We construct a majority cellular automata based model to explain the power-law signatures in Indonesian general election results. The understanding of second-order phase transitions between two different conditions inspires the model. The democracy is assumed as critical point between the two extreme socio-political situations of totalitarian and anarchistic social system - where democracy can fall into the twos. The model is in multi-party candidates system run for equilibrium or equilibria, and used to fit and analyze the three of democratic national elections in Indonesia, 1955, 1999, and 2004

Situngkir, Hokky

Surya, Yohanes

English

arXiv

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Democracy: Order out of Chaos

Cognitive Sciences ePrint Archive

Democracy: Order out of Chaos 
Understanding Power-Law in Indonesian Elections  
 
 
 
Hokky Situngkir 
(hs@compsoc.bandungfe.net) 
Dept. Computational Sociology 
Bandung Fe Institute 
Yohanes Surya 
(yohaness@centrin.net.id) 
Dept. Physics 
Universitas Pelita  Harapan 
 
 
 
 
Abstract 
We construct a majority cellular automata based model to explain the power-law 
signatures in Indonesian general election results. The understanding of second-order 
phase transitions between two different conditions inspires the model. The democracy is 
assumed as critical point between the two extreme socio-political situations of totalitarian 
and anarchistic social system – where democracy can fall into the twos. The model is in 
multi-party candidates system run for equilibrium or equilibria, and used to fit and 
analyze the three of democratic national elections in Indonesia, 1955, 1999, and 2004.  
Keywords: majority cellular automata, phase transitions, power-law, elections. 
 
 
 
 
 
 
1. Our understanding on Democracy 
What is democracy? If each citizen can vote the leaders or representatives 
according to her own opinion, can the result of the voting or election show the sense of 
democracy? For some democratic transitional countries, the questions are very important 
to have answers, since a ‘democratic election’ is believed to be the very first step to a 
democratic regime.  
In recent work, Situngkir & Surya (2004) proposed an alternative way to extract 
information from the data of the general election in Indonesia and showed the clustering 
among political parties based upon the political stream realized as the fundamental for 
each political party. The political actions based on ideological streams in Indonesia have 
been accepted even since the first democratic election 1955 (Feith, 1970). The fact 
 2 
implies that the success of a political party depends upon the networks of the social 
organizations circling certain political parties.  
The voters are not very free even in the democratic regime, since individual 
choices depend very much on the choices of the social networks where the voter 
embeds. However, this is natural for human being, since the different social identities 
may result social tensions, thus the micro-social is attracted to reduce the tensions by 
adjusting the political choices or ideological streams (Lustick & Miodownik, 2002).  
The probability of a newborn political party to become majority is extremely hard 
but may occur in strangely special occasions. There have been some agent-based and 
Monte-Carlo models on how a minor political candidates can eventually gain a significant 
votes, e.g. Sznajd model (Stauffer, 2001) that simulating based on the Ising spin model – 
in the spatial model, certain number of agents persuade their neighbors to have the same 
political choices. In the other hand, some models inspired from the cellular automata 
showed some different rule patterns to understand social complex dynamics 
(Hegselmann & Flache, 1998). Moore (1996) shows some computational facts of such 
majority-vote 3-dimensional cellular automata dynamics. 
The paper presents a little modification on majority vote cellular automata. The 
basic idea is to understand the microstructure of voters whose macro-properties showed 
facts on political streams turning out from the circling of societal identity. We construct 
the spatial model of virtual world in which agents choices depend much on the political 
streams of neighbors. Eventually, we showed that the numbers of neighbors become 
important variables presenting the macro-properties showing democracy as a critical 
situations among the extreme totalitarianism and anarchic society.  
 
2. The Locality of the Voters Model to the Landscape of Voting 
Individual voter is symbolized as a cell or square lattice located at a two-
dimensional virtual world of nyx ,...,1, =  and she chooses any political party 
of },...,,{ 21 mcccCc =∈ , where m is the number of candidates. Aggregately, all voters 
choose ci can be stated as: 
 
∑=
yx
yxc
ici
tvtV
,
, )()(       (1) 
 
 3 
The change of votes (states) from one choice to another as a transformation from t to 
t+1: ( )r
jjyxyx
tvtvftv
1,,
)(),()1( ==+      (2) 
iyx ctv =+ )1(,  iff [ ] ⎟⎠⎞⎜⎝⎛ ⊕= = mrjjyxi tvtvc 11, )()(max   (3) 
or [ ]r
jjtyxyx
tvvmajoritytv
1)(,,
)(,)1( ==+     (4) 
where j  is the neighbor index, and r is the number of the neighbors. In other words, the 
changes of the states depend on the recent states of immediate neighbors and her own. 
For each neighbourhood of the adjacent cells, the next state of certain cell is decided by a 
majority vote among herself and the neighbours. The neighbours, conducting as the 
political circle around individuals force agent to change her state to the majority state. 
Technically, we use several modes of neighbourhood, as described in figure 1.  
 
 
 
 
 
 
 
 
The more the number of the neighbors, the less the political freedom owned by an agent.  
Consequently, the probability of changes to certain political parties, c, is 
ic
i tV
tVcc
)(
)()Pr( ∆=→       (5) 
where 
 
iii ccc
tVtVtV )()1()( −+=∆      (6) 
as the addition or subtraction of voters in each round of the game.  
Eventually, the virtual world where the voters laid on consists of lattices and 
grids, while the global view is more like a torus (figure 2); the lowest two-dimensional 
grids are pasted together with the highest, and the right grids with the left one.  
 
Figure 1 
Various type of neighborhood (left-right): Von Neumann, Moore, extended Moore (4 
added), extended Moore (12 added) neighborhood.  
 4
 
 
 
 
 
 
 
 
 We do several simulations by using the rule explained above and discover that 
after several iterations the lattices are clustered altogether with neighborhood votes for 
the same choices (figure 3) – we denote it as an equilibrium condition (or equilibria1) that 
sensitive to the initial condition since the square lattices are not going to changes any 
further.   
 
 
 
 
 
 
 
 
 
 
Along the iterations, the square lattices organize themselves to the equilibrium. An 
example of our simulations is described in figure 4. The self-organized square lattices run 
for the equilibrium, states in which we can count as voting process; the voters organized 
themselves concerning their own choices and their neighbor’s. 
  
3. Democracy beyond totalitarian and anarchistic society 
There are two extreme situations for each agent, i.e.: a totalitarian state in which 
every individual agent will turn to one totalistic state and in the other hand an anarchistic 
state in which individual does not take care about what her neighbors on their political 
choices – nobody count on the state. We can recognize the first extreme representation 
                                                 
1 Several initial conditions do not stop at certain eventual condition but wavy or fluctuating tallies.   
Figure 2 
The torus as the model of the virtual political world 
Figure 3 
The initial condition (uniformly distributed votes among people) and the eventual one 
(clustered votes among people) for 20 competitive political parties. 
 5
in a result of election of only one majority and the second one of uniformly distributed 
political choices that are no clustering among agents (figure 5). 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Thus, the born of a nation state can be understood as the way to dim the societal anarchy 
begun from the social contract among citizens (Rousseau, 1762; Hobbes, 1651). 
However, too much endeavor on damping the societal anarchy, the state may emerge the 
totalitarianism – a democratic state can turns out to be totalitarianism of majority rule 
(Tocqueville, 1840) or a dictator bureaucracies from the lack balances in governmental 
powers (Situngkir, 2003). Democracy is then laid in critical points between those two 
extreme situations. If the transitional phases from the anarchistic society to the 
totalitarian one are seen as second order phase transition, then we can say that the most 
critical system between the two extreme phases are the democracy – in a democratic 
election the citizens have the property of sustainable self-organized criticality. Second 
order transitions are transitions in a more gradual sense - on one side of the transition, a 
system is typically completely disordered, but when the transition is passed, the system 
does not immediately become completely ordered. Instead, its order increases gradually 
and evolves as the parameter is varied (Wolfram, 2002:981). 
Since the transition from the two extreme phases represents the transition from a 
disorder level to the order one, then logically the critical points of democracy emerge the 
power-law properties (Schuster, 70-72).  The understanding of the transitional states as 
an impact of self-organized in critical situations can be used in the analysis of statistical 
Figure 4 
The ranked tallies of political parties in each round from 200 iterations over 100x100 square 
lattices of agents. It begins from the uniform distribution and eventually distribution 
presenting certain slope.  
 6
properties of election results in some countries like Indonesia to see how the nation state 
passes such transitions to assemble a more democratic system (Situngkir, 2004).  
 
 
 
 
 
 
 
  
 
 
 
Furthermore, in micro level the two extreme situations can be represented by using the 
parameter of the number of neighbors influencing a voter. In the first phase, the society 
is in the anarchistic social system, the average number of neighbors, denoted as r, can 
influence social agent is at the minimum ( 0→r ) – agent acts and chooses the political 
state as she wants it to be privately and no social consensus exists. In the second phase, 
the totalitarianism rules in the society and there is only one majority since in the micro-
level the agents are forced to have the uniform political streams by referencing the 
majority of the global ( ∞→r ).  Henceforth, the highest-level democracy lays in certain 
critical points of ∞<<<< r0 , of the power-law exponent around the unity, ( ∞≠slope  
as vertical line and 0≠slope  as horizontal line in the log-log plot). 
 
4. Simulations and Discussions 
As described in detail in Situngkir & Surya (2004), voters cluster in social 
institutions and organizations become the micro-property of nation-ship in Indonesia 
and shape the statistical properties of Indonesian election. This is the nature of 
Indonesian voters. The totalitarianism exists on the microstate depends on the global 
majority of the political system and the anarchistic society depends on the local majority 
of agents. Therefore, theoretically we can justify how statistically we have the mean of 
three democratic election ever had in Indonesia, 1955, 1999, and 2004. The normalized 
ranked votes on political parties in the three elections are different in the fitted slopes 
concerning the number of neighbors of each. The election 1955 as the most democratic 
Figure 5 
Recognizing the political situation (whether totalitarian - represented by dotted 
line - or anarchistic - represented by solid line) from the ranked political parties 
in the whole population. 
 7
election ever had in Indonesia is fitted with the von Neumann and Moore neighborhood 
while the 1999 with both of the extended Moore we use in simulation. The election of 
2004 is fitted with the 2-agents neighborhood; an interesting result as compared to the 
recent political issues grew in the election 2004. All of the simulations conducted employ 
100x100 square lattices run up to 200 iterations. 
 
 
 
 
 
 
 
.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 6 
The normalized simulated data and the normalized real ranked tallies of political parties from 
the election 1955, 1999, and 2004 in log-log plot – different in number of neighbors. 
 8
However, the three election results reflect a self-organization among Indonesian 
voters to have democracy by holding general elections. The three figures plotted in the 
ranked political votes show us the evolution of the democracy in Indonesian nation-wide. 
Furthermore, we can see it from the figures how democracy grows based on different 
institutionalized ideological-streams and social identities. 
 
5. Concluding Remarks 
We present a spatial model captured the evolution of socio-political system 
evolves to democratic state. A fair and just election is an important milestone and 
important moment for every country to have national democracy. The spatial model 
presented incorporates the square lattices or cellular-automata based modeling. It is 
shown also that democracy can be assumed as critical points of self-organized agents in 
the transition from anarchistic society to the totalitarian one.  
The model is implemented to the result of three democratic general elections 
held in Indonesia. The three national elections result the power-law signatures and fit 
with different types of neighborhood. Theoretically, the microstates of macro-properties 
transition of order to disorder and totalitarian to anarchistic can be approached as type of 
neighborhood chosen in the virtual world of social simulations.  
The model can be useful to explain the power-law signature found in election 
results in Indonesia and furthermore to see how a democratic harmony evolves through 
heterogeneous social identities.  
 
 
Acknowledgement 
The authors thank Tiktik Dewi Sartika for discussions on Sznajd model and Surya 
Research Int’l. for funding the research. All faults remain the authors. 
 
Works Cited 
 
Feith, H. (1970). Indonesian Political Thinking 1945-1965. Cornell University Press. 
 
Lustick, I. & Miodownik, D. (2002). “The Institutionalization of Identity: Micro 
Adaptation, Macro Effects, and Collective Consequences”. Studies in Comparative 
International Development  37(2):24-53.  
 
 9
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Simulations 1(3). URL: http://www.soc.surrey.ac.uk/JASSS/1/3/1.html.  
 
Hobbes, Thomas. (1651). Leviathan. Re-print in Ebenstein, William. (1960). Great 
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Completeness. Working Paper 96-08-060, Santa Fe Institute.  
 
Rousseau, Jean Jaques. (1762). The Social Contract. Re-print in Ebenstein, William. 
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Schuster, H. G. Deterministic Chaos: An Introduction 3rd ed. VCH.  
 
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Tocqueville, Alexis de (1840), Democracy in America I, transl. Henry Reeve, The 
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