Revising the Human Development Sequence Theory Using an Agent-Based Approach and Data

Agent-based models and computer simulations are promising tools for studying emergent macrophenomena. We apply an agent-based approach in combination with data analysis to investigate the human development sequence (HDS) theory developed by Ronald Inglehart and Christian Welzel. Although the HDS theory is supportedby correlational evidence, the sequenceof economicgrowth, democracyandemancipation stated by the theory is not entirely consistent with data. We use an agent-based model to make quantitative predictions about several di erent micro-level mechanisms. Comparison to data allows us to identify important inconsistencies between HDS and the data, and propose revised agent-basedmodels that modify the theory. Our results indicate the importance of elites and economic inequality in explaining the data available on democratisation.


Introduction
. The human development sequence (HDS) theory, proposed by Ronald Inglehart and Christian Welzel (Inglehart & Welzel ), is one of the most prominent modernisation theories (Wucherpfennig & Deutsch ), stating that economic development, changes in emancipative cultural values and democratisation are intimately linked. These three processes are hypothesised to follow a common causal direction, with economic resources providing the means for emancipation, which in turn provides motivation for more democratic institutions. Over time countries undergo a transition as their citizens' values change from reflecting the need to survive to the need to live a self-determined life. Ultimately, the way a country is governed changes to reflect these emancipative values (Inglehart & Welzel ; Welzel ). .
The HDS theory has not remained unchallenged (Duch & Taylor ; Hadenius & Teorell ; Teorell & Hadenius ; Teorell ). Recent empirical analysis show that the assumed sequence of economic development, emancipation and democratisation is not entirely supported by the data. Spaiser et al. ( ) show that crosscountry time-series data suggests that the implementation of human rights and democratisation in fact precedes the emancipation of the wider population. In line with the HDS theory, data analyses confirm that prior to democratisation and emancipation countries need to progress economically. However, data seems to suggest that the emancipation of wider segments of the population requires not only existential security in terms of basic economic well-being but includes also security granted by human rights (ibid.). In this paper we use an agent-based approach in combination with data analysis to further investigate the HDS theory. We contrast the theory against alternative democratisation theories and suggest several revisions of the HDS theory that would make the theory consistent with the data and with some alternative democratisation theories.

Critique of the Human Development Sequence Theory
. The HDS theory is a highly influential modernisation theory that assumes that people's cultural values and beliefs change across the world as nations worldwide become more a luent. With economic development that frees people from extreme poverty and existential struggle, people become less focused on security and conservative, collectivist traditions. They develop more individualistic and liberal views (Inglehart & Welzel ). The theory assumes an universal human desire for self-determination. Emancipation is the process of exemption from external constraints and emancipative values thus prioritise freedom of choice and equality of opportunities. However, emancipative values cannot fully unfold and guide people's actions as long as they are hampered by existential constraints. Only, with improving living conditions emancipative values can gain utility and spread in a society that has reached a su iciently high economic development level (Welzel ).
. These fundamental changes in people's values lead to political changes as the increasingly emancipated people demand to have a say in political decision making (Inglehart & Welzel ). Emancipative values are the psychological basis and the major inspiration for democratisation movements and according to Welzel ( ), rulers cannot withstand the mass political action of capable and highly motivated people. Drawing on World Value Survey data, Inglehart and Welzel (Inglehart & Welzel ; Welzel & Inglehart ) demonstrated the sequence pattern empirically, controlling for prior measures of democracy and thereby arguing that cultural change towards more self-expressive values is a cause and not a consequence of democracy. And Abdollahian et al. ( ) presented recently an agent-based model that supports the HDS theory. The HDS theory and its empirical evidence has however also been repeatedly challenged (Hadenius & Teorell ; Teorell & Hadenius ; Teorell ; Spaiser et al. ). Spaiser et al. ( ) have for instance argued that lawlessness and rights violations do constitute existential constraints as well as material living conditions and therefore some level of human-rights democratic rule must be implemented before emancipative values can truly thrive within the majority of a population. .
It has been argued that elites are decisive for democratisation to happen and for democracies to stabilise (O'Donnell et al. ; Casper & Taylor ; Higley & Burton ). Democratisation is most likely when there is a regime opposition, o en consisting of a highly educated middle class and a fraction of regime elites that build a liberal camp and that split from the status quo regime elite. This liberal camp joins forces with the regime opposition and conjointly they may bring about democratic change (O'Donnell et al. ; Casper & Taylor ; Higley & Burton ). Under this scenario the proportion of emancipated individuals to induce a democratic transition is rather low and democratisation could precede emancipation of the general population. .
Inequality may also play a role in democratisation, because extreme inequality may prevent the majority from getting hold of su icient resources that would allow their emancipation. The relation between democratisation and inequality has been studied for some time with di erent conclusions (Bollen & Jackman ; Muller ; Barro ; Houle ). Acemoglu & Robinson ( ) for instance state that the relation between democratisation and inequality should be an inverted U-shape. Transitions towards democracy are most likely at moderate levels of inequality, while very low and very high inequality make democratic changes unlikely. Boix ( ) on the other hand predicts a straightforward negative relation between inequality and democratisation, holding a country's level of wealth constant. Contrary to this, Ansell & Samuels ( ) predict that democratisation is most likely "when newly wealthy economic groups accumulate an increasing share of national income, leaving the poor far behind", as they will be interested in setting up (democratic) rules that protect them "against expropriation of their income and assets by the autocratic governing elite" (Ansell & Samuels , pp. -). .
The HDS theory but also theories on elite-driven democratisation and on inequality and democratisation focus on a set of endogenous or internal factors (socio-economic, cultural) that contribute to a country's democratisation. Others have been suggesting rather exogenous factors to explain in particular the di usion of democratisation, thus the empirically observed geographic and temporal clustering of democracies (Gleditsch & Ward ; Doorenspleet ). Elkink ( ) for instance has used an agent-based simulation to show that individual attitudes towards democracy can explain democratic di usion. He argues that not solely socio-economic development results in attitudinal changes that precede democratisation, but public opinion dynamics in neighbouring areas are decisive to understand the changes in cultural values and attitudes in a country prior to democratisation. In fact, Wejnert ( ) suggests that when comparing the di erent sets of factors, endogenous and exogenous, di usion factors outperform the endogenous factors in predicting democratisation. The external factors that predict democratisation best are spatial factors such as proximity to neighbouring democratic countries and the density of neighbouring democratic countries, network factors, thus the embededdness of countries in certain international networks that may support or suppress democratisation and media communication that can provide information about democracy (ibid.).

.
It is certainly the interplay of endogenous and exogenous factors, which can be very context specific, that explains and predicts best why certain countries become democratic and others not. Given the point of departure for our analyses is the HDS theory, which builds on endogenous predictors, we will focus here on endogenous explanatory factors, which can be also more easily integrated in a revised HDS theory that we propose here as a result of our analyses. An integration with the di usion theories of democratisation goes beyond the scope of this paper but could be an interesting future step. Ultimately, democratisation processes are a (re-)negotiation of power relations within more or less favourable contexts. In the course of this (re-)negotiation institutional innovations are made, o en taking neighbouring countries as models. And the process requires time to create stable, enduring democratic structures (Lindenfors et al.

Formalising Human Development Sequence theory
. We now elaborate on the HDS theory and formulate an agent-based model. The economy is a macro-level input, which influences whether agents have the means to become emancipated, and then through micro-level interactions the agents produce macro-level democracy. The stages of our model are illustrated in Figure . We now explain each of the steps of the model in turn.

Economic growth .
We consider an economic situation in which there are limited existential resources. Resources are increasingly available on the micro level if a society's economy is developing and prospering, so that the expected number of available resources is a function of economy's development. We assume that existential resources are growing at each time step twhich we assume to represent a year-at a positive constant rate, such that In a growing economy the growth constant g is positive and the economy grows exponentially. This assumption is standard to economic development models (Basu ) and consistent with observations across countries (Durlauf et al. ). Over the last years, most of the world's nations have experienced a sustained period of economic growth, measured either in GDP (Gross Domestic Product), GNI (Gross National Income) or HDI (Human Development Index) (WorldBank ; UNDP ). .
In terms of Coleman's boat diagram, the distribution of resources is the step from A to B (see Figure ). At each time step t we distribute R t action resource units uniformly at random amongst the whole population N . The assumption that economic resources are distributed uniformly at random between all N individuals is not based on empirical observation. Within societies, resources are typically skewed towards certain individuals. We return to this assumption in subsection Revising the HDS theory: economic inequality. For now, we note . The contribution of each pair depends on the level of democracy, so that the value on the le of the | separator is taken with probability 1 − D t and the right value is taken with probability D t .
that by excluding social inequality from the model at this point, we isolate the e ect of emancipation prescribed by HDS theory on the transition to democracy. For large N the number of resources each individual received can be assumed Poisson distributed. Thus, the expression gives the probability that any particular agent receives k resources on time step t of the model.

The process of emancipation .
Based on individuals' resource status, and thus the resource distribution at any given time step t, we can derive the distribution of emancipated E t and unemancipated U t = N − E t individuals within the whole population N . Individuals can be assigned to one of two states, emancipated (E) or unemancipated (U), based on their resource level. The step from B to C, is then made via the following rules for emancipation and unemancipation (see Figure ): . If an unemancipated individual receives two or three resource units then he/she will become emancipated. Otherwise, he/she will remain unemancipated.
. Emancipated individuals remain emancipated, unless they receive no resource units within a time step. In this case, they become unemancipated again.
. If an unemancipated individual receives four or more resources then he/she remains unemancipated.
. The first rule reflects individuals' existential wellbeing. Following the HDS theory, when people have relatively few resources (zero or one), their preferences are focused on materialistic goals, like making a living, ensuring some form of existential security. They also tend to cling to extended family or clan structures. Community is of great value to these people since the community provides support and protection. This focus on existential security that goes along with traditional cultural values makes the unemancipated more receptive to autocratic regimes and collectivist social systems, which claim to guarantee stability, security and order (Inglehart & Welzel ; Welzel ). The first rule also reflects the prediction that once a certain relative level of resources (two or three in our model) is acquired and existential needs are satisfied then people draw their attention to other objectives in life, such as self-realisation and participation (Inglehart & Welzel ; Welzel ). A transition back to disempowerment (second rule) is possible, but only in the extreme situation where no resources are available. Once emancipated, some degree of hardship is tolerated but a complete removal of resources leads to a change in perspectives, because people again need to struggle for their and their families' survival. The third rule is not part of the original HDS theory. It is included for consistency with both theoretical and empirical observations. Empirical evidence suggests that a superfluous amount of resources on the macro-level may lead to an exceeding availability of resources on the micro-level (through spending programs and low taxation for instance), and people are less likely to develop political aspirations (Ross ; Vanderwalle ; Kessler ; Vanderwalle ; Bellin ). Theoretically this observation is explained by the "spending e ect" where governments (for instance Qatar or Saudi Arabia) use their resource revenues for generous patronage and welfare, to lower pressures for democratisation (Ross ; Brand ; Crystal ; Entelis ).
. The choice of two or three resource units is arbitrary, but since the resource unit is also arbitrary this does not a ect the results that follow. Rather, it is the relative level of resource units that is relevant. The key ingredient of these three rules is the existence of a threshold of resources needed for emancipation, and the numerical value of this threshold is unimportant. This corresponds with the assumption that existential needs have to be fully (not gradually) met before people can focus on higher-level needs. It follows from Abraham Maslow theory of a hierarchy of needs (Maslow ) that underlies HDS assumptions about emancipation (Inglehart & Welzel ; Welzel ).
Deriving equations for emancipation . We now turn to the mathematical derivation of equations, which describe the change in emancipation generated by the three rules discussed in the previous subsection. Here we go from the agent-based description to deriving mean-field di erence equations (Johansson & Sumpter ; Czárán ; Parunak et al. ). The expected number of individuals who become emancipated in a time step is determined by the proportion of unemancipated individuals receiving either two or three resources. Specifically, applying rule above and equation , the expected increase in emancipation is Similarly, according to rule , emancipated individuals become unemancipated if they receive zero resources, so that the expected decrease in a time step is For large N we can thus express the change in emancipation as The first term is, by equation , the average proportion of emancipated individuals in the previous time step who don't lose their emancipation. The second term is, by equation , the proportion of individuals who become newly emancipated. The final term is a random term resulting from variations from simulation to simulation in the number of individuals receiving two or three resource units. For large N , the variance V (E) t can be approximated by . The random variable t is normally distributed with mean and standard deviation . Taken together, equation and give a full description of the change in emancipation in the population.

From emancipation to democracy
.
We now turn to the step from C to D in the boat diagram ( Figure ). In line with Inglehart & Welzel ( ), we assume that political change, in terms of the level of democracy D t , is a function of emancipation. A continuum between and defines the level of democracy. To understand the link between emancipation and democratisation, we see democracy as a public good (Nelson ; Barr et al. ), since people need to participate in Figure : The public good contribution table for pairwise agent interaction. (a) With probability 1 − D t each emancipated agent individually contributes a and, if two emancipated agents are paired, they collectively contribute additionally b to democratisation. (b) With probability D t the unemancipated reduce democracy, individually with −c and collectively with −d.
democracy building and democracy maintaining and since democracy is a good from which individuals cannot be e ectively excluded and which does not decrease due to people's utilisation (Ostrom & Ostrom ). The process of political change is conceptualised as an interaction between the emancipated and unemancipated individuals. At each time step of the model, the individuals form pairs and interact both with each other and the current democracy level to decide their contribution to democracy (see Figure ). Specifically, for each pair, their contribution to democracy is determined by Figure (a) with probability 1 − D t and by Figure (b) with probability D t . Thus, when democracy is low, then emancipated individuals tend to create democracy (e.g. by building civil society associations, publishing critical information, protesting, etc.), and when democracy is high, then unemancipated individuals tend to hinder democracy (e.g. by strengthening the autocratic government, propaganda, repression, etc.). The conceptualisation of democracy as a public good, allows us to capture the micro-macro dynamic of democracy (arrow from C to D, see Figure and Figure ). Democracy is a public good (macro-level institutions, procedures etc.) which however requires a contributing participation (micro-level). This follows from the democracy understanding advanced by the HDS theory: democracy is not only formal democratic institutions and election procedures, it is likewise a political condition where citizens think and act democratically (Inglehart & Welzel ; Welzel ). .
The parameter a, respectively c, in Figure captures independent contributions to democracy creation, respectively democracy reduction. The parameter b, respectively d, is a collective contribution towards, respectively against, democracy. By collective we mean that two interacting agents may join forces if both are either emancipated or both are unemancipated. The b and d parameters thus reflect our hypothesis that people who have a preference for democracy and join forces (e.g. build civil society associations) are more likely to bring about political change than if they act on their own (e.g. go individually to protests), or only interact with people who do not have a preference for democracy. Equivalently, unemancipated agents actively prefer an autocratic state and when they join forces (e.g. build repression structures) they may prevent or slow down democratic transitions more e ectively.

Deriving democracy equations .
We can use the rules for interactions in pairs to derive the rate of change of democracy. The derivation is done for each pair of possible interactions, one at a time. For example, the proportion of pairs of two emancipated individuals is E 2 t . From Figure we see that they contribute 2a+b units to democracy with probability 1−D t and 0 units with probability D t . Thus the overall contribution to democracy of pairs of two emancipated individuals is

Similarly, pairs in which one individual is emancipated and the other is not, contribute on average
and pairs of two unemancipated individuals contribute .
The interaction contributions are summed up and form the basis of democracy building, which represents the third arrow in Coleman's boat diagram, C to D (see Figure and Figure ). When all contributions are independent (i.e. b = d = 0) then democracy grows according to: This democratisation model follows the HDS theory, where democratisation is essentially a damped linear function of emancipation. It is important to test this linear assumption, since it ensures that any interesting simulation results obtained arise directly from HDS. Democratic change is o en associated with dramatic and sudden increases, rather than the linear increase prescribed by the model. Our aim is that these dramatic changes should emerge from the model, rather than being incorporated directly in the equations. By assuming that the relationship between emancipation and democracy is linear, we can be certain that we have not built in these dramatic changes. .
That said, we also test the e ect of non-linear interactions, that occur when we include collective democracy building and deconstruction, i.e. b > 0 and d > 0. For these parameter values the collective action of individuals enhances the respective individual contributions. This gives the full non-linear model for democracy: This second, collective democratisation model allows for non-linear threshold e ects, where democratisation is made possible even if the majority of the population has not yet become emancipated, if an emancipated minority has su icient collective "power" (if b is su iciently big) to trigger political change.

Implementation and Parameters
.
In the previous sections we have derived stochastic di erence equations for the models that describe the change in emancipation and democracy. The complete model is encapsulated by equations , , and . We implemented the model in Matlab. The pseudocode for the simulation is given in Appendix A . and A . .

.
The model was solved numerically over time steps, with each time step representing a year, for N = 10, 000, 000 individuals. Resource units were parameterised as described in subsections Economic growth to Deriving equations for emancipation. For the parameters g, a, c, b, d di erent parameter values were used, examining di erent scenarios, albeit the standard basis model parameterises g = . and a = c = . and b=d= . .
In order to aid readability we primarily focus on these general parameter values and units in the main results, and refer the reader to Appendix A for model validation and sensitivity tests with di erent sets of parameter values and units (for instance empirically informed resource units) and di erent time scales (for instance months).

Data
. To test Human Development Sequence (HDS) theory hypotheses and agent-based model results against data, we used di erent open data sources. In particular, we used the same indicators and indices that were previously used for testing the HDS theory (Inglehart & Welzel ; Welzel ). To measure resources we used log GDP (Gross Domestic Product) per capita data provided by the World Bank (http://data.worldbank.org). GDP per capita is a widely used measure for wealth and resources in development and political science literature. .
To operationalise democracy we used a human-rights weighted democracy index, suggested by Christian Welzel in the context of the HDS theory (Welzel ). This index is based on Freedom House's civil liberties and political rights scores (FreedomHouse , ), weighted for the actual human right performance in the respective countries, with two indices from the Cingranelli/Richards Human Rights data project (Cingranelli & Richards , ). Freedom House relies mostly on the judgement or regional experts, supplemented by o icially documented information to rate societies regarding their civil liberties and political rights. The Cingranelli/Richards human-rights data project (CIRI) indices of personal integrity rights and political empowerment rights on the other hand rely on actual rights violations, documented by the US State Department and Amnesty International. Moreover CIRI uses a standard coding scheme to translate the obtained information into scores that measure to what extent particular types of rights are respected in a society (Welzel ). .
To build the index, Freedom House political rights and CIRI empowerment rights scores are added to give political participation. Similarly, Freedom House civil liberties and CIRI personal integrity rights are added to give personal autonomy. Political participation and personal autonomy are then multiplied to give the human-rights democracy index. Using a product results in low index scores, making human-rights weighted democracy index a rather rigorous indicator for democracy (Welzel ). For a discussion of other democracy measures used to test the HDS theory see Spaiser et al. ( ).
. We measured emancipation with the World Values Survey emancipative values index. The World Value Survey is a survey of representative sample of citizens from various nations. The survey is carried out by face-to-face interviews or phone interviews in remote areas. The World Values Survey provides longitudinal survey data on the level of individual respondents that may be aggregated on the national level. In our cross-national study we worked solely with aggregated data (for details on aggregation method see http://www.jdsurvey.net/jds/ jdsurveyMaps.jsp?Idioma=I&SeccionTexto=0404&NOID=101). Emancipative values are measured on four dimensions: choice, equality, voice and autonomy. These values represent preferences for "decision-making freedom of the individual human being and the equality of all human beings in this decision-making freedom" (Welzel , p. ). On the choice dimension respondents are asked for instance to what extent they tolerate abortion, diversity and homosexuality. At the equality dimension, three items measure gender equality in the domain of politics, education and jobs. To measure the emancipation level on the voice dimension, respondents had to indicate to what extent they demand that people have more say on the local and national level and what priority they assign to the freedom of speech. At last, the fourth dimension autonomy was measured by people's prioritisation of independence and imagination and their rejection of obedience as a desired quality (WorldValueSurvey ).
. Finally, we included the GINI coe icient to analyse empirically the relation between democratisation and economic inequality. The GINI coe icient data was obtained from the World Bank (http://data.worldbank. org). It measures the statistical dispersion in order to represent national income distributions. The GINI coe icient is frequently used to measure income inequality. However, it has been criticised that the index does not necessary reflect inequality adequately (Bollen & Jackman ; Stewart ; Ansell & Samuels ). We used the GINI coe icient because of data availability and because it is so far still the most common measure for economic inequality.

Model simulations and data evidence
. We now analyse the above models and directly test the predictions against the data. We start with the first democratisation model (equation ), where contributions to democracy-building are independent. This model is our starting point because it implements the Human Development Sequence without any modifications.

HDS theory at the macro level: resources and democracy
. Figure a shows the simulated dynamics of the macro-level variables, resources (economic prosperity) and democracy, in countries with initially low levels of economic development, emancipation and democracy. The log of resources grows linearly, as we would expect from equation . The level of democracy remains stable on the low initial level for some period, before increasing suddenly and rapidly a er years of simulated time. Figure b shows changes in democracy in six example countries, where a democratic transition took place between and . These rapid changes are representative of how democracy has arisen, once low income countries become middle income countries (Huntington ; Welzel ).
. showing that initially small changes in democracy in two exemplary cases, Chile and South Africa, were followed by sudden rapid shi s. .
The relationship between democracy and resources depends on the starting position of the countries. For example, Figure c shows that democracy decays in the absence of su icient resources. A similar pattern is seen in the data for Nigeria and India for instance, where GDP per capita is low and democracy has decreased ( Figure  d). The model predicts that in the near future democracy will increase in these countries, as GDP per capita grows. .
The democratic dynamics of rich countries depend on the initial level of emancipation. Democracy fails to increase in extremely rich countries with initial low levels of democracy ( . Although we only present a subset of the country data here, the model is generally consistent with large scale patterns of rapid democratic change seen across the world in the last years (Spaiser et al. ; Lindenfors et al. ; Jansson et al. ). The model reproduces the macro-level relationship between economic development and democracy: first economies develop and grow, followed by an increase in democracy. The comparison to data provides a validation of the HDS framework at the macro-level, but leaves open the question of whether the implicit micro-level assumptions are correct.

HDS theory at the micro level: emancipation
. We now look at the micro-level dynamics of the HDS model, starting with the case where democracy is not driven by collective action (i.e. as in equation ). Figure a illustrates the change in emancipation, measured as the proportion of emancipated individuals, and change in democracy in the simulation. All three variables (democracy, resources and proportion of emancipated individuals) are highly correlated. This correlation implies that simply plotting one variable against the other and calculating best fit regressions does not allow us to infer which is the causal factor. However, our ABM model implies a specific causal pathway, and we can use this to make testable predictions about the relationships between the variables under HDS theory. In particular, we can predict how the rate of change of emancipation is determined by levels of democracy, and vice versa. If the model holds then we expect to see the simulated relationships also in the data, while if the model is incorrect then the simulated predictions will fail to represent the data. , the model thus predicts that emancipation increases when democracy is low, and the growth of democracy increases with level of emancipation. Once both emancipation and democracy reach a maximum then they stabilise. We would now expect to see a similar pattern of emancipation and democratisation in the data.

.
In the World Value Survey data, emancipation can be measured by looking at the aggregate level of emancipative values in the population. We use this data to test the simulation predictions and thus the HDS theory implications against empirical evidence. Figure a shows the change in emancipation as a function of the level of democracy derived from the data. Here we see a rather clear pattern of increasing emancipation with level of democracy (F-test with F = 14.2053 and p = 0.0044), which is the opposite pattern than that predicted by the model.
.  To avoid bias due to interpolated data for yearly changes for emancipative values we used the actual available data only, therefore the changes refer not to yearly changes but to changes usually between four to six years. Data was available for the period from to .

Similarly
and emancipative values shows the opposite direction than predicted by the model. In the data, emancipative values increase only a er democracy has already shown significant increases and democracy increases most frequently with emancipative values scores between . and . . The fact that the data shows a statistically di erent relationship between emancipation and democracy than predicted by the standard HDS theory leads us to reject it as a model at the micro-level.
Revising the HDS theory: power relations and the role of the elite .
One reason for the discrepancy of the model results and data may be in the way parameters were chosen. To investigate this we now systematically explore the two parameters a, the democracy promoting e ect, and c, the democracy inhibiting e ect. Simulation results obtained when keeping parameter a constant at . and varying parameter c. The bigger c gets relative to a, the more is democratisation delayed. data ( Figure ). A larger value of c relative to a on the other hand has the e ect of delaying democratisation (Figure b). .
The relation of a and c represents the power relation of di erent groups in a society. If those who favour democratisation are very powerful, that is, if they can make a much higher contribution to political change, then a >> c and democratisation happens even if the majority of the population is not yet emancipated. On the other hand, if anti-democratic individuals are powerful, that is, if they can make a much higher contribution to keep the undemocratic political status quo, i.e. c >> a, then democratisation is delayed until the point when a large majority of the population becomes emancipated and enforces democratic transition. Comparing the model and data, we see that the data seems to be consistent with the former case only: a >> c with democratisation preceding emancipation (Figure ).
. This scenario (i.e. a >> c) is however not entirely consistent with the way the HDS theory is formulated. According to the HDS theory a rather small but powerful (i.e. a >> c) and liberal minded group alone would not be su icient to trigger democracy. Instead it is claimed: "Democratization processes of recent decades have been most far-reaching and most successful where the masses were mobilized into democracy movements in such number and so ubiquitously that state authorities could not suppress them easily" (Welzel , p.  ), do not specify the necessary size of the democracy movement, this statement implies that the proportion of emancipated individuals required to cause a regime shi is rather large. In terms of the simulation model, the HDS assumption is then that a = c or even that c >> a, that is, the emancipated are not particularly powerful, but once their number is large enough their influence becomes su icient to bring about political change. While our model allows such scenario, the data presented here suggest that this HDS assumption is not correct. Our comparison of model predictions and data is however consistent with the idea that democratisation is started by a liberal minded (i.e. emancipated) and influential (i.e. a >> c) "elite"   1)) refer to four to six years as no interpolation was used. We labelled countries where a democratic transition took place somewhen between and and for which emancipative values data was available prior to the transition. Labelled are also some of the most democratic and emancipated countries. The colours indicate whether the country was democratic (D ≥ 0.5) (blue) or undemocratic (D < 0.5) (black) when the change in democracy was measured. unemancipated individuals in a society determine the timing of emancipation and democratisation. With or without collective interaction e ects, the important factor in determining the sequence of events in the transition to democracy is the relative power relations. .
Looking again at the data and the change in democracy as a function of emancipation over all countries ( Figure  ), we see that those countries where a rapid democratic transition occurred, had emancipative values scores between . and . . These scores represent a scenario where a certain proportion, but not the majority of the population was emancipated when the democratic transition occurred. Thus, the available data is again only consistent with models in which democracy starts to increase when a rather small but powerful proportion of individuals is emancipated.

Revising the HDS theory: economic inequality .
The assumption in the previous models that resources are equally distributed amongst all individuals, is rather doubtful. We also assumed that the amount of resources obtained by each individual was independent between years. We now remove both these, somewhat unrealistic, assumptions by introducing a tuneable preferential attachment model of resource distribution (Merton ; Rigney ; Newman ). The model we choose, and describe in full below, has a parameter q that determines how equal the distribution of resources is. For q = 1 resources are distributed uniformly at random, producing a Poisson distribution (as in the previous section). For q = 0 the model produces a power law distribution of resources, similar to Zipf's law (Zipf ). While neither the Poisson nor the power law distribution reproduces exactly the empirical distribution of wealth seen in country data (Atkinson & Bourguignon ; Benabou ), they do produce extremes of equality and inequality, respectively. Thus by investigating the e ect of q on model outcomes we can understand how the degree of inequality a ects the emergence of democracy. .
In our revised model each individual i is represented by two variables: an integer r i (t) which is the amount of resources possessed by the individual; and a state x i (t) ∈ {U, E, S} which is the state of emancipation. State U is unemancipated and E is emancipated as in the previous implementation. Moreover, now the individual can also be in the state S, i.e. satisfied. The total resources are now R t = r i (t) and the aggregate emancipation E t is the proportion of individuals with state E, S t is the proportion of individuals who are satisfied and U t is the proportion of individuals who are unemancipated. Initially, r i (0) = 0 and x i (0) = U , for all individuals.

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In the inequality model each time step t in the simulation represents a month instead of a year. The changed time unit was necessary, along with a changed economic growth dynamics (linear economic growth, see following paragraphs), as the current model consists of only individuals. To simulate similar dynamics with N = 1000 as in the previous models with N = 10, 000, 000, the time and economic growth dynamic had to be adjusted. Reducing the number of individuals on the other hand was necessary as the individuals are tracked in their resource and emancipation status during the simulation in the inequality model. With a large number of individuals, the tracking becomes computationally intensive. The inequality model was run over time steps, which then represents years of simulation (see Appendix A . , for model validation result with other time units). With the tracking of individuals over the course of the simulation and the new resource distribution mechanism, our model resembles now a full agent-based model and we can no longer approximate it with equations only (see the pseudo-code in Appendix A . ).

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On each time step all individuals with r i (t) > 0 have probability p of losing one resource unit. These resource units are then redistributed amongst all individuals, together with additional g new resource units. Redistribution is carried out as follows. For each resource unit, we assign the resource unit to one individual selected uniformly at random with probability q (the 'equality' parameter). Alternatively, with probability 1 − q, we assign the resource unit to individuals in proportion to their current wealth, i.e. the probability that individual i receives the resource unit at time t + 1 is . This is a standard rule of preferential attachment (Merton ; Rigney ; Newman ). The more resources an individual has the more likely it is to acquire more resources. Under this model, and unlike in the earlier version, resources grow linearly, i.e. R t+1 = R t + g.

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The rules for updating the emancipation state are similar to the previous models, but we now make the satisfied state explicit. We assume that unemancipated individuals with or resource units become emancipated. Unemancipated and emancipated individuals with or more resources become satisfied. Emancipated or satisfied individuals with zero resource units become unemancipated. The state of individual i is thus updated as follows: We adjust the model of democracy to account for the new satisfied state. In this model, because we now track individuals' state through time, it is important to distinguish these rich, satisfied individuals from those who are The contribution e of the satisfied S is set to be the lowest because of the assumption that the satisfied are only interested in preserving the status quo and not in changes and therefore they will be less active (see Appendix A . , for model validation result with other resource units and parameter values). (d) q = 0 (high inequality), a = 0.6, b = 1. All parameter values were selected to match empirical results given the changed model dynamics of the inequality model (linear economic growth, changed time units) as described above. The GINI coe icient was computed based on the simulated resource distributions among agents using the standard method to compute the GINI coe icient from income distributions (Gini ).
unemancipated. We assume that these individuals prefer the status-quo, so that their contribution to democracy is negative when D t < 0.5, and the satisfied individuals produce a pressure for less democracy. On the other hand, if D t ≥ 0.5 then the satisfied individuals demand more democracy and their contribution is positive. To reflect this, and to ensure that democracy remains between and , we assume that the per satisfied individual contribution to democracy is The assumption here is that individuals benefiting from the current system prefer the status quo (Boix ; Acemoglu & Robinson , ; Przeworski ).
. We assume that the satisfied individuals make their contributions independently of who they interact with, as they only care about the status quo. These specifications then result in a modified threshold democratisation model: and with increasing q at each step by . .

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Simulation results show a strong e ect of economic inequality on democratic change. Figures a-c show model outcomes for low, middle and high levels of equality, q. Democracy grows faster and reaches higher values when economic inequality is low (q= ) ( a). On the other hand if inequality is extremely high (q= ), then democracy is never achieved: democracy rises at first but then decreases again. For middle inequality levels (q= . ) a transition to democracy takes place but democracy never reaches very high levels. In the simulation, inequality allows agents to move to the satisfied state before democracy has been achieved. The result is a small rich elite with little interest in developing democracy and a large population of poor unemancipated individuals, preoccupied with existential constraints.
. The empirical data support a similar relation between democracy and inequality as we find in our simulation. The data show that democratisation is most likely at a GINI level between . and . (see Figure a), and this is similar in our model simulations (see Figure b). Specifically, between and democratic changes happened mostly in rather equal societies. These were typically communist countries before their democratic transitions, and thus countries with low inequality.

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South Africa, which had both economic and political apartheid before its democratic transition, is one of the few exceptions (the others are mostly Latin-American countries, see . These results suggest that any theory about the emergence of democracy needs to take into account inequality. The HDS theory stresses the importance of people's socio-economic well-being for emancipation without taking into consideration socio-economic inequality and its consequences in terms of emancipation and democratisation. Figure a reveals that democratisation can only take place and stabilise, if a su icient proportion of the population has access to resources to improve its socio-economic situation. In societies with high inequality this is unlikely to happen, as the majority of the population is excluded from socio-economic well-being. As a result emancipation and democratisation will fail to materialise.

Conclusions
. The HDS theory establishes a close relation between emancipation and democratisation to explain why democratisation is most likely to occur in countries that have undergone a considerable economic development. The data confirms that there is indeed a relation between democracy and emancipation. Consequently, we do not reject the political culture congruence theory (Sheafer & Shenhav ) that underlies the HDS theory and assumes that stable democracies require a congruence between emancipative or broader speaking democratic values among the population and democratic political institutions. The questions is rather does institutional democratisation precede emancipation or is the other way round? Contrary to the postulations of the HDS theory, data shows that human-rights democracy seems to lead to an increase in emancipation. Rather, in accordance with the data, our models suggest that democratisation is led by a influential and emancipated elite of around -% of the population, using their influence to initiate democratic change (O'Donnell et al. ; Casper & Taylor ; Higley & Burton ). That is, the transition to democracy is initiated when a small proportion of the population becomes emancipated and, if this group has su icient political power relative to other political groups, it triggers political changes. Such a pattern of emancipation is not measurable in aggregated measures of emancipation, but it is reflected in the growth of democracy before emancipation seen in the data. .
We arrived at the conclusion above because our agent-based models make predictions that were partly testable against data. Unfortunately, more fine-grained data, panel data on the individual level to track changes in emancipation of individuals for instance, is not available. Such data would have allowed to test the simulation model predictions more directly. .
In previous empirical tests of the HDS theory, that were supposed to confirm the theory (Inglehart & Welzel ; Welzel ), a method was applied of looking at correlations in the rate of change of variables. Fitting a model can reveal a correlation in growth of the variables of y t and x t but it can never reveal that a change in x t causes a change in y t or vice versa (Freedman , ). Such an approach was nevertheless adopted by Inglehart & Welzel ( ); Welzel ( ) in their original test of the Human Development Sequence. Changes in GDP, democracy and emancipative values were fitted as a set of three simultaneous di erence equations. The change in the three variables are taken in turn as independent variables in equations where the change in all three variables are included as dependent variables. The argument is that the fitted terms with the most explanatory power in this linear regression provides the strongest possible causal link (ibid.). We would argue that in the absence of a micro-level explanation of why such a correlation should exist, these correlations do not allow us to say anything about the likelihood or otherwise of the HDS theory. Recently, an attempt has been made to formulate the micro-level mechanisms for the HDS theory (Abdollahian et al. ), but, the simulation results were not compared against data (ibid.). In Figure we however show that important aspects of the data fail to match the HDS theory. These findings correspond to recently published empirical analyses that similarly suggest the inconsistency of the HDS theory with data (Spaiser et al. ). .
In our study, a er rejecting the initial HDS model, we revised it to account for di erent power relations of di erent political groups. These revised models are consistent with the available data. We also went on to test the role of inequality and again found patterns in our model that are reflected in the data. We hypothesised that egalitarian societies do not have wealthy elites who oppose democratisation, because they fear losing their benefits and accumulated wealth. Democratisation is eased by the fact that there are no materialist interest in keeping the undemocratic status quo (Boix ). Moreover, the high economic equality allows a su icient share of the population to get access to existential resource and become emancipated (Inglehart & Welzel ; Welzel & Inglehart ).
. Exceptions, where rich countries have failed to become democratic, could be partially explained by inequality (Acemoglu & Robinson , ). In unequal societies there is a strong class of wealthy elites who might lose some of their privileges in a democratic society. However, under certain circumstances they will be supportive of democratic change, for instance if they fear mass uprisings that might threaten their privileges even more then a democratic transition, which they can try to shape according to their preferences. Giving the emancipated more power in relation to the unemancipated and satisfied, i.e. further increasing a and b (see Figure  d), allows for democratisation even in highly unequal societies. This captures some of the empirical examples of democratisation in highly unequal societies, where a wealthy but emancipated elite advocated democratisation to preserve their privileges and wealth. However, our ABM simulation suggests that democratisation is unstable in highly unequal societies and democracy will decrease eventually (see Figure d). Moreover, if the economic growth is big enough then a su icient number of people becomes emancipated in a short period of time and demands democracy even in an unequal society. .
Despite producing models that are consistent with the data, there remain other highly plausible explanations of the relationships observed in the data (Barro ; Krieckhaus ; Wucherpfennig & Deutsch ; Spaiser et al. ). For instance, in our models we focused on democratisation processes, not further examining what drives the economy for instance and in how far the economic dynamic itself is linked with democratisation, emancipation or inequality processes. This focus was set by the HDS theory, which we investigated in this paper against data and in terms of mechanism consistency. The HDS theory conceptualises economy as independent of democratisation and emancipation.
. It has been also suggested that the third democratisation wave that took place in the s and s was mostly geographically confined to the European continent and in that context other explanations for the di usion of democracy in these countries have been advanced (Doorenspleet ; Elkink ). In fact, the di usion of democracy theory o ers an additional explanation for the important role of elites for democratisation. If we conceptualise democracy as an innovation, then, according to the theory of di usion of innovations (Rogers ), the innovation is first adopted by early adopters. These early adopters are typically the educated and resource-rich elite of a country. The majority follows the early adopters somewhat later and the innovation spreads across the society. Research seems moreover to suggest that the di usion of democracy across countries is geographically and culturally rooted (Wejnert ; Elkink ). It remains to be seen whether the diffusion of democracy will continue globally or whether alternative development models, like the one promoted by China, will become an alternative to the democratisation (Lin et al. ). These questions go beyond the scope of this paper, which focuses on the examining and theoretical revision of the HDS theory, but should be more in the focus of research in future.

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Our analysis shows how a combination of simulation models and data analysis can be used to examine and revise a theory. Linking models to data as closely as possible, ideally not only to macro-level but equally to micro-level data, can give us some confidence about the validity of simulation models. The combination of the two used here allows us to get closer to an understanding of the relationship between macro-level phenomena and their underlying micro-level processes.

Appendix A . Validation
In this section we present validation and sensitivity analyses results. A simulation model requires validity, that is, the model has to be an accurate and correct representation of the system that is modelled, for the particular objectives of the study (Law ; Galán et al. ). Only then can we draw conclusions from simulation results. A simulation can be validated in various ways. Zeigler ( ) for instance di erentiates between three levels of validity: replicative, predictive and structural. Generally, a validation should show that the model produces reasonable and plausible outcomes within the frame of the theory to which the simulated system refers. Moreover, if data is available, it should be shown that the simulation results reproduce empirical results and thus make correct predictions. Sensitivity analyses are an essential method of validation and show the e ect of the di erent parameters and their values (Klügl ). In the main manuscript we show that our simulation models make valid predictions that are coherent with empirical data analyses. The first simulation model (HDS Base Model, see A . ) generates moreover outcomes as predicted by the Human Development Sequence (HDS) theory (see Figure in the main manuscript), which we are examining and revising in this work. Thus the model is valid within the theoretical framework of the HDS theory. The revisions we suggest to the HDS theory based on our simulation models and empirical data analyses, naturally deviate from the original theory, but still follow the basic logic of the HDS theory. Given the simulation model presented in the main manuscript is equation-based, the mathematical tractability of the model -with simulation outcomes corresponding to theoretical and empirical predictions -show as well the internal validity of the model (Law ; Galán et al. ; Klügl ; Zeigler ). In Appendix A we have provided the MATLAB-based pseudocode for the simulation models which would allow researchers to replicate the model results. In this section we will mainly focus on sensitivity analyses that do not contribute to the substantive understanding of the model, but which serve model validation purposes.

A . Sensitivity Analyses: Time Units
We have conducted sensitivity analyses with di erent time units, instead of years, we used months as time units. Changing time units requires also changing parameter values. Economic growth within smaller time units is respectively lower for instance. We thus divided the parameter values by , to represent the monthly proportion of the original parameter values. Figure A shows the results with months as time units. The figure shows that changing the time units does not a ect model outcomes. The simulation results and predictions remain coherent with those reported in the main manuscript.

A . Sensitivity Analyses: Resource Units
We have conducted sensitive analyses with di erent resource units. In the main manuscript, individuals became emancipated if they had or resources. If they had less or more resource units they were considered unemancipated. To test the simulation model with di erent resource units we logarithmised and rounded up yearly income values. We used for instance the ten income categories listed in the Word Value Survey ( , $ and more, which is approximately and beyond We can now define that individuals who have or resources become emancipated, otherwise they are unemancipated. Figure A shows that changing resource units this way does not a ect the model outcomes, the simulation results and predictions remain coherent with those reported in the main manuscript. The important feature of the model is to define two thresholds, the first threshold defines when individuals become emancipated and the second when they have an excessive amount of resources that prevents emancipation.

A . Sensitivity Analyses: Parameter Values
. In the main manuscript we have already discussed the di erent scenarios that di erent parameter values represent and the di erent simulation outcomes based on di erent model parameter values (see Figure  Here we conduct sensitivity analyses of some parameter values, exploring not di erent scenarios as in the main manuscript but rather the e ect of changing the units or scales of parameter values extremely. Generally, we have to note that public goods game parameter values have to be aligned to the growth parameter and to the democracy scale to produce numerically stable results. If the public goods game parameter values exceed the growth parameter value significantly the simulation results for democratisation become discontinuous (see Figure A ). This makes sense since these parameters represent power to induce or prevent political change. Power is however mostly tied to the availability of resources. Another reason for this discontinuity is the scaling of democracy between and , parameter values that exceed this scale significantly render numerically unstable results. stead of years as in the previous models. The changed time unit was necessary, along with a changed economic growth dynamics (linear economic growth, main manuscript), as the current model consists of only individuals. To simulate similar dynamics with N = 1000 as in the previous models with N = 10, 000, 000, the time and economic growth dynamic had to be adjusted. Reducing the number of individuals on the other hand was necessary as the individuals are tracked in their resource and emancipation status during the simulation in the inequality model. With a large number of individuals, the tracking becomes computationally intensive. The inequality model was run over time steps, which then represents years of simulation. .
In this section we present sensitivity analyses results with years instead of months as time units. As we reduce the number of time steps to , representing years, we have on the other hand to increase N to , , , moreover the economic growth rate has to be adjusted as well, g is therefore now set to , (remember the economic growth in this model is linear, see main manuscript), so it produces su icient resources for the larger N in the specified period of time to reproduce the results reported in the main manuscript. Figure A shows the simulation results if the time units are changed to years. The figure shows that when adjusting the other model parameters (N and g) as required by the changed time units, we can largely reproduce the results in the main manuscript, thus the model is not sensitive to time units.