can democratic innovations improve the performance of representative governments? an agent based...

7/23/2019 Can Democratic Innovations Improve the Performance of Representative Governments? An Agent Based Model Ap

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Can Democratic Innovations Improve the Performance

of Representative Governments? An Agent Based Model

Approach

Vicente Ros, Vctor Garca

August 30, 2015

Abstract

In this study we investigate emergent legislative dynamics in a variety of political systems by

means of Monte Carlo simulations of agent based models. We find that Representative Government

systems solely organized around political parties generate higher social welfare in scenarios of sim-

ple majorities than in the case of absolute majorities. We also explore the behavior of Participatory

Democracy systems that combine political parties and direct citizen participation in the legislative

process. At this regard, we find that Participatory Democracy systems outperform Representative

Government systems in terms of legislative quality and deliver lower volatility. A remarkable feature

of Participatory Democracy systems is that they display an inverted U-shaped pattern between the

power share of citizens in the parliament and the social gains generated by the legislative process.

Finally, we explore the performance of a bicameral setting, the Citizen Senate, where citizens are

allocated in the second political chamber and have the ability to veto proposals stemming from

the political chamber conformed by political parties. In order to compare and evaluate the per-

formance of the various political systems we take into account different attitudes towards politicaluncertainty by integrating the results obtained within a representative agent utility analysis. We

find that risk averse profiles will penalize severely the instability of legislative outcomes associated

to Representative Government systems.

Keywords: Agent based models, Democracy, Participation, Representative Government.


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1 Introduction

In a recent study analyzing social protests occurring over the period ranging from 2006 to 2013 in 87

countries covering 90% of world population, Ortiz et al. (2013) show that one of the main grievances

and causes of outrage is the failure of political representation of the current political systems. Their

most relevant finding is the overwhelming demand for a real democracy. Moreover, they find that

the crisis of political representation affects not only authoritarian governments but also representative

regimes of developed countries. In this context, we find that it is especially relevant to analyze the

performance of alternative political systems that may involve actively citizens in the decision making

process. To that end, we use agent based modeling techniques to simulate and approximate the

functioning of various prototypical political systems.

According to classical political theory, there are two main parameters that allow the characterization

of any political system. The first one is the degree of distribution or concentration of political power

among the agents populating the political system. Along this dimension, Aristotle (350 B.C) developed

a first taxonomy of political models taking into account its pure and degenerated form. Monarchies

and tyrannies are characterized as political systems in which political power achieves its maximum

concentration level since it is vested in a single individual. With a lesser degree of concentration,

aristocracies and oligarchies are political systems where power is in the hands of a few. On the contrary,

democracies and oclocracies describe political systems characterized by egalitarian distributions of

political power among agents. The second key parameter is the selection mechanism of legislators.

At this regard, Montesquieu (1748) and Aristotle (350 B.C) among others, argued that lotteries

were typical of democracies while election by suffrage was typical of oligarchies or aristocracies. In a

detailed historical review Manin (1997) shows that the three main mechanisms to select representatives

define prototypical political regimes in a historical context. Blood heritage is the mechanism typically

associated to Monarchies, elections are related to oligarchic Representative Governments (RG) and

lotteries are associated to Democracies (D).

Table 1: Political Regimes and Selection Mechanisms

Political Regime Procedure Historical Application

Autocracy Blood Heritage European Absolute Monarchies, 15th to 19th century A.COligarchy Elections, suffrage Representative Governments, 19th to 21st century A.CDemarchy Lotteries Athenian Democracy, 5th and 4th centuries B.C

Therefore, RG1 regimes where political power is concentrated in few professional politicians selected

1The characteristics that define RG systems are four:i) the governors are elected by the governed at regular intervalsby means of suffrage, ii)rulers organized in political parties preserve independence from the governed in a range of

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by suffrage and organized around parties contrast markedly with democracies, characterized by egal-

itarian distributions of political power and by the fact that their legislators were selected by lotteries

on a set of citizen volunteers, as it was the case of the Athens of centuries V and IV BC (Chouard

2011; Dupuis-Deri 2004). Hansen (1991) explains that the word democracyis mentioned for the first

time in Herodotus (484-425 BC) and that it emerged to designate a sophisticated system of politicalpower sharing that involved a comprehensive use of citizens to formulate policy and choose leaders. A

thorough institutional analysis of the Athenian Democracy (AD) shows that the assignation of charges

combined lot and suffrage (Hansen 1991; Manin 1997). However, while a small number of political

positions associated with certain technical skills were chosen by suffrage, a distinct feature of the Athe-

nian regime was that the majority of positions in the judicial, executive and legislative power were

selected by lot and rotated at a high frequency in order to avoid political oligarchization. Importantly,

even if AD is well known by the fact that legislation had to be approved in the popular assembly,

quantitatively speaking , the key institution in the legislative process was the council whose members

were selected by lot.2 In this study we implement a characterization of the various political systems

according to the mechanism to select legislators following Manin (1997). However, we acknowledge

that the mechanism used to select the legislator, by itself, may not entirely define the nature of the

political system given as there are additional elements of great influence in the characterization of any

political system (McCormick 2006; Sintomer 2010).3

Recently, some applications of agent-based modeling in political science have been used for the

discovery of new relationships and principles. Laver and Sergenti (2012) analyze party competition

dynamics while Pluchino et al. (2011) explore whether the legislative effect caused by introducing

random legislators within a two-party Parliament may counteract the effect caused by party discipline.

Nevertheless, in the field of political system modeling there are still many open questions. What

political systems generate socially desirable legislations? Could democratic innovations including

citizens in decision-making process improve the social performance of RGs? We investigate these

issues by means of Monte Carlo simulations of agent based models that emulate the functioning and

structure of different political systems. At the computational level, political systems are modeled as

systems of agents interacting with each other, proposing and voting laws according to pre-specified

behavioral rules, with a specific distribution of power among themselves and a spatial location in the

Cipolla Diagram (1976) which reflects a specific selection mechanism. In this study we build on the

initiatives, iii) public opinions on political issues can be expressed beyond the control of the rulers and iv) the collectivedecision is taken by the rulers at the end of the discussion (Manin, 1997)

2As Hansen (1991) estimated, more than half of the laws passed by the assembly were proposed by the council.3Political scientists have argued that there are other relevant features in systemic classification such as: i)the universe

of population on which the selection mechanism is applied, ii) the rotation frequency of the legislators and iii) the degree

of control over the legislative flow and the political charges.

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framework developed by Pluchino et al. (2011). However, a variety of new innovative and relevant

features are introduced in the model. These extensions are relevant for several reasons.

The first relevant change is that we include a third political-party in order to approximate RG

dynamics. The modeling of multi-party systems allows us to analyze simple majority RG legislatures

in a stylized manner without introducing randomly selected citizen legislators. Thus, our modeling

approach departs from the model developed by Pluchino et al. (2011) where there are only two

political parties and by construction, one of the two will be governing with absolute majority. This

is not a minor issue given that in their study, legislative quality improvements are solely attributed

to the inclusion of randomly selected citizens while the positive effect they observe is due to the

transition from an absolute majority regime to a simple majority one. Moreover, by extending the

number of parties we can analyze RG outcomes with a higher degree of realism, as political power is

usually distributed among more than two parties and the scenario of absolute majority is not frequent

(Diermeier and Merlo, 2000).

The second significant change is that we depart from the unrealistic assumption of a fixed and

uniform number of proposals for each legislature with independence of the Parliament composition.

In order to approximate the behavior ofParticipatory Democracies(PD), that integrate legislative

proposals from political parties and citizens4, we assume the number of proposals is variable and

dependent on the number of parties and citizen legislators participating in the policy-making process.

Hong and Page (2001; 2004) analyze how artificial agents solve problems and explore the returns

to additional problem solvers, finding that groups of problem solvers can exhibit arbitrary marginal

returns to additional members. The change implied by the integration of citizens in the legislative

process generates two opposing effects that need to be explored. On one hand, an increase in the

number of proposals will rise the potential social gains by augmenting the number of candidate laws

to be approved in the voting phase. On the contrary, the increasing number of participating citizens

will fragment the parliament making more difficult to get the needed majority to pass acts which may

freeze and decrease legislative output.

A third novelty of the present analysis is that when analyzing PD systems, we do not restrict the

analysis to unicameral parliamentary configurations but we also consider a bicameral system labeled

the Citizen Senate (CS) that closely follows the proposal of Zakaras (2010). This form of political

organization combines lot and elections as main procedures to select and assign representatives to each

4In the PD system considered here, the representative component is articulated through the vote applied to partyagents and direct participation is articulated through lotteries applied to select citizens who directly participate in

legislative work.

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chamber. A fundamental difference with respect classical bicameralism of Madison (1788), is that in

the CS, control and supervision is directly undertaken by citizens and not by any other political party

members. The main difference with respect the unicameral PD model is that citizens do not launch

legislative proposals but preserve the ability to veto legislation that comes from the camera of political

parties. Within this framework, we analyze the optimal consensus level for applying a veto to lawspassed by political parties.

A final difference with respect previous work is that we do not only consider the average quality

of the political system but also the average legislative volatility. Authors such as Landemore (2012a,

2012b) or Ober (2010) have pointed out the fact that the use of lotteries to select legislators may

increase the diversity of agents and the appearance of negative correlations in their skills. Likewise,

Page (2007) shows that negative correlations between the skills of the various agents will produce

a cognitive diversification. In this context, political diversification may help to reduce the risk of

the political system. This issue is relevant as different political systems will differ in the amount of

uncertainty. Additionally, different risk attitudes may generate different evaluations of such outcomes.

We compute metrics of legislative volatility and compare the performance of each of these political

systems within a mean standard deviation utility framework (Meyer 1987; Saha 1997).

The paper is organized as follows. Section 2 describes the agent based model methodology used

to carry out the simulation exercises of the political systems. Section 3 presents the hypothesis and

results of each of the computational experiments that characterize each of the political systems under

consideration. Section 4 compares the different models within a unifying utility analysis that takes into

account risk attitudes. Section 5 offers the main conclusions from our work and possible extensions

to it.

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2 The Agent Based Model

In this section we describe the agent-based modeling approach undertaken to simulate the different

political systems under consideration. The model parliament consists of legislators l(x,y) defined by

a pair of coordinates associated to a concrete position in a Cipolla diagram. The Cipolla diagram

represents the nature of legislators according to their ability to promote personal or social interest

and it is the theoretical device used to elaborate the computational agent based model. The pair

of coordinates (x,y) captures the attitude to promote personal and general interest. Therefore, each

legislator has the possibility to propose laws that can result into a i) benefit/damage for himself or

ii) benefit/damage for others. We normalize the values so that the effect of the legislators initiatives

oscillate between -1 (highly damaging) and +1 (highly beneficial) for each of the axis, x and y. Given

the heterogeneity of legislators and the possibility of different capabilities to promote either privateor social gains, there are four prototypes of legislators based on their proposals: intelligent legislators

will benefit themselves and the others (+,+), altruistic legislators (-,+) will benefit the others but not

themselves, selfish legislators will benefit themselves and damage others (+,-) and stupid legislators

will damage themselves and other citizens (-,-).

In the model, differences characterizing the theoretical political systems outlined above, emerge

due to differences in the nature of legislators but also because of the method of selection of legislators.

The specificity of the legislator-selection mechanism is captured by the spatial distribution of agents

in the Cipolla Diagram. We assume that AD type of political systems organized through lotteries

will tend to scatter legislators across the Cipolla Diagram while RG systems where suffrage is applied

to select representatives of parties will form clusters of agents around certain coordinates. On the

other hand, PD hybrid systems are assumed to combine both type of agents and mechanisms. We

model randomly selected citizen-type legislators, denoted by li(x, y), as uniformly-distributed points

U [1, 1], in the Cipolla Diagram. On the other hand, legislators belonging to a political Party k, are

denoted bylk(x, y). The function used to generate the locations of the agents belonging to a party inthe Cipolla space is the Gaussian density function. In particular, all the points ljk(x, y) representing

members of a given party Pk will lie inside a circle with a given radius of tolerance rk with a center in

Pk(xc, yc). The center of each Pk is fixed by the average collective behavior of all its members, while

the length of the radius indicates the extent to which the political party tolerates dissent within it

(i.e, the larger the radius the greater heterogeneity in the party).

Figures 1, 2 and 3 below display the spatial configuration in the Cipolla Diagram of the different

political systems under consideration. Figure 1 plots the Cipolla Diagram of a parliament that consists

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only of partisan agents and approximates the behavior of the RG. Figure 2 plots the PD representation.

As it is observed, it includes both partisan agents and randomly selected citizen legislators in the

decision making process. Notice that this model nests the AD if we eliminate political parties from

the design. Finally, Figure 3 plots the CS, a bicameral parliamentary configuration that allocates all

professional politicians ljk in the first chamber and all citizens li in the second one.

Figure 1: Representative Government

The dynamics of the legislative process are the following. During a legislatureL, each independent

legislator li(x, y) or belonging to a party ljk(x, y) can perform two actions: iproposing a law and ii)

voting for or against a proposal of law. Independent legislators and political parties have different

propositive capabilities and in this model we assume the number of proposals in a legislature L to be

dependent on the number of randomly selected politicians and the number of parties. Specifically, we

assume that each political party Pk, generates 100 law proposals per legislature (CPk = 100) while

in the baseline scenario individuals propose on average a single act per legislature (CPi = 1). The

proposal action does not depend on the membership of the agent so that each legislator generates an

actan, withn = 1, 2,..Np, beingNpthe total number of acts proposed by all the legislators during the

legislatureL, with a given personal and social gain such that: an(x, y) =l(x, y) for every act proposed.

It follows that legislators belonging to a party Pkcan propose acts which are not perfectly in agreement

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Figure 2: Participatory Democracy

Figure 3: Citizen Senate

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with the Partys collective center Pk(xc, yc) and some divergence within the correspondent circle of

tolerance is allowed. The total number of proposals Np, discussed in legislature L depends on the

systemic configuration such that:

Np(L) =

Kk=1

PkCPk+

Ii=1

liCPi (1)

where Pk refers to political party k, CPk denotes its propositive ability, li denotes independent legis-

lator i and C Pi the propositive ability of legislatori. On the other hand, the shares of political power

among political parties and independent citizens satisfies that:

W(L) = (1 c)K

k=1

k+ cI

i=1

i (2)

where W(L) = 1, c [0, 1] is the share of citizens in the distribution of political power, i is the

share of an individual and k is the share of the political party k. In the PD system, where parties

and citizens coexist, the power share of any political party k, will decrease as c increases. Notice that

if all the political power is in the hands of the citizens, political parties have no role and the system

converges to a prototypical model of Athenian Democracy. At this regard, we equalize the number

of proposals in the extreme RG and the AD model so that outputs of the two political systems are

comparable. However, we assume that in a PD system, the quantity of the proposals starts from the

initial RG level and then rises with the number of citizens. The increase will be more pronounced the

higher the propositive ability of citizens (CPi). Thus, we allow for scenarios of highly participative

agents and scenarios of passive citizens.

The action of voting for or against a concrete proposal is more complex and strictly depends on

the membership of the voter and his/her acceptance window. The acceptance window is a rectangular

window on the Cipolla diagram into which a proposed act an(x, y) has to fall in order to be acceptedby the voter. Therefore, while each randomly selected legislator has his/her own acceptance window,

so that his/her vote is independent from the others vote, all legislators ljk(x, y) belonging to a party

Pk vote by using the same acceptance window, whose lower left corner corresponds to the center of

the circle of tolerance of the party Pk. However, following the party discipline, any member of a party

accepts all the proposals coming from any other member of the same party k. Notice that the fact

that a certain act an(x, y) would be favorable for a given legislator does not imply that it should be

favorable for another legislator or Party. Hence, the coordinatex (an) of any act is different for any

legislator or Party and it will be expressed by a random numberx, uniformly extracted in the interval

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[-1,1]. This new position, x(an) = (x, y), is called voting pointand it will lie on the line y = y(an).

The voting point has to be compared with the acceptance windows of legislators and Parties. It follows

that from the personal advantage point of view, the act can be either approved or rejected depending

on whether the voting point lies on the right or left of the acceptance window corner. A diagram of

the voting process and pseudo-code of legislative dynamic is shown in Figure 4 below.

Figure 4: Voting

Step 1: Proposal. Legislatorljk(x, y) belonging to Partyk, proposes an actan(x, y). This proposal

generates the liney = y (an). From this line, a new voting point an(x, y) [1, 1] is created for each

agent.

Step 2: Voting. The independent legislator li(x, y) who has an acceptance window defined by

wi(x, y) checks whether the specific an(x, y) falls inside wi(x, y). As it is the case in the example

given that the pair x, yn xi, yi, legislator li will vote favorably. The same proposal would be

positively voted by all the members ljk of the PartyPk since it also falls within the window wk(x, y).

Step 3: Acceptance or Rejection. Finally, once all the members of the Parliament voted for or

against a certain proposal, the latter will accepted only if it gets at least N2

+ 1 favorable votes. In

other case it is rejected.

Step 4: Go to step 1 and repeat s times the process for all legislators. This is necessary in order

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to avoid spurious results given that there might be extreme cases where all legislators are virtuous or

stupid and we are interested in obtaining the metrics that characterize every political system regardless

of specific locations. Hence, legislative dynamics of each parliament are simulated through a Monte

Carlo exercise with s = 10000 repetitions of the process. The average quality of the legislature in each

political system is computed as:

Q= 1

S

Ss=1

Naccm=1

y (am(s)) (3)

where S is the total number of Monte Carlo experiments and y (am) is the social gain delivered by

the proposal m. Given a spatial configuration determining the quality of the set of proposals y (am),

the key driver of the total legislative quality is the number of accepted proposals Nacc. Equation

(4) below implies that the number of approved proposals is a positive unknown function f of the

number of parties K, the number of citizens li and the concentration of power among political agents

. Importantly, is a negative unknown function of the number of independent citizens li.

Nacc = f(K+, Ni(li,+) , (li,)) (4)

Therefore, by differentiating with respectliwe find that the net effect of increasing citizen participation

on the rate of accepted proposals depends on two forces moving in opposite directions such that:

Naccli

= f

K

K

li+

f

Ni

Nili

+f

li(5)

where the first term of the equation (5) is zero (as the number of parties does not depend on the

number of citizens), the second is positive and the third one is negative given that the derivative of

with respect li is negative. Therefore, the effect of increased participation in the phases of proposal

and voting cannot be determined a priori and needs to be simulated.

In order to assess political instability we compute the volatility of the legislative quality associated

to each parliamentary design. The volatility of a political system refers to the amount of uncertainty

or risk about the size of changes in legislative outcomes. A higher volatility means that outcomes

generated by the political system can be spread out over large range of values and that the system

performance may change dramatically over a short period of time. A lower volatility implies that

outcomes of the system do not fluctuate dramatically. The volatility metric is computed as the

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standard deviation of the legislative quality over the s repetitions:

V =

1S

Ss=1

(y (s) Q)2 (6)

where Q denotes the average legislative quality over the s repetitions and ys refers to the quality of

the legislature in a given repetition s which is given by:

y (s) =Naccm=1

y (am) (7)

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3 Experiments

In this section we explore the outcomes emerging from the different political systems.

3.1 Representative Government System

The average quality and political instability in RG systems, are functions of the number of parties

(and their proposals), the radius of tolerance, the distribution of power among parties and the spatial

location of the parties in the Cipolla Diagram. Therefore, in the analysis of the RG system we test the

performance of this political regime with respect the number of parties (bipartidist or multipartidist),

the distribution of power between the parties (concentrated or equi-distributed) and the degree of

party discipline (strong/weak).

Typically, two-party systems typify majoritarian electoral rules (i.e, the winner takes all) where the

concentration of power is high, while multiparty systems are related to consensual party systems with

a more equally distributed power (Duverger, 1954). Theoretical literature considered that two-party

systems have direct and indirect benefits: i) they offer voters a clear choice between two sets of public

policies, ii) they have a moderating influence and iii) they provide stable and effective policies (Lowell

1898). Conversely, other authors argue that although majority governments may be able to make

decisions faster than consensual governments, quick decision-making does not imply better outcomes.

In fact, the opposite may be more valid given that the more parties in the Parliament, the more likely

it is that every voter or group of voters will be faithfully represented by one of them (Taagepera and

Grofman 1985). Moreover, coherency of policies adopted by majority governments may be invalidated

by changing majority governments, since alternating between parties may lead to frequent drastic

changes and political instability (Lijphart 2012). According to this view, policies that are supported

by a broad consensus are more likely to be carried out successfully and last than those imposed by

absolute majorities.

We also run an additional experiment and we test whether party discipline affects either positively

or negatively legislative outcomes. In modern RG systems, political parties have gradually increased

and mantained high levels of internal discipline, with legislators sticking closely to the party line

or ideological position. This feature of the system, has been documented by several authors for

different countries (Cox 1987; Synder and Groseclose 2000; Huber 1996). However, to the best of

our knowledge there is no evidence on whether this feature is positively related with overall system

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functioning beyond simulations of Pluchino et al. (2011) who find a negative effect. Table 2 shows the

results of the RG. Parliaments composed by one party generate the lowest level of social welfare, with

an average quality ofQ = 0.0 points and a volatility value ofV= 58. Under this distributive regime,

the percentage of approved proposals is around the 100% provided that the political party holding the

power controls all the legislative flow. As can be seen, in the two-party parliament, social gains arehigher than in one-party regimes and achieve an average legislative performance of 8 points. Notice

that in this scenario, the party with a minority passes few laws while the party in power approves

all of its proposals. However, both systems display a lower legislative quality than what is obtained

within a three-party framework. In the later, the average legislative quality of the system increases

due to the positive effect of an increasing number of proposals. This is because of the increase in the

number of proposals generated by additional political parties offsets the fall in the rate of adopted

laws stemming from a greater parliamentary fragmentation. Within the set of three-party systems, we

find that simple majority regimes generate higher social gains (Q= 36 + / 2) than those obtained

when one party enjoys absolute majority (Q= 15 + / 2). On the other hand, volatility outcomes

display a different pattern. With regard to the values of political system instability, we find that RG

systems with two parties are at an intermediate point between the maximum instability of three-party

models and absolute majority and that of the three-party simple majority RG regime.

Table 2: Baseline Representative Government Results

Number of Parties Average Quality Volatility Number of Proposals % Proposals

of Legislation Approved

One Party 0.0 +/- 2 58 100 100Two-Party 8 +/- 2 61 200 62.5Three PartiesAbsolute Majority 15 +/- 2 66 300 50Simple Majority 36 +/- 2 51 300 41.7

Notes:These results are obtained with a radius of tolerance of r = 0. The distribution of power in thesystem with two political parties is 60-40.In the three party system the distribution of power for theabsolute majority regime is 60-30-10 while in the simple majority is given by 40-30-30.

In order to test the effect of party discipline we run simulations assuming a lower degree of party

discipline, that is, by increasing the radius of tolerance to r = 0.4. Table 3 shows the results of the

RG system in this new scenario. As observed, a lower level of party discipline increases the overall

quality of the system and generates less volatility. This result supports previous findings of Pluchino

et al. (2011).

It is important to highlight that previous results depend on the relative political power of each

party. In order to check whether previous results hold for all possible combinations of political power

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Table 3: Representative Government Results. Radius of tolerance r = 0.4

Number of Parties Average Quality Volatility Number of % of ApprovedProposals Proposals

1 Party 0.0 +/-2 + 58 100 1002 Parties 12 +/- 2 67 200 67.23 PartiesAbsolute Majority 18 +/- 2 66 300 51.6Simple Majority 41 +/- 2 49 300 41.8

Notes:These results are obtained with a radius of tolerance of r = 0.4. The distribution of power inthe system with two political parties is 60-40.In the three party system the distribution of power for theabsolute majority regime is 60-30-10 while in the simple majority is given by 40-30-30.

weights we undertake a deeper analysis by means of a phase-diagram whose results are presented in

Figure 5 below. As it is observed, the highest levels of legislative quality are obtained in the red zone

where no party controls more than the 50% of the parliament, which ultimately implies it cannot

approve the 100% of its proposals. One level below, we find orange and yellow zones where there

is at least one party enjoying the 50% of the seats share. In such scenario, the dominant party is

always part of the government and will be able to approve its proposals. Green and blue zones are

characterized by absolute ma jorities which yield the lowest levels of legislature quality. This is due

to the fact that in such situations i) there are no parliamentary mechanisms to stop socially harmful

measures andii) parties in minority do not have almost any of their proposals approved. These results

imply that the set of combinations where political power is more equally distributed among the three

parties tends to generate the highest social performance.

Figure 6 provides evidence on the possible states of volatility by exploring the whole set of power

combinations between political parties A, B and C. As it is observed, absolute majorities are char-

acterized by a higher level of uncertainty in terms of legislative quality. Combinations that reduce

uncertainty are obtained in green and yellow zones where the concentration of political power is low.

Interestingly, the phase diagram shows the lowest levels of volatility are obtained when two of the

three parties have an equal weight of the 50% and the third party has no power.

Our results support Lipjharts (2012) thesis given that consensual systems typified by multi-party

parliaments are more likely to generate higher legislative quality than two-party parliaments. Taken

together, our findings suggest that i) multi-party systems outperform two-party ones in terms of

legislative quality,ii) egalitarian distributions of power increase legislative quality and lower volatility

and iii) party discipline decreases legislative quality and has no clear effect on political stability.

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Figure 5: Legislative Quality Phase Diagram

Figure 6: Legislative Volatility Phase Diagram

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3.2 Participatory Democracy

Participatory democracy is a form of political organization that advocates more involved forms of

direct citizen participation and greater political representation than traditional RG systems. Many

political scientists consider PD has several advantages when compared to RG systems (Burnheim1985; Martin 1992; 1993; Barnett and Carty 2008). First, the inclusion of citizens to perform political

tasks, provided they are selected by lot from census, implies that social and demographic features

(income, race, religion, etc) will get an accurate representation in the Parliament. Second, partici-

patory democracies organized through lotteries are essentially egalitarian since they guarantee equal

political power to everyone. Third, independent citizens selected by lot do not owe anything to any-

one for their position, so they would be loyal only to their conscience, not to political Party, also

because they are not concerned in their re-election. Additional sound arguments are given by Lande-

more (2012a; b) or Ober (2010) who argue that PD systems organized through lotteries will produce

collectively-intelligent parliaments that will undertake correct decisions because of the existence of

negative correlations between members cognitive abilities. This, in turn, will reduce fluctuations of

legislative quality.

In order to analyze the net effect caused by citizen participation in a political system originally

consisting of three political parties, we augment the previous RG model with randomly selected leg-

islators. This experiment allows us to disentangle the welfare gain effects related to the legislative

contribution of random citizen legislators from those originated by the transition from absolute to

simple majority regimes. We first simulate absolute majority regimes where the distribution of power

among parties is 6030 10 for different radius of tolerance r = 0, 0.1 andr = 0.4. In a second place

we consider simple majority regimes where the distribution of power among parties is 40 30 30.

Figure 7 shows the sensitivity of the PD legislative quality as we vary the relative political power

share of random legislators in the legislative process, c. Absolute majorities are plotted with marked

continuous lines while simple majorities are plotted with dashed lines. Notice that the absolute major-

ity regime is not conserved through all the experiment given that as we increase citizen participation,

political parties will lose their relative power share proportionally. To be precise, in this context we

can only talk about absolute majorities in the interval ranging from 0 to 16.84% of citizen legislators

given that beyond that threshold there is a regime transition.

As it is shown, legislative quality in a RG system just consisting of parties where one of them

has absolute majority is relative low when compared to simple majority scenarios. As in the previous

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Figure 7: Participatory Democracy Baseline Results

experiment with the RG system, we observe a considerable welfare gain in the transition from absolute

majority regimes to simple majority ones for the different radius of tolerance considered. In particu-

lar, when moving from the scenario of 15% to that of 20% (crossing the distributive regime break up

threshold) of citizens we find the legislative quality experiences a positive jump which implies a consid-

erable increase in social welfare. The implied legislative quality growth rates for the different regime

transitions are 88.01% ifr = 0, 84.46% ifr = 0.1 and 59.38% ifr = 0.4 respectively. This change is

what Pluchino et al. (2011) solely attributed to the introduction of randomly selected legislators while

in fact reflects a regime transition. However, from this threshold onwards, any change in legislative

quality or volatility cannot be attributed to the changing distribution of power among political parties

but to citizen participation net effects. In particular, for the PD system where one party initially

enjoyed absolute majority, for r = 0, 0.1, 0.4 the maximum levels of quality are obtained with a citizen

share of 40% (QA,0.4= 55.92) and 55% (QA,0.1= 52.26) and (QA,0 = 51.74). Thus, we find the net

effect of citizen participation is positive implying an increase in the social welfare generated of about

39.27% in the case ofr = 0.4 and 34.46% and 32.93% in the case ofr = 0.1 and r = 0 respectively.

In the PD model with simple majority, for r = 0, 0.1, 0.4, the maximum levels of quality are

obtained with a citizen share of 45% (QS,0= 57.37), 40% (QS,0.1= 56.37) and 35% (QS,0.4= 54.35)

respectively. Therefore, the net effect of direct citizen participation is positive and implies an increase

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in social welfare with respect the RG of about 58.26% in the case of r = 0. If r = 0.1, the net

contribution of citizens yields an increase in legislative quality of 53.47% and 33.89% while in the case

of r = 0.4. An important feature emerging from this model is that legislative quality is a concave

function of the relative share of citizens which ultimately implies there is a maximum after which a

higher level of direct citizen participation will drop legislative quality. Moreover, it should be stressedthat the maximum legislative quality is obtained with a certain degree of political inequality between

agents. As a point of fact, above the 70% citizen share threshold, the performance of the system

starts to decrease abruptly. Indeed, our results suggest that the scenario of the AD, where all the

legislative tasks are implemented by randomly selected legislators and where political power is equally

distributed, delivers the lowest levels of legislative quality (Q= 6.08) and volatility (V=5.04).

Figure 8: Different Propositive Behavior

In Figure 8 we show how the effect of different propositive abilities affect legislative outcomes. As

it is shown, forr = 0, the legislative quality outcomes with passive citizens (CPi = 0, QA = 39.06) are

below those obtained with the baseline scenario (CPi = 1, QA= 51.6) or the highly-proactive scenario

(CPi = 2, QA= 66.7). This is also the case when we perform the analysis in the simple majority

scenario given that (CPi = 0, QS= 46.11) < (CPi = 1.QS= 57.91) < (CPi = 2, QS= 68.52). As

observed, in all cases, the relation between the power share of citizens and legislative quality displays

an inverted U shape and the effect of increasing the proactive ability of citizens always yields a positive

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impact on final legislative outcomes.

Regarding the aggregate behavior of political volatility, we find that increasing citizen participation

always reduces political instability achieving its minimum level in the AD regime scenario (V = 5.04).

While the set of PD configurations yield an intermediate level of political volatility ranging from

Vmax = 46 to Vmin = 25, we find that RG systems with independence of the distribution of power

among parties are the most volatile ones with legislative quality fluctuations ranging from a maximum

of Vmax = 66 to a minimum volatility of Vmin = 48. This pattern is robust to different propositive

abilities. These results support the thesis of Landermore (2012a, b) given that increasing citizen

participation will produce collectively-intelligent parliaments and will reduce fluctuations from one

legislature to another.

3.3 The Citizen Senate

The last model we explore is the CS (Zakaras 2010). This system is similar to the PD parliament

where citizens are passive CPi = 0 but faces the problem of institutionalizing a democracy from

another angle. The idea of a citizen camera at the heart of political institutions comes from the

need to create a national, democratic and institutionalized control to monitor political activity the

emergence of corruption (Testa, 2010). In order to simulate CS dynamics, we model a bicameral

system where every law passed by the chamber composed by political parties needs to be reviewed

by randomly selected citizens allocated in the second chamber. Therefore, laws with a negative social

return may never get to be approved by the citizens, preventing governments to legislate against the

common good. In this model, citizens are required to achieve a level of consensus in order to veto any

proposal. However, if the majority needed to veto first chamber acts is too low, it may be the case

of the Senate to vote against too many laws, causing a government paralysis and hampering overall

legislative quality. In order to explore how to optimize the legislative performance of this political

system, we study the majority needed in the second chamber to veto first chamber acts. Our tests

are dedicated to explore the role played by different requirements to apply veto, taking into account

ranges going from absolute majorities (i.e, 50% + , with >0) to unanimity (100%).

As it is shown in Figure 9, the CS model displays the same result in absolute majority and simple

majority regimes as model simulations under both scenarios deliver the same optimal threshold in the

75% level, with an optimum value of of Q = 47.1 in the simple majority scenario and with r = 0.

Above the 75% level, the consensus is hardly ever achieved which in turn implies that vetoes are rarely

applied. In this situation, a number of bad proposals generated by political parties will be approved

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and overall system quality will decrease. On the contrary, if the requirement to apply veto is below

the optimal level, the citizen senate will block too many socially desirable proposals. However, it is

important to note that in this model, under the optimal parameterization, citizen control enables a

higher legislative quality and lower instability than in the RG system. We conjecture that in models

with the possibility of abstention the optimal level for the veto will be below the 75% threshold.

Figure 9: Citizen Senate Results

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4 Political Systems Evaluation

Under uncertainty, preferences on political system are significantly influenced by risk attitudes. As

a result, it is difficult to assess the merits and consequences of alternative systems without information

about the risk preferences of the population. We propose the use of a flexible utility function in the

nonlinear mean-standard deviation framework. The proposed form nests alternative risk preference

structures as special cases. We start by formalizing an agent risk attitude and choices over the set of

random legislative outcomesYi characterizing each political system i. TheV (i, i) decision criterion

hypothesizes that an agents optimal choices are made by ranking alternatives through a preference

function defined over the first two moments of Yi, where i and i denote the mean and standard

deviation ofYi. Consider a decision maker whose utility function V is defined over the mean and the

standard deviation ofYi. Her risk attitude is reflected by:

S(, )

V(, )

V(, )

(8)

where subscripts denote partial derivatives. Note that S(, ) is the slope of the indifference locus in

the space. In particular we use the following flexible mean-standard deviation utility (MSU)

function:

V(, ) =M S (9)

where and are the parameters describing attitudes towards risk. Under previous MSU form, it

follows that the risk attitude measure, Sis given by:

S(, ) =

V(, )

V(, )

=

M1 S1 (10)

It has been shown by Meyer (1987) and Saha(1997) that MSU exhibits i) risk aversion, neutrality and

affinity as >0, = 0 and < 0, ii) decreasing, constant and increasing absolute risk aversion as >1,

= 1 and < 1 and iii) decreasing, constant and increasing relative risk aversion as > , = and

< . The various risk preference configurations considered in the simulations are summarized in

Table 5 below. The parametric values used the simulations were chosen in order to minimize utility

gaps and fluctuations between the variety of utility functions. As shown, not all functional forms

considered are consistent with risk lover profiles while risk adverse profiles admit a wider variety of

functional forms and parameter combinations. Specifically, if the purpose is to model a risk lover

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valuation profile, some incompatibilities emerge in CARA + (CRRA, IRRA) and DARA + (CRRA

+ IRRA) combinations. This is because of risk affinity parameter values require < 0 and =

when 1 at the same time, which is impossible. It is important to note that the comparison of

political systems through the adoption of different functional forms depends heavily on the inputs of

the system: the quality and the volatility of the system. This, in turn, depends on the propositivecapability for the independents in the PD model and the tolerance radius and distribution of power

for the political parties in the RG. Here we will use the baseline values employed along the paper to

perform the comparison. Figure 10 shows the value in terms of utility of the different political systems

Table 4: Simulation Coefficients

Risk Averse DRRA CRRA IRRA

DARA = 1.05, = 1 = 1.05, = 1.05 = 1.05, = 1.1

CARA = 1, = 0.95 = 1, = 1 = 1, = 1.05IARA = 0.95, = 0.9 = 0.95, = 0.95 = 0.95, = 1.05

Risk Lover DRRA CRRA IRRA

DARA = 1.05, = 1 NR NRCARA = 1, = 1 NR NRIARA = 0.95, = 1 = 1, = 1 = 1.05, = 1

Notes: DARA(CARA, IARA) denotes decreasing(constant, increasing) absolute riskaversion and DRRA(CRRA, IRRA) denotes decreasing(constant, increasing) relativerisk aversion

.

for risk-averse agents. The modeling of risk aversion in each of the political subsystems has been made

by computing the average over the entire set of compatible functional forms. As observed, risk averse

individuals prefer simple majority regimes over absolute ma jority ones. Maximum utility levels are

obtained under the PD where randomly selected individuals weight is obtained with c = 45% 50%.

An emerging feature of this modeling exercise is that by comparing RG with the AD we find that

risk averse individuals will tend to prefer the AD over the RG. This result is due to the fact that

although the RG generates a higher legislative quality, but the change in the type of parties with a

sufficient power share to pass all their initiatives from one legislature to another makes the systemhighly unstable. On the contrary, the AD model is highly stable given that the rate of proposals is

very low, only selecting those who yield higher level of social welfare. Hence, risk averse individuals

will severely penalize fluctuations associated to RG and will obtain higher utility levels in lottery-

based parliament designs. Finally, Figure 11 shows the corresponding utility measures of the political

systems when agents display risk affinity. Again, risk loving individuals prefer simple majority regimes

over absolute majority ones. We find that the best system irrespective of the risk profile is the PD

model. As regards the comparison between the RG with AD our findings suggest that risk loving

individuals prefer RG over the AD.

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Figure 10: Utility of Risk Averse Individuals

Figure 11: Utility of Risk Averse Individuals

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5 Conclusions

In this study we have investigated emergent legislative dynamics in a variety of political systems

by means of Monte Carlo simulations of distinct parliamentary agent based models. Political systems

based on suffrage and political party representatives such as the RG display higher social gains in multi-

party environments than in two-party designs. Simple majorities display a superior social performance

than those obtained in the case of absolute majorities, which suggests that egalitarian distributions

of political power between political parties tend to increase overall social welfare. Furthermore, this

results are robust to the set of all possible combination of weights between the parties. Additionally,

by exploring the effect of party discipline in legislative outcomes we find such a property it is negatively

related to the political system performance.

On the other hand, unicameral PD political systems that combines political parties and random

legislators display an inverted U-shaped pattern between the power share of randomly selected politi-

cians in the parliament and the total social performance. Our baseline modeling results suggests an

optimal share of citizens of about c = 45 50%. Under this distribution of power, society takes profit

of the higher diversity associated to random legislators and the di-congestion effects caused by some

political power concentration in the political parties. PD framework nests the prototypical AD, where

the share of citizens is 100%. The AD displays a low level of legislative quality but a marked stability.

We also explored the dynamics of a bicameral PD system, where randomly selected politicians are

allocated in the second chamber and have veto power. Among the set of possible consensus require-

ments to apply veto so that social welfare is maximized, we find a threshold on the 75% level. In this

model, under the optimal parameterization, citizen control enables a higher legislative quality and

lower instability than in the RG system.

In order to compare the performance of the different institutional systems we take into account the

different risk profiles of the population and we integrate each model results within the mean-standard

deviation utility analysis. With independence of the risk attitudes PD system delivers the higher

levels of utility. However, we find that risk-averse agents will prefer AD than RG. On the contrary,

risk lovers will prefer RG systems than AD.

We pursue to develop three extensions of the framework developed here. The first one is associated

to the simulation of the deliberative process. In our model, legislators are fixed entities in the Cipolla

diagram and they do not evolve as they listen other proposals and interact with other agents. Secondly,

we find that it may be interesting to simulate the model with abstention. Our legislators just vote

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in favor or against any proposal and the possibility of abstention may affect the legislative outcomes.

A final extension of this model could be related to the introduction of time dependence in terms of

political power by simulating elections and voters behavior.

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