes that might lead to an early end of their regime. Once an autocracy has been firmly established, the autocrat can no longer voted out of office. Elections can not be lost for the incumbent anymore. People living in it have therefore a strong incentive to avoid cricizing the autocratic ruler and his family (or in totalitarian systems his party) if they do not want to be imprisoned or killed.

Democrats in a democracy have an incentive to strengthen institutions to remain in power because independent courts, freedom of speech and free elections enable them to obtain power in democratic elections in the first place. Stronger political institutions in turn lead to less power for those who are not democrats. Elections create an incentive for politicians to act in favor of the public if they want to be reelected. People in a democracy have as democratic citizens an incentive to raise their voice to criticize the government. Criminals and conmen have an incentive to remain silent to avoid persecution.

Therefore autocracy and democracy are like two fix points. These fix points are the stable states to which the system returns to after any pertubation. If a country is democratic, i.e. conducts fair elections, protects basic freedoms and holds elected leaders accountable, then it will remain democratic, even if it is disturbed slightly by unrests and protests. If a country is authoritarian, i.e. has fradulent or no elections, ignores basic freedoms and does not hold elected leaders accountable, then it will remain authoritarian, even if there are unrests. If we use a kind of “democracy score” from 0 to 1 to measure fair elections, public checks and accountability (similar to Hyde, 2020), the system has two fix points at 0 and 1.

The Model

In evolutionary game theory which has been known for more than 40 years (John Maynard Smith, 1982) two fix points can be found in the stag-hunt game or the coordination game, and we can try to use the well-known replicator equations for these games to model the transition between an autocracy and a democracy. Normally the system returns to a stable democracy, but if the system is pertubed and a certain tipping point is crossed, then the system moves inevitably towards an autocracy (and vice versa). For a symmetric coordination game or the stag hunt game the mixed Nash equilibrium is in the middle. Both have similar dynamics – two fixed points, and one instable equilibrium between. As Brian Skyrms (2012) as argued, these kind of games can be applied to model cooperation and the evolution of social structure.

If the reward for not deviating from the majority increases dramatically (or alternatively the punishment for a strategy that deviates from the majority), then the equilibrium shifts accordingly. The idea is that we can model this democratic erosion by shifting the instable fixpoint in a coordination game model, which represents the equilibrium between those who cooperate to support autocracy and those who support democracy.

Backsliding as Transitions between Fix Points

Bermeo (2016) argues that democratic backsliding happens in different ways – coups d’état, election-day vote fraud, and in recent years in slightly more sophisticated forms suchs as promissory coups, executive aggrandizement, and strategic manipulation of elections. There are many types of election manupulation and election fraud in order to rig elections.

Although coups take place by definition suddenly and violenty, and can certainly be seen as the climax of democratic backsliding, democratic institutions like independent courts, and critical media can prevent them. Democratic erosion is necessary for coups to be successful because it eliminates these safeguards. Courts in authoritarian systems are special (Ginsburg & Moustafa, 2008).

A process of democratic erosion can begin slowly and can take a long time. Democracies erode and finally disappear step by step by

  • manipulation of fair elections (=> no accountability)
  • manipulation of the judiciary (=> no accountability)
  • manipulation of critical media (=> no public checks)

Therefore Levitsky & Ziblatt (2018) propose a three stage model of the democratic backsliding: attacking referees (esp. the judicial system), targeting opponents (political opponents, critical media outlets), and changing the rules of the game (changing constitutions, legislative bodies and electoral systems to consolidate power).

But if we see the group of people which has a special role like police officers, judges, opponents, and journalists and their extended families and friends as part of the population, we can model such a transition simply by counting the number of people who cooperate with the aspiring autocrat. The number of people who cooperate can be described by the replicator equation of the coordination game.

If a major part of the population supports democracy and it is well established and well protected by stable institutions like independent parliaments and courts, then the systems returns after an pertubation towards autocracy to a stable state (for instance the United States Capitol attack on Jan 6 2021 by Trump supporters where the institutions remained strong enough and the courts rejected attempts to manipulate the elections). If the magnitude of the unrest is high enough and the system is in a general crises, then it is possible to cross a tipping point towards an authoritarian regime.

In this model the tipping point which corresponds to the nash equilibrium represents the fraction of people which support autocracy or democracy. If a majority of people (in the model 67%) in an autocracy cooperate, i.e. by avoiding criticism of the autocratic ruler, it will remain one even for large pertubations which represent unrests. If such a system is disturbed by anti-government protests, then the system returns after a short pertubation to a stable state (for example the Arabic Spring uprisings). This makes sense because once an authoritarian regime is firmly establised, a major part of the population has an incentive to support the autocracy by silent agreement if the autocracy persecutes dissidents with the full power of the state.

If a only a minority of people in an autocracy cooperate (in the model 33%), while even many police officers, politicians, judges, and journalists are against it, then already small pertubations can lead to a regime change if the conditions are right.

If a majority of people (in the model 67%) in an democracy cooperate, i.e. by supporting the political institutions and fighting for fair elections, it will remain one even for large pertubations. If such a system is disturbed by riots or right-wing movements, then the system returns after a short pertubation to a stable state (for example the unsuccessful Capital Riot Jan 6 in the US). This makes sense because once an democratic regime is firmly establised, a major part of the population has an incentive to support the democracy and to obey the law since the regime persecutes criminals with the full power of the state.

The situation looks different if a democracy is severely weakened, for example by a heavy economic crisis. If only a minority of people in an democracy still cooperate (in the model 33%), while even many police officers, politicians, judges, and journalists are against it, then already small pertubations can lead to a rapid regime change if the conditions are right.

Since the model is symmetric, the same argument can be applied to the opposite situation where the system moves from an autocracy to a democracy.


Thanks to Glen Ropella for helpful comments how to improve the simulations & notebooks




  • John Maynard Smith, Evolution and the theory of games, Cambridge University Press, 1982
  • Josef Hofbauer and Karl Sigmund, Evolutionary games and population dynamics, Cambridge University Press, 1998
  • Robert Paxton, The Anatomy of Fascism, Alfred A. Knopf, 2004
  • Martin A. Nowak, Evolutionary Dynamics: Exploring the Equations of Life, Harvard University Press, 2006
  • Tom Ginsburg and Tamir Moustafa, Rule by Law: The Politics of Courts in Authoritarian Regimes, Cambridge University Press, 2008
  • William H. Sandholm, Population Games and Evolutionary Dynamics, MIT Press, 2010
  • Daron Acemoglu and James A. Robinson, Economic Origins of Dictatorship and Democracy, Cambridge University Press, 2012
  • Brian Skyrms, The Stag Hunt and the Evolution of Social Structure, Cambridge University Press, 2012
  • Jan-Werner Müller, What is populism?, University of Pennsylvania Press, 2016
  • Steven Levitsky and Daniel Ziblatt, How Democracies Die, Penguin Random House, 2018
  • Pippa Norris and Ronald Inglehart, Cultural Backlash: Trump, Brexit, and Authoritarian Populism, Cambridge University Press, 2019
  • Ruth Ben-Ghiat, Strongmen: Mussolini to the Present, W. W. Norton & Company, 2020
  • Sarah Kendzior, Hiding in Plain Sight: The Invention of Donald Trump and the Erosion of America, Flariron Books, 2020
  • Anne Applebaum, Twilight of Democracy: The Seductive Lure of Authoritarianism, Doubleday, 2020
  • Andrew Wilson, Belarus: The Last European Dictatorship, Yale University Press, 2021

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