International Studies Quarterly (2004) 48, 603–629
Conquest and Regime Change: An
Evolutionary Model of the Spread of
Democracy and Peace
LARS-ERIK CEDERMAN
Swiss Federal Institute of Technology Zürich
KRISTIAN SKREDE GLEDITSCH
University of California, San Diego
Whereas the literature on the democratic peace tends to treat the
phenomenon as a causal law, we follow Immanuel Kant in interpreting it
as a macro-historical process that expanded from a small number of
democracies to about 50% of all states. In order to account for this
development, we introduce an agent-based model that combines a
natural-selection logic with an adaptive mechanism of regime change.
The latter is implemented as an empirically calibrated, contextual rule
that prompts democratization as an S-shaped function of the democratic
share of a state’s immediate neighborhood. A similar transition rule
governs regime change in the opposite direction. The computational
results show that regime change and collective security are necessary to
produce realistic trajectories of democratization at the systemic level.
The International Relations literature has usually interpreted the democratic peace
as a causal law operating on pairs of states. Yet, in his classical formulation, Kant
(1970a[1874], 1970b[1795]) viewed it as a dynamic, macro-historical process. This
development started about two centuries ago, at a point when there were very few
democracies. Subsequently, however, the process of democratization, and its
concomitant pacification, spread throughout the international system. Currently,
more than half of all states are democracies. What explains this striking expansion
of democratic rule in the international system?
Because answering such a question requires massive counterfactual rewriting of
history, this article explores the puzzle within the context of a computational model.
Building on an earlier attempt to model the democratic peace as an evolutionary
process (Cederman, 2001), we broaden the theoretical focus to encompass adaptive
changes of authority structures, calibrated to conform with empirically derived
contextual mechanisms. Following Gleditsch’s (2002) regional approach, we
postulate that shifts from democratic to non-democratic rule, as well as transitions
in the opposite direction, depend on states’ local neighborhood. The more
democracies there are surrounding a non-democratic state, the more probable
democratization becomes. Likewise, isolated democracies in non-democratic
regions are more likely to turn authoritarian.
r 2004 International Studies Association.
Published by Blackwell Publishing, 350 Main Street, Malden, MA 02148, USA, and 9600 Garsington Road, Oxford OX4 2DQ, UK.
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An Evolutionary Model of the Spread of Democracy and Peace
Our computational findings indicate that, together with collective security,
democratization through locally dependent transition probabilities contributes
strongly to the emergence of the democratic peace in systems with few initial
democracies. Despite considerable fragility in the early stages of the democratization process, the geographical clustering due to adaptive regime change can make it
easier for democratic states to survive in a hostile, non-democratic environment.
Beyond a certain point, regionally operating regime change drives a positive
feedback process that gives rise to Huntingtonian ‘‘waves of democratization’’
capable of shifting the balance decisively in favor of the democratic peace.1
We first outline in the following section the empirical puzzle we are trying to
model. Then we turn to a discussion of evolutionary explanations with respect to
the democratic peace, as well as an analysis of the empirical parameters of regime
change. A section describing the agent-based model follows before three sections
presenting the computational results in the base system, with regime change, and
with added collective security respectively. A concluding section sums up the
theoretical repercussions of our analysis.
The Puzzle: The Emergence of a Democratic Security Community
Most theories of democracy and democratization focus exclusively on internal
attributes or processes within societies. As we will explain in greater detail later,
work on democratization has generally paid little attention to international factors
or relations between states. Nonetheless, the distribution of democracy has varied
over time in ways that changes in domestic attributes alone cannot fully account for.
Figure 1 displays the changes in the distribution of democracy over time,
measured by the proportion of democratic countries. We consider states
democracies if their institutions are assigned a score of 6 or above on the 21point scale in the Polity data ranging from 10 to 10, with lower values indicating
more authoritarian polities (Jaggers and Gurr, 1995).2 The figure shows that the
proportion of states in the world with democratic institutions has increased from
less than 5% at the starting point in 1816 to more than 50% at the present. Only the
United States and Switzerland qualified as democracies in 1816.
However, the expansion of the share of democracies in the system has not followed
a gradual or linear trend. Huntington (1991) has popularized the idea that the extent
of democracy in the world has expanded and contracted in three ‘‘waves of
democracy.’’ Periods of expansion of democratic institutions have been followed by
periods of contraction, or waves of transitions to autocracy. These changes to and
from democracy have sometimes been related to changes in international conflict and
cooperation. The share of democratic states increased notably following the peak of
war involvement due to World War I. The first wave of expansion in democracy
began to contract after the outbreak of World War II as the proportion of democracies
fell from around 40% and essentially reverted to the level in the late 19th century.
Similarly, the bulk of changes often referred to as the third wave of democracy
followed in wake of the end of the Cold War and the collapse of the Soviet Union.3
1
We do not study the impact of different types of democratization or the effectiveness of different strategies to
promote democracy. Our results should therefore not be interpreted as an argument in favor of the Bush
administration’s efforts to impose regime change in Iraq through military force.
2
This corresponds to Jaggers and Gurr’s (1995:479) threshold for delineating ‘‘coherent democracies.’’
Countries classified as coherent democracies have political institutions characterized by competitive executive
recruitment, competitive political participation, and constraints on the chief executive (Jaggers and Gurr, 1995:471).
3
Although Figure 1 in addition to changes within existing states also reflect changes from new states entering
the system, a plot based only on the states in continuous existence from 1816 to the present indicates similar trends
over time. Likewise, weighting each country by its population size rather than letting each state count equally
irrespective of its relative size yields a similar total increase and ebb-and-flow pattern over the two centuries. These
figures are not included for considerations of space, but are available on request.
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Proportion of democracies
0.5
0.4
0.3
0.2
0.1
0.0
1850
1900
1950
2000
Year
FIG. 1. Democracy in the International System, 1816–1998
The seeming waves of democracy and autocracy have sensitized researchers
to the possibility that regime change may be related to events or processes at the
global level. However, it is also easy to show that there is a marked tendency for
democracies to cluster geographically, and that transitions tend to occur on a
regional basis. The likelihood that a state chosen at random at a given point in time
will be a democracy varies notably depending on whether its geographically
proximate neighboring states are democratic or not. The probability that a
randomly selected state is a democracy by usual criteria in the widely used Polity
data in a given year is about .30. However, the probability increases to .84 when the
average level of democracy among geographical neighbors exceeds the common
democracy threshold.
Conflict is of course closely related to geographical features and opportunities for
interaction, and it can likewise be shown that the prospects for democracy also seem
to vary by a country’s exposure to conflict and peace. Democracies and nondemocracies are generally held to be equally likely to wage war or participate in
conflict. However, if we look at the geographical location where conflicts take place,
we find that democracies are much less likely to experience conflict on their own
territory than non-democracies. The probability of a country being a democracy in
a given year is about .31 for states that are not involved in conflict on their own
territory, but falls to .17 for countries experiencing conflict. Although actual
outbreaks of conflicts are relatively rare and occur in less than 10% of all country
years, the stability of peace measured by years since last conflict involvement differs
markedly among democracies and non-democracies. The number of consecutive
years at peace without conflict on a country’s territory is generally much higher for
democracies than non-democracies, and few non-democracies have accumulated a
high number of consecutive years of peace.
Despite these hunches and empirical facts, the powerful trend toward
democratization in the international system remains a puzzle. To better understand
it, it is necessary to consider the evolutionary and contextual nature of the
democratization process, which are the topics to which we now turn.
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An Evolutionary Model of the Spread of Democracy and Peace
Evolutionary Explanations of the Democratic Peace and Contextual Regime
Change
Following Doyle’s (1983) influential ‘‘rediscovery’’ of Kant’s peace plan, most of the
contemporary literature on the democratic peace focuses on the dyadic relationship
(for overviews, see Russett, 1993; Chan, 1997). Today, few analysts contest the
finding that democratic states rarely, if ever, fight each other (although see the
critical contributions in Brown, Lynn-Jones, and Miller, 1996). As already noted,
some researchers have even elevated it to the status of a covering law (Levy, 1998;
Russett, 1993; Ray, 1995).
Yet, due to its mostly micro-level focus on pairs of states, the empirical literature
on the democratic peace tells us little about how the remarkable historical trajectory
in Figure 1 could have unfolded. In a truly scientific sense, the systemic pattern of
democratization remains a puzzle because by treating the democratic peace as a
constant, de-contextualized causal force, the conventional analysis, whether critical
or supportive of the democratic peace, ignores the spatio-temporal mechanisms
that helped bring about the phenomenon as we know it today.
In contrast to most recent writings, Kant’s classical theory of peace outlines an
explicitly dynamic sketch that helps us understand how the international system
could have become, and actually became, gradually more democratized and
pacified. Rather than being the end point of his analysis, the assumption that
democratic authority structures at the domestic level contribute to such outcomes
should be seen as a part of a dynamic, macro-historical process. Mindful of the
geopolitical realities of world politics, Kant did not assume that democracy itself
would automatically engender democratic security communities. To bolster this
point, he advanced a series of causal mechanisms that together would drive the
process toward peace. Perhaps the most important of these was the notion of a
growing peaceful federation that could repel attacks from non-democratic
competitors, but Kant also considered norm-based, power-related, and dialectical
mechanisms (see, e.g., Hurell, 1990; Huntley, 1996).
In retrospect, it can be argued that Kant’s theory is evolutionary (e.g., Modelski,
1990). Obviously, Kant did not have access to the intellectual discoveries of Darwin,
but it seems clear that at least in a vague sense, there is an evolutionary logic built
into most of Kant’s arguments, at least if we interpret evolution in a broad sense
such that it includes both natural selection and adaptation. What is less clear,
however, is the extent to which this logic relies on one or the other of these types of
evolution.
By contrast, modern evolutionary theory draws a sharp distinction between
selection-based arguments and Lamarckian adaptation (see, e.g., Harré, 1981;
Nelson and Winter, 2002). As conjectured by Darwin’s original theory of biological
evolution, social systems can exhibit processes of natural selection whereby the
system as a whole changes thanks to selective turnover that weeds out less fit
individuals. Arguments relying on adaptation and learning assume that not only the
system as a whole adapts, but also the individual parts themselves. In this case,
selection is not ‘‘blind’’ since the agents actively adjust themselves to their
environment.
Applying this classification to international politics, Wendt (1999) separates
‘‘natural selection’’ from ‘‘cultural selection’’ (see also Kahler, 1999). His analysis
generalizes Waltz’s (1979) reference to ‘‘competition’’ and ‘‘socialization,’’ both of
which are used to support the neorealist contention of uniformly competitive
strategies. Given Wendt’s constructivist leanings it does not come as a surprise that
he criticizes especially the former, natural-selection-based argument. Following a
number of critics (e.g., Keohane, 1983; McKeown, 1986), Wendt asserts that the
international system does not feature a sufficiently high ‘‘selection pressure’’ to
account for the evolutionary changes at the macro-level. Cultural selection, by
L.-E. CEDERMAN AND K. S. GLEDITSCH
607
contrast, is known to operate much more quickly and, therefore, offers a more
convincing explanation in such environments (Boyd and Richerson, 1985). In the
following, we will refer to cultural selection using the more neutral term adaptation
in order to avoid reading in too much specific theoretical contents into the content
of the process itself.4
Whereas natural selection is usually invoked to justify realist positions, Cederman
(2001) relies on such a Darwinian logic as a way to account for the democratic
peace. In brief, the idea is that through their mutual cooperation, democracies
increase their survival chances to such a degree that a democratic security
community may materialize. However, if the realist theories are vulnerable to
criticism of the empirical foundations of the natural-selection logic, then so is
Cederman’s model. It seems likely that in the last couple of centuries, changes
of regime type have been far more common occurrences than extinction and
birth events at the state level. France, for example, has experienced 23 different institutional arrangements since 1816 as measured by the Polity data. The
collapse of the Weimar Republic, and the reconstitution of democracy in Germany
represent obvious examples of how regime types may change more quickly
than the state identity itself (although the country obviously underwent very
profound changes in other respects, including division and other significant border
changes).
There is a broad spectrum of adaptive mechanisms ranging from simple
behavioral imitation to complex learning (Wendt, 1999:ch. 7). Having analyzed
mostly the first of these poles, the formal literature has paid more attention to the
evolution of strategies (e.g., Axelrod, 1997:ch. 1; Young, 1998). It is obvious that
change in regime type presumes deep structural transformations of both state and
society, including cognitive shifts affecting political culture. Still, in this article, we
are less concerned with this distinction than with the difference between internal
and external mechanisms of adaptation. Whereas the internal explanations assume
that the state adapts in isolation through an inherent process that could unfold in
parallel ways in more than one country, the external accounts postulate that
adaptation is a deeply social and interactive process between states.
Applied to regime change, the same theoretical division recurs. The overwhelming majority of explanations rely on an internal logic, where socioeconomic
factors within each individual state drive democratization and transitions (see, e.g.,
Lipset, 1960; Vanhanen, 1990; Przeworski and Limongi, 1997).5 However, the
factors driving regime change may also be located in interactions between states or
processes spanning national boundaries (Huntington, 1991). Gleditsch (2002)
explores several plausible dimensions of democratization, and introduces an
ecological perspective in which shifts of regime type depend on the proportion of
democracies among neighboring states.
The local variation in transition probabilities depending on the regime type of
neighboring states can easily be demonstrated from the observed Polity data and
geographical information (Gleditsch and Ward, 2003). Figure 2 displays estimates
of the probability of a transition from one regime to another in a given year, as a
function of the proportion of other states that are democracies within a 500 km
4
Because we focus on very simple evolutionary processes, we refrain from referring to the related term
learning, although such complex mechanisms are in principle compatible with our argument (cf. Haas, 1990). It
should also be noted that, in a different and wider use of the term, adaptation can refer to natural-selection
processes where the entire system adapts.
5
The so-called social requisites thesis holds that a society’s level of development, wealth, or disposable income is
a primary determinant of its prospects for democracy (e.g., Lipset, 1960). This tradition has been criticized by other
researchers who emphasize the importance of political conditions such as pacts between elites (e.g., O’Donnell,
Schmitter, and Whitehead, 1986). Yet, these schools are in one sense all similar in that they set forward explanations
relating a country’s prospects for democracy to internal factors.
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An Evolutionary Model of the Spread of Democracy and Peace
0.12
Transition to democracy
Transition to autocracy
Pr. regime transition
0.10
0.08
0.06
0.04
0.02
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Proportion of democratic neighbors
FIG. 2. The Two Empirical S-Curves
radius of a country.6 As can be seen, the estimated probability that an autocracy will
become a democracy, indicated by the solid line, increases as an S-curve with the
proportion of democratic neighbors. Likewise, the risk that a democracy will break
down and be replaced with an autocracy, indicated by the dashed line, also follows
an S-shaped function given the regional context. Watts (2003:ch. 8) shows that
many social systems feature local decisions governed by S-shaped thresholds that
are functions of the views held by each actor’s neighbors. Save for two minor kinks
at the extreme when all neighbors are either democratic or authoritarian, the
smoothed curves do indeed display an S-shaped pattern. Interestingly, the top
probability of democratization reaches roughly twice the level of the corresponding
measure for states going authoritarian.
Without belittling the substantive effect of internal factors, we will here focus
entirely on the external dimension. Gleditsch (2002, see also Gleditsch and Ward,
2003) demonstrates that this geographical clustering of democracies does not
disappear when controlling for other prominent factors in the social requisites
tradition, such as GDP per capita and economic growth.7 The persistent effects of
the share of neighbors that are democracies suggest that the external adaptive
process remains quite strong. Assuming that the empirical S-curves describe the
transition probabilities between regime types reasonably well over time, our task is
to trace the development of a democratic security community in world-historical
6
These curves are non-parametric estimates from a local regression model. In essence, local regression finds a
local estimate of the effect on a response variable (in this case, regime transition) over certain ranges of values of a
predictor variable (i.e., proportion of neighbors that are democracies). See Beck and Jackman (1998) for an
introduction to local regression.
7
It could be argued that clustering in regime type and transitions may reflect common conditions among
geographically proximate states rather than local regime change mechanisms. Gleditsch and Ward (2003) estimate a
Markov process model of regime transitions, controlling for a large number of internal and external factors
hypothesized to be related to democratization, as well as global trends in the share of democracies. They find that
states surrounded by democracies still are about twice as likely to experience transitions to democracy, holding all
other variables at their median values.
L.-E. CEDERMAN AND K. S. GLEDITSCH
609
perspective. To do this, we introduce a computational framework that allows us to
explore counterfactual histories in an artificial geopolitical system.
The Geopolitical Model
The current model builds on a modeling tradition that dates back to the work of
Bremer and Mihalka (1977), who introduced an imaginative agent-based model
featuring conquest in a hexagonal grid, later extended and further explored by
Cusack and Stoll (1990).8 Building on the same principles, the current model,
which is implemented in the Java-based toolkit Repast (see http://repast.sourcefor
ge.net), differs from its predecessors in that it is based on a square grid with a local
combat mechanism and quasi-parallel execution designed to create a more realistic
geopolitical environment.9 In a further quest for realism, the framework presented
in this article improves on its predecessors by featuring a larger grid, distance
dependence with respect to both resource extraction and power projection, less
intense warfare, more gradual resource updating, and most importantly,
technological change. The model presented in Cederman (2003) is the closest
descendant of the current framework. Unlike the present article and previous
models applied to the democratic peace (Cederman 2001), however, the model in
Cederman (2003) does not differentiate between actors as democracies and
autocracies. All the new features in the model, which will be described below and in
the appendix, expose democratic cooperation to a tougher test than in Cederman
(2001).10 The idea is to mimic the geopolitical consolidation process that reduced
the polarity of the Westphalian state system.11
In essence, the model is constituted by an endogenous network of states with
variable boundaries residing in a square grid. The standard initial configuration
consists of a 50 50 square lattice populated by about 200 composite, state-like
agents interacting locally. To generate trajectories as the one shown in Figure 1, we
let a small percentage (10%) of the states be democracies at the outset of the runs.
Figure 3 illustrates a typical initial configuration with the democracies shaded and
the other states in white. The lines indicate the states’ territorial borders and the
dots their capitals.
In each time period, the actors allocate resources to each of their fronts and then
choose whether or not to fight with their territorial neighbors. While a small part of
each state’s resources is allocated evenly to its fronts, the bulk goes to a pool of
fungible resources that are distributed in proportion to the neighbors’ power. This
scheme assures that military action on one front dilutes the remaining resources
available for mobilization, which in turn creates a strong strategic interdependence
that ultimately affects other states’ decision making.
For the time being, let us assume that all states, whether democratic or not, use
the same ‘‘grim-trigger’’ as their base strategy. Normally, they reciprocate their
neighbors’ actions. Should one of the adjacent actors attack them, they respond in
kind without relenting until the battle is won by either side or ends with a draw.
Unprovoked attacks can happen as soon as a state finds itself in a sufficiently
8
Agent-based models of this type can be seen as a more advanced version of cellular automata, such as the
‘‘Game of Life’’ (Gardner, 1970). For introductions, see Epstein and Axtell (1996) and Axelrod (1997).
9
See Cederman (1997) for an early implementation of this geopolitical framework programmed in Pascal.
10
This also means that the results of the current model are not directly comparable to Cederman (2001).
Nevertheless, below, we present findings with and without adaptation, thus allowing an approximate comparison
with the earlier model, which only features the former.
11
For example, Tilly (1975:24) claims that there were about half a thousand independent units in Europe in
1500. If one factors in decolonization, the last few decades have been marked by an increase in polarity. Since the
current model does not capture oceans and naval warfare, however, we do not purport to model such far-flung
processes.
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An Evolutionary Model of the Spread of Democracy and Peace
FIG. 3. The Initial State of the Sample System
superior situation vis-à-vis a neighbor. This is where the difference between
democratic and non-democratic states appears. Quite simply, democracies never
launch unprovoked attacks against one another. This rule implements the
democratic peace at the micro-level. Technically speaking, the democracies’
strategy is ‘‘tagged’’ in that they tailor their behavior to the type of the state they
encounter (Axelrod, 1984:ch. 8; Holland, 1995; see also Cederman, 2001).
Apart from this important difference, both types of actors select potential targets
of their attacks randomly. Combat ensues provided the attacking states’ relative
power falls above a stochastic threshold set to three-to-one. Defining the offense–
defense balance of the system, this threshold is identical to all states. Due to the
difficulties of planning an attack, actors challenge the status quo with a .01
probability per period. War in a neighboring state puts an unmobilized state on
alert, which lasts until the adjacent action is over. This mechanism of contextual
activation captures the shift from general to specific deterrence in crisis situations.
In order to achieve strategic consistency, states retain the focus on the same target
state for several moves. Once it is time for a new campaign, the target selection
selects a random neighbor.
An identical stochastic threshold function determines when a battle is won. When
the local capability balance tips decisively in favor of the stronger party, conquest
results, implying that the victor absorbs the targeted unit. This is how hierarchical
actors form. If the target was already a part of another multi-province state, the
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1
0.9
0.8
Power extraction and projection
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
10
20
30
40
50
Distance from capital
FIG. 4. Technological Change Modeled as a Sliding Loss-of-Strength Gradient
latter loses its province. Successful campaigns against the capital of corporate actors
lead to their complete collapse.12
Territorial expansion has important consequences for the states’ overall resource
levels. After conquest, the capitals of conquered territories are able to ‘‘tax’’ the
incorporated provinces including the capital province. As shown in Figure 4, the
extraction rate depends on the loss-of-strength gradient that approaches one for
the capital province but that falls quickly as the distance from the center increases
(Boulding, 1963; Gilpin, 1981). Far away, the rate flattens out around 10% (again
see the appendix for details). This function also governs power projection away
from the capital. Technological change is modeled by shifting the threshold to the
right (from 2 to 22 steps), a process that allows the provinces to extract more
resources and project power farther away from the center. In the simulating runs
reported in this article, the transformation follows a linear process in time.
Together all these rules entail four things: First, the number of states will
decrease as the power-seeking states absorb their victims. Second, as a consequence
of conquest, the surviving actors increase in territorial size. Third, decentralized
competition creates emergent boundaries around the composite actors. Fourth,
once both sides of a border reach a point at which no one is ready to launch an
attack, a local equilibrium materializes. If all borders are characterized by such
balances, a global equilibrium emerges. Yet, such an equilibrium is meta-stable
because, decision making always involves an element of chance, and technological
change affects the geopolitical environment of the states.
12
Because the main rationale of the article is to study democratization within the context of geopolitical
consolidation processes, the current model excludes the possibility of secession (although this option has been
implemented in an extension of the model).
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An Evolutionary Model of the Spread of Democracy and Peace
The main question remains: how well do the democracies fare in this harsh
environment? To find out, we ran systematic replications both without and with
locally dependent regime change probabilities. The experimental design features
two main phases. In an initial stage from time period 500 until time period 0, the
initial 200 states are allowed to compete. After the initial phase, technological
change is triggered and increases linearly for the rest of the simulation until time
period 10,000. At the same time, regime type is initialized by turning 10% of the
power-seeking states into democracies.
Baseline Results without Regime Change
As a reference point, this section presents runs in systems that do not feature locally
dependent regime change probabilities. This assumption mirrors the selectionbased approach adopted by Cederman (2001). Starting with 10% democracies in
the initial system at time 0, we let the states depicted in Figure 3 compete in terms
of natural selection. It soon becomes clear that in this specific sample run, the
democratic states stand no chance of long-term survival. A bit less than half-way into
the simulation run, at time period 3567, for example, the balance is tipping
decisively in favor of the three larger non-democratic states that have benefited
from technological change (see Figure 5). States that have undergone change have
capitals marked as hollow, rather than filled, squares.
Is this a typical outcome? To find out, we ran twenty replications of similar
systems, all with 10% democracies at time zero. The first result column in Table 1
presents the results of the base systems. Adding a graphical depiction of the runs,
Figure 6 illustrates the historical trajectories in terms of the democracy-dominated
territory over time.13 It becomes clear that most of the runs end up with very few
democracies at time 10,000. In fact, only 15% of the runs improve on the initial rate
of 10% democracies, and in the final system no outcome transgresses the 50% line.
The average density of democracies is .072, thus well below the average initial
value. It should be noted that the initial democratic polarity rate may deviate from
10% since the y-axis measures the territorial share of democracy.
Within the constraints of the current configuration, Kant’s perpetual peace
cannot be explained based on the mere presence of conditionally cooperating
democracies. We therefore turn to regime change processes in an effort to generate
more robustly liberal outcomes.
Adding Adaptive Regime Change
The most obvious way to study the influence of regime change is to implement a
stylized version of the transition rule described in Figure 2. Focusing entirely on
externally induced transitions, we model democratization as an S-shaped curve that
increases with the number of democracies surrounding a non-democratic state.
The falling curve specifies the probability of the opposite process. The diagram
reveals that the probability of democracy going authoritarian at .001 is about half
that indicated by the democratization curve for comparable environmental
densities.14
Based on this figure, it becomes clear that the democracies face a formidable
obstacle at the beginning of the runs. Due to the very low share of democracies in
13
To make the graphs easier to read, we suppressed short-range changes by only plotting once every 500 time
steps.
14
The calibration of these top probabilities derives from the assumption that each calendar year corresponds to
roughly 50 time periods in the simulation, which means that each run could be expected to cover 200 years. Given
this interpretation, the max probability of democratization at .1 in Figure 2 translates into .002 in the simulations.
Note also that in order to prevent regime change from being a zero-probability event at the extreme values, a small
probability .00001 has been added for all x-values.
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FIG. 5. The Sample System at Time Period 3567
TABLE 1. Replication Results
Mean democratic share
Fraction of runs 410%
Fraction of runs 450%
Number of runs
Reference to graph
Base Runs
Adding Regime Change
Adding Collective Security
.072
15%
0%
20
Figure 6
.064
15%
5%
20
Figure 8
.636
80%
65%
20
Figure 12
the initial phase, the likelihood of autocratization is much higher than
democratization. If the proportion of democracies increases beyond the lowest
values on the x-axis in Figure 7, however, a powerful positive-feedback effect sets in,
ultimately securing the world for democracy.
Having once implemented this simple rule, we turn to an exploration of its
aggregate consequences. Starting with our sample system without collective security
(see Figure 3), it can be established that locally dependent regime change continues
to frustrate the spread of the democratic peace. We again reach an outcome without
any democracies in the final grid. This result proves to be quite typical for the
behavior of the modified model, as suggested by Figure 8. Here regime change
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An Evolutionary Model of the Spread of Democracy and Peace
1.0
Democratic share of territory
0.8
0.6
0.4
0.2
0
0
2e+03
4e+03
6e+03
8e+03
1e+04
Time
FIG. 6. Simulated Democratic Share of Territory Without Regime Change or Collective Security
Probability of Regime
0.002
Probability of regime change
0.0015
0.001
0.0005
0
0
0.2
0.4
0.6
Share of democratic neighbors
FIG. 7. A Probabilistic Model of Regime Change
0.8
1
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L.-E. CEDERMAN AND K. S. GLEDITSCH
1.0
Democratic share of territory
0.8
0.6
0.4
0.2
0
0
2e+03
4e+03
6e+03
8e+03
1e+04
Time
FIG. 8. Simulated Democratic Share of Territory Without Collective Security
without collective security leads to a general downward trend starting early on. In
the overwhelming majority of the 20 runs, total or near extinction of democracy
occurs. Yet two of the histories seem to break out from the authoritarian
dominance. Clearly under these conditions, it is much harder for a democratic
zone of peace to take root than in Figure 6. Moreover, the trajectories appear to be
more volatile compared to the relatively stable trajectories in the systems without
regime change. The average democratic density at .064 lies well below the initial
rate. All in all, only 15% of the runs improved on the initial system (see the middle
data column of Table 1).
Based on the distribution shown in Figure 8, it is hard to account for democratic
configurations in the real world, such as the 50% observed in today’s international
system (see Figure 1). However, the situation changes if we reintroduce collective
security.
Adding Collective Security
Until this point, we have assumed that the democracies cannot resort to cooperative
defense mechanisms. It is conceivable that the democratic actors would do better if
they could rely on such an arrangement. Drawing on Kantian theory, Cederman
(2001) investigates both ideological alliances and collective security. Here we
content ourselves with an exploration of the latter mechanism.15 Collective security,
as implemented in the current model, mandates that all democratic states have to
aid any other democratic state involved in warfare with a non-democratic neighbor,
a ‘‘pariah’’ state, if that state is contiguous. See the appendix for details.
15
Kant’s notion of a pacific federation approximates collective security rather than a defensive alliance, cf.
Hurrell (1990). See also Cusack and Stoll (1990) for a different implementation of collective security that does not
depend on regime type.
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An Evolutionary Model of the Spread of Democracy and Peace
To better understand the operation of the collective-security mechanism, we turn
to three figures that trace the evolution of the sample run with regime change and
collective security. Figure 9 illustrates the importance of clustering as a survival
strategy. As opposed to the corresponding system without regime change, in which
the democratic peace depends crucially on conquest by large democratic states, the
current one is much less dependent on such a crude expansion process. A
comparison reveals that democratization creates more compact clusters with regime
change.
This multitude of clusters makes the democracies less vulnerable to attack. As a
matter of fact, the large state in the northeastern corner was at one point a
democratic regime, but democracy broke down early in the run. Still, in this case,
the democratic peace does not depend on this change of affairs since, aided by
collective security, the democratic states muster a common defense against pariah
states (as the one shown in darker shade).
To continue our tracing of the sample run, Figure 10 reports on the situation at a
much later stage. At that point, technological change has expanded the size of the
states. On the democratic side, however, many small states remain, including
several unitary enclaves that have been allowed to survive thanks to interdemocratic cooperation. At this point, two large authoritarian pariah states (again
shown in a dark shade) are involved in a battle with the democratic security
community.
FIG. 9. The Sample Run with Regime Change and Collective Security at Time 2805
L.-E. CEDERMAN AND K. S. GLEDITSCH
617
FIG. 10. The Sample Run with Regime Change and Collective Security at Time 6430
The fact that they ultimately fail to absorb their much smaller democratic
neighbors confirms that collective security serves a very important function in the
consolidation of the democratic peace, as illustrated by Figure 11. This is the final
outcome, which comes close to Kant’s ideal of ‘‘perpetual peace.’’ In such a uniform
system, the equilibrium is very stable, though there is a small possibility that an
occasional state could become authoritarian. Yet, due to the ‘‘peer pressure’’ from its
democratic neighbors, such a deviation from the equilibrium would be short-lived.
So far, we have only considered a single sample run. Does the addition of
collective security make any systematic difference compared to the results
generated so far (see Figures 6 and 8)? Based on replication data, Figure 12 and
the rightmost column of Table 1 reveal that the answer to this question has to be
affirmative. Together with the mechanism of alternating authority structures,
collective security assists the democracies to such an extent that 65% of them
transgress the 50% threshold. As many as 80% of the runs go beyond the 10% initial
democratic density. Here the average rate of democracy-controlled territory ends
up at an impressive .636.16
In contrast to the previous experiments, the current set of runs generates a very
large variance and rapid changes. Some of this volatility is present in the systems
16
Collective security alone without the regime change mechanism yields a very limited average improvement in
the share of democratic territory over the initial 10%, with a high degree of variation. In our replications, no final
outcome reaches more than 50% democratic-held territory, and in a majority (60 %) of the runs the share is actually
reduced.
618
An Evolutionary Model of the Spread of Democracy and Peace
FIG. 11. The Final Outcome of the Run with Regime Change and Collective Security
without collective security (see Figure 8), where reversals deviate from the upward
trend in the two runs that reach moderate levels of democratization, but with
collective security, the upward surge becomes much more significant. This effect
accentuates the path dependence and creates a bifurcation between the runs that
take off and those that fail to do so.
Above, we discussed the role of clustering as a key mechanism generating
democratic outcomes. Figure 13 offers a systematic confirmation that this effect is
much stronger in systems with democratization, and even more impressive if
collective security enters the picture. By looking at a measure of geographical
clustering, we can examine the extent to which the regime of a specific state
resembles the regimes prevailing among its neighboring countries. The Moran’s I
statistic allows testing whether observations in an observed sample cluster
significantly more geographically than would be expected under the null
hypothesis of no spatial clustering. Essentially, large values of Moran’s I indicate
geographical clustering, while values close to 0 indicate that the distribution is
random in space.17
17
More technically, the Moran’s I statistic is defined as
n
I¼P P
i
~ij
jw
X X
i
j
ðxi xÞðxj xÞ
~ij P
:
w
Þ2
i ðxi x
For a set of n spatial units, we define an n n connectivity matrix W to represent the hypothesized pattern of
dependence. An entry wi; j is assigned a non-zero value if the two units are hypothesized to be dependent on one
619
L.-E. CEDERMAN AND K. S. GLEDITSCH
Democratic share with collective security
1.0
0.8
0.6
0.4
0.2
0
0
2e+03
4e+03
6e+03
8e+03
1e+04
Time
FIG. 12. Simulated Democratic Share of Territory with Regime Change
Using averages of Moran’s I statistic across the 20 replications as a measure of
global clustering, the diagram in Figure 13 compares all three configurations of the
different assumptions. Advancing from the bottom, the curves represent replications in the base system, systems with regime change, and finally those with both
regime change (see the hollow dots) and collective security (marked with filled
dots). It is obvious from Figure 13 that all runs exhibit significant spatial clustering.
However, the extent of spatial clustering is much stronger in the systems that
include contextual regime change processes. As expected, collective security also
appears to have an additional effect on global clustering.
Interestingly, the trend in geographical clustering over time in the run with
regime change resembles the observed historical trends in the international system
since 1816. In fact, Moran’s I for the spatial clustering in regime type based on the
Polity data starts close to zero in the late 19th century, but then grows to levels
above .5 around 1920. After a falling trend until the late 1950s, following the
expansion of the number of states with decolonization, the extent of geographical
clustering increases and has at the end of the 1990s reached levels nearly as high as
in the 1920s. Figure 13 indicates that regime change is necessary to reach levels of
clustering comparable to those observed in the empirical data.
~ij denotes an element
another. In the above, xi indicates the individual observations on the variable of interest, and w
e where each row i sum to 1. Moran’s I is not bounded by 1, and
[i, j] of a row standardized connectivity matrix W
the expected value E(I) is 1=ðN 1Þ rather than 0. The ratio of Moran’s I to its estimated standard error allows
testing whether the extent of geographical clustering is statistically significant. The expected value of the variance of
Moran’s I depends upon sampling assumptions, see Cliff and Ord (1973:15).
620
An Evolutionary Model of the Spread of Democracy and Peace
0.8
Regime change &
Collective Security
Average Moran’s I
0.6
Regime change
0.4
0.2
Base runs
0
0
2e+03
4e+03
6e+03
8e+03
1e+04
Time
FIG. 13. Average Global Clustering in the Three Series of Replications
Conclusion
The computational experiments have told us that natural selection by itself is
unlikely to generate realistic-looking trajectories capturing the historical origins of
the democratic peace. This strengthens the case against liberal theories relying
exclusively on Darwinian evolution (and probably against realist theories of the
same type as well). Qualitative analysis, such as that offered by Wendt (1999),
stresses that evolutionary speed in social settings depends crucially on culturalselection mechanisms, such as imitation and learning, but without formal tools, it
is hard to reach firm conclusions about the balance between natural and cultural
evolution. With a computational model, however, the dynamic properties of simple
adaptive processes can be scrutinized more precisely through experiments
conducted in artificial worlds.
Adaptive regime-type change appears necessary to generate the powerful tipping
phenomena that characterize the waves of democratization. Initially, this contextual
mechanism makes it harder for a small concentration of democracies to survive due
to the pressure from a mostly non-democratic environment. Nevertheless, should
the process overcome this obstacle, a powerful positive feedback process that makes
the world safe for democracy sets in.
An especially strong tendency toward local clustering, accelerated by the
contextual rule of regime change, helps tip the process toward liberal outcomes.
As expected by Kant, however, some type of defensive arrangement among the
democracies is also required to get to the point of democratic take-off. For sure, the
collective-security mechanism proposed in this article exaggerates the historical
L.-E. CEDERMAN AND K. S. GLEDITSCH
621
effectiveness of such defenses. For example, Britain and France failed to defend
Czechoslovakia and Poland against Hitler’s Germany in the late 1930s. Yet, much of
the American containment of the Soviet Union during the Cold War can be
interpreted as a version of collective security. Whether exaggerated or not, there
was a keenly felt concern that a non-linear process might set in were a West
European country to ‘‘fall’’ to communism, such as Italy.18 In the end, of course,
something resembling the predicted domino effect did play out in Eastern Europe,
although the regimes that toppled one after the other were the seemingly stable
socialist autocracies rather than fragile democracies (e.g., Kuran, 1991; Starr, 1991).
To the extent that the current collective-security mechanism overstates the
defensive capacity, an explanation of the impressive trend toward the democratic
peace would have to be viewed as fortuitous or otherwise explained by adding
other mechanisms. The contingency of world history should not be understated.
For example, it is not inconceivable that Hitler could have won WWII.
Nevertheless, it seems reasonable to search for supplementary explanations.
Already Kant suggested that the democracies may benefit from a more efficient
state–society nexus that generates superior levels of wealth. Moreover, it has been
suggested that democratic states are more efficient war-fighters (e.g., Lake, 1992).
It should also be recalled that, in the name of analytical simplicity, we have made no
assumptions about the influence of warfare on the changes of regime change in
either direction. Finally, idiosyncratic geopolitical factors relating to the strength of
some of the initial democracies (e.g., France, Great Britain, and the U.S.A.), and
their insular position (Great Britain and the U.S.A.), may have helped these
democracies to survive long enough for the waves of democratization to set in.19
Although we leave these additional mechanisms for future research, it should be
noted that they could all be studied within the current computational framework.
Despite this relative lack of realism, we believe that the agent-based approach
elucidates important aspects of the emerging democratic peace by adding analytical
rigor to qualitative attempts to capture the process. Like Schelling’s (1978) famous
model of neighborhood segregation, our findings illustrate that it is possible to
generate dramatic outcomes at the systemic level by assuming that individual actors
adapt to the local context. While our formalization differs by letting the actors
change their characteristics in response to environmental signals rather than move
to another area, both models feature ripple effects that propagate through the
system and generate strong spatial patterns (see also Watts, 2003:ch. 8). It is difficult
to see how a democratic security community could emerge solely from a link
between development and democracy or from democracies not fighting one
another. Our approach highlights plausible mechanisms and conditions that allow
the systemic democratization process to emerge. Future computational research,
aided by even more fine-tuned empirical calibration, may help filling in the gaps in
our account of how the democratic peace originated in the international system.
Appendix: Detailed Model Specification
The model is based on a dynamic network of relations among states residing in a
square lattice. Primitive actors live in each cell of the grid and can be thought of as
the basic units of the framework. Although they can never be destroyed, many of
them do expand territorially. This also implies that some of them can lose their
sovereignty as other actors come to dominate them hierarchically.
18
Obviously, these observations refer to non-contiguous democracies. The fact that strong democracies can
project their power beyond their immediate neighbors renders the democratic peace more likely in the long run.
The current model could be extended to encompass this possibility.
19
It could even be argued that the insular position helped these countries to retain, or develop, democratic
institutions (see Hintze, 1975; Barzel and Kiser, 1997).
622
An Evolutionary Model of the Spread of Democracy and Peace
All actors, whether primitive or compound, keep track of their geopolitical
context with the help of a portfolio holding all of their current relationships. These
can be of three types:
territorial relations point to the four territorial neighbors of each primitive
actor (north, south, west, and east).
interstate relations refer to all sovereign neighbors with which an actor
interacts.
hierarchical relations specify the two-way link between provinces and
capitals.
Whereas all strategic interaction is located at the political level, territorial
relations become important as soon as structural change happens. Combat takes
place locally and results in hierarchical changes that will be described below. The
order of execution is quasi-parallel. To achieve this effect, the list of actors is
scrambled each time structural change occurs. The actors keep a memory of one
step and thus in principle make up a Markov process.
In addition to a model-setup stage, the main simulation loop contains six phases
that will be presented in the following. In the first phase, the actors’ resource levels
are calculated. In the second phase, regime change takes place. Then they allocate
resources to their fronts followed by a decision procedure, during which they decide
on whether to cooperate or defect in their neighbor relations. The interaction phase
determines the winner of each battle, if any. Finally, the structural change procedure
carries out conquest and other border-changing transformations.
To help the reader identify the model parameters, Table A1 provides a summary
of their name, function, and value.
Model Setup
At the very beginning of each simulation, the square grid with dimensions
nx ¼ ny ¼ 50 is created and populated with a preset number of composite actors:
initPolarity ¼ 200. The algorithm lets these 200 randomly located actors be the
founders of their own compound states, the territory of which is recursively grown
to fill out the intermediate space until no primitive actors remain sovereign.
Resource Updating
As the first step in the actual simulation loop, the resource levels are updated. The
simple ‘‘metabolism’’ of the system depends directly on the size of the territory
controlled by each capital. It is assumed that all sites in the grid are worth ten
resource units. A sovereign actor i begins the simulation loop by extracting
resources from all of its provinces. It accumulates a share of these resources
determined by a distance-dependent logistical function f (see Figure 4 above):
fðdÞ ¼ offset þ ð1 offsetÞ=f1 þ ðd=dist tÞ^ ðdist cÞg
where 04 offset 41.0 sets the flat extraction rate for long distances. In all runs
reported on, in this article, it is fixed at .1. The location of the threshold is
determined by dist_t ¼ 2, and the slope by dist_c ¼ 3 (higher numbers imply a
steeper slope). Thus, the extraction rate is 100% for small distances, but because of
technological constraints, it falls rapidly to the flat part of the function beyond the
threshold. In addition, the battle damage is cumulated for all external fronts (see
the interaction module below). Finally, the resources of the actor res(i, t) in time
period t can be computed by factoring in the new resources (i.e., the nondiscounted resources of the capital together with the sum of all tax revenue plus the
total battle damage) multiplied by a fraction resChange ¼ .01. This small amount
assures that the resource changes take some time to filter through to the overall
L.-E. CEDERMAN AND K. S. GLEDITSCH
623
TABLE A1. A Summary of the Model Parameters
System parameters
nx, ny
initPolarity
initPeriod
propDem
propMobile
pDropCampaign
pAttack
pDeactivate
pTwoFront
sup_t,sup_c
vic_t,vic_c
propDamage
pOblig
Description
Values
Dimensions of the grid
Initial number of states
Length of initial period
Share of democracies in initial grid
Share of mobile resources to be allocated as opposed
to fixed ones
Probability of shifting to other target state after battle
Probability of entering alert status
Probability of leaving alert status
Probability of opening second front
Superiority criterion (logistical parameters t and c)
Victory criterion (logistical parameters t, c)
Share of damage inflicted on opponent
Probability of democratic states’ fulfilling their collective
security obligation
50 50
200
500
.1
.9
.2
.01
.1
.01
3.0, 20
3.0, 20
.1
.5
resource level of the state:
tax ¼ 0
for all provinces j of state i do
tax ¼ tax þ fðdistði; jÞÞ
totalDamage ¼ 0
for all external fronts j do
totalDamage ¼ totalDamage þ damageðj; iÞ
resði; tÞ ¼ ð1 resChangeÞ resði; t 1Þ þ
resChange ð1 þ tax totalDamageÞ
In order to simulate technological development, the threshold of the distance function
f(d) is gradually shifted outward starting with dist_t ¼ 2 up to 22 as a linear
function of simulation time. This shift represents the state of the art of technological
change with which each state catches up with a probability pShock ¼ .0001 per time
period. This probability is contextually independent of the strategic environment.
Regime Change
The process of regime change starts after the transitory period, lasting
initPeriod ¼ 500 steps, has been completed. After this initial phase, the regime
types are allocated according to the parameter propDem ¼ .1 which stipulates what
proportion of the states are going to be democratic. From this point, the regime
type of a state will shift from democracy to authoritarian rule or vice versa with a
small probability that depends on the political context of the state. The probability
of non-democratic states going democratic increases as an S-shaped function
dem(d) of the share d of democratic states among their neighbors (see Figure 9):
demðdÞ ¼ :002 ð:2 d þ ð1 :2 dÞ=f1 þ ðd=:6Þ^ 5gÞ þ :00001
Similarly, the opposite transition probability varies as a function aut(a) where
a ¼ 1 d is the proportion of non-democratic neighboring states:
autðaÞ ¼ :001 ð:2 a þ ð1 :2 aÞ=f1 þ ða=:6Þ^ 5gÞ þ :00001
Note that the democratization curve dem(d) approaches twice as high a maximum
value (.002) as the opposite curve aut(a). Figure 9 offers a graphical illustration of
624
An Evolutionary Model of the Spread of Democracy and Peace
these two functions where the upward-sloping curve is dem(d) and the downwardsloping one aut(a).
Resource Allocation
Before the states can make any behavioral decisions, resources must be allocated to
each front. For unitary states, there are up to four fronts, each one corresponding
to a territorial relation.20 Resource allocation proceeds according to a hybrid logic.
A preset share of each actor’s resources is considered to be fixed and has to be
evenly spread to all external fronts. Yet, this scheme lacks realism because it
underestimates the strength of large actors, at least to the extent that they are
capable of shifting their resources around to wherever they are needed. The
remaining part of the resources, propMobile ¼ .9, are therefore mobilized in
proportion to the opponent’s local strength and the previous activity on respective
front. Fungible resources are proportionally allocated to fronts that are active (i.e.,
where combat occurs), and also for deterrent purposes in anticipation of a new
attack. Resources are always allocated under the assumption that no more than one
new attack might happen.
For example, a state with 50 mobile units could use them in the following way
assuming that the five neighboring states could allocate 10, 15, 20, 25, and 30,
respectively. If the previous period featured warfare with the second and fourth of
these neighbors, these two fronts would be allocated 15/(15 þ 25) 50 ¼ 18.75 and
25/(15 þ 25) 50 ¼ 31.25. Under the assumption that one more war could start,
the first, third, and fifth states would be allocated respectively: 10/(15 þ 25
þ 10) 50 ¼ 10, 20/(15 þ 25 þ 10) 50 ¼ 20, and 30/(15 þ 25 þ 10) 50 ¼ 30.
Formally, resource allocation for state i starts with the computation of the fixed
resources for each relationship j. A preset proportion of the total resources res are
evenly spread out across the n fronts:
fixedRes ði; jÞ ¼ ð1 propMobileÞ res=n
Note that democracies mobilize only against non-democratic neighbors, which
means that in those cases, n stands for the number of fronts with authoritarian
states. The remaining part mobileRes ¼ propMobile * res is allocated in proportion to the activity and the strength of the opponents. To do this, it is necessary to
calculate all resources that were targeted at actor i:
X
enemyRes ðiÞ ¼
fjg fres ðj; iÞg
Again, democratic states do not need to factor in neighboring democracies’
resources, which are therefore excluded from enemyRes. The algorithm of actor i’s
allocation can thus be summarized:
for all relations j do
in case enemyRes ðiÞ ¼ 0 then ½actor not under attack res ði; jÞ ¼ fixedRes ði; jÞ þ mobileRes
in case i and j were not fighting in the last period then
resði; jÞ ¼ fixedResði; jÞ þ rðj; iÞ=enemyResðiÞ mobileRes
in case i and j were not fighting the last period then
resði; jÞ ¼ fixedResði; jÞþ
rðj; iÞ=ðenemyResðiÞ þ rðj; iÞÞ mobileRes
20
We have chosen to model bounded worlds without wrap-around borders since all known geopolitical systems
have fixed borders except for the globe as a whole.
L.-E. CEDERMAN AND K. S. GLEDITSCH
625
Decisions
Once each sovereign actor has allocated resources to its external fronts, it is ready to
make decisions about future actions. This is done by recording the front-dependent
decisions in the corresponding relational list. As with resource allocation, this happens
in quasi-parallel through double-buffering and randomized order of execution.
All states start by playing unforgiving ‘‘grim trigger’’ with all their neighbors. Because
democracies never attack states with the same regime type, such relationships will
remain peaceful. If the state decides to try an unprovoked attack, a randomly chosen
potential victim j0 has to be selected. In addition, a battle-campaign mechanism
stipulates that the aggressor retains the current target state as long as there are provinces
to conquer unless the campaign is aborted with probability pDropCampaign ¼ .2. This
rule guarantees that the conquering behavior does not become too scattered. Normally,
states refrain from opening new fronts if they are already engaged in combat, but this
rule is overridden with probability pTwoFront ¼ .001.
A contextual activation mechanism ensures that the actors can be in either an
active or inactive mode depending on the combat activity of their neighbors.
Normally, the states are inactive, which means that they attempt to launch
unprovoked attacks with a probability pAttack ¼ .01. If they or their neighboring
states become involved in combat, however, they automatically enter the active
mode, in which case they contemplate unprovoked attacks in every round. Once
there is no more action in their neighborhood, they reenter the inactive mode with
probability pDeactivate ¼ .1 per round.
The actual decision to attack depends on a probabilistic criterion p(i, j 0 ) which
defines a threshold function that depends on the power balance i’s favor (see
below). If an attack is approved, the aggressor chooses a ‘‘battle path’’ consisting of
an agent and a target province. The target province is any primitive actor inside j 0
(including the capital) that borders on i. The agent province is a province inside
state i (including the capital) that borders on the target. In summary, the decision
algorithm of a state i can be expressed in pseudo-code where the underlined square
brackets pertain to democratic states:
Decision rule of state i:
for all external fronts j do
if i or j played D in the previous period then
act ði; jÞ ¼ D
else
act ði; jÞ ¼ C
½ Grim Trigger if there is no action or with pTwoFront and
with pAttack or if in alerted status or campaign then
if ongoing campaign then
select j0 as the ongoing campaign
else if state i is democratic
select random nondemocratic neighbor j0
else
select random neighbor j0
with pði; j0 Þ do
change to act ði; j0 Þ ¼ D ½ launch attck against j0 randomly select target ði; j0 Þ and agent ði; j0 Þ
campaign ¼ j0
626
An Evolutionary Model of the Spread of Democracy and Peace
Note that the democracies’ exclusion of democratic victims implements the
democratic peace at the micro-level.
The precise criterion for attacks p(i, j 0 ) remains to be specified. The current
version of the model relies on a stochastic function of a logistic type. The power
balance plays the main role in this calculation:
balði; j0 Þ ¼ fðdÞ resði; j0 Þ=ffðd0 Þ ðresðj0 ; iÞg:
where f(.) is the distance function described above and d and d 0 the respective
distance from the capitals of i and j to the combat zone. This discounting
introduces distance-dependence with respect to power projection.
Hence, the probability of an unprovoked attack can be computed as:
pði; j0 Þ ¼ 1=f1 þ ðbalði; j0 Þ=sup tÞ^ ðsup cÞg
where sup_t ¼ 3.0 is a system parameter specifying the threshold that has to be
transgressed for the probability of an attack to reach .5, and sup_c a tunable
parameter that determines that slope of the logistic curve which is set at 20 for the
runs reported in this article.
Interaction
After the decision phase, the system executes all actions and determines the
consequences in terms of the local power balance. The outcome of combat is
determined probabilistically. If the updated local resource balance bal(i, j 0 ) tips
far enough in favor of either side, victory becomes more likely for that party. In the
initial phase, the logistical probability function q(i, j 0 ) has the same shape as the
decision criterion with the same threshold set at vic_t ¼ 3 and with an identical
slope: vic_c ¼ 20:
qði; j0 Þ ¼ 1=f1 þ ðbalði; j0 Þ=vic tÞ^ ðvic cÞg
This formula applies to attacking states. In accordance with the strategic rule of
thumb that an attacker needs to be about three times as powerful than the defender
to prevail, the defender’s threshold is set to 1/vic_t ¼ 1/3.
Each time-step of a battle can generate one of three outcomes: it may remain
undecided, one or both sides could claim victory. In the first case, combat continues
in the next round due to the grim-trigger strategy in the decision phase. If the
defending state prevails, all action is discontinued. If the aggressor wins it can
advance a claim, which is recorded and processed in the structural change phase.
The interaction phase also generates battle damage, which is factored into the
overall resources of the state as we saw in the resource updating module. If j
attacks state i, the costs incurred by j corresponds to propDamage ¼ 10% of j ’s
locally allocated resources: .1 * res(j, i). The total size of a war is the cumulative
sum of all such damage belonging to the same conflict cluster.
Structural Change
Structural change is defined as any change of the actors’ boundaries. This version
of the framework features conquest as the only structural transformation, but other
extensions of the modeling framework include secession and voluntary unification.
Combat happens locally rather than at the country level, as in Cusack and Stoll
(1990). Thus, structural change affects only one primitive unit at a time. The
underlying assumption governing structural change enforces states’ territorial
contiguity in all situations. As soon as the supply lines are cut between a capital and
its province, the provinces becomes independent. Claims are processed in random
order, which executed conquests locking the involved units in that round.
L.-E. CEDERMAN AND K. S. GLEDITSCH
627
The units affected by any specific structural claim are defined by the target
(i, j) province. If it is
a unitary actor, then the entire actor is absorbed into the conquering
state,
the capital province of a compound state, then the invaded state
collapses and all its provinces become sovereign,
a province of a compound state, then the province is absorbed. If, as a
consequence of this change, any of the invaded states’ other provinces
become unreachable from the capital, these provinces regain sovereignty.
Collective Security
The collective security mechanism follows as a third, additional step after the
alliance formation phase imposing additional combat obligations on democratic
states. If a democratic state k gets engaged in a conflict with a non-democratic state
j, the latter is declared a ‘‘pariah’’ state as long as combat continues. Provided a
democratic state borders on such a state, it is under the obligation to launch an
unconditional attack against the pariah. This is done by extending the if-clause that
implements alliance obligations:
Modified decision rule for a democratic state i with collective security:
for all external fronts j do
if i or j played D in the previous period then
actði; jÞ ¼ D
else if j attacked an ally of i or j is pariah then
with pOblig do act ði; jÞ ¼ D
else
act ði; jÞ ¼ C ½ Grim Trigger unprovoked attacks against non-democracies as in the standard rule
This rule makes sure that all democracies, regardless of whether they feel
sufficiently superior to attack or not, will contribute to the defense of the
democratic security community. The effectiveness of this mechanism is discounted
by the probability pOblig ¼ .5, which stipulates the probability of a democratic
state’s fulfilling its collective-security obligation.
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