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Explaining reforms of assembly sizes

Reassessing the cube root law relationship between population and assembly size

Kristof Jacobs,

Institute of Management Research, Radboud University (NL)

Simon Otjes, Documentation Centre Dutch Political Parties, University of Groningen (NL)

Abstract One of the consequences of the current economic crisis and the ensuing austerity measures is that many people question the number of politicians. Governments in Austria, Ireland, Italy, the Netherlands and Portugal have considered reducing the size of their assembly. Has the state of the economy historically affect actual reforms of the assembly size? We distinguish between three explanations: (1) the dominant technocratic approach which holds that assembly sizes vary with (the cube root of) population sizes (Taagepera & Shugart, 1989) and (2) a rational choice inspired explanation focusing on the effective number of parties (Benoit, 2004; Colomer, 2004). In this paper we test which of these two explanations explains assembly size best using regression and event history analysis for the period 1950-2010. We find that the technocratic explanation works well for the design of assembly sizes, but such factors are far less important once electoral systems are established: afterwards increases in assembly size are best explained by rational choice explanations. It seems then that the correlation between assembly size and cube root of the population size is more of a historical artefact than a law-like correlation. Paper prepared for the ECPR General Conference in Glasgow, 3 - 6 September 2014.

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1. Introduction

One of the consequences of the current economic crisis and the ensuing austerity

measures is that citizens, journalists and politicians started to wonder: how many

politicians do we really need? In France (2012), Hungary (2010, 2011), Ireland (2011),

Italy (2012), Japan (2012), Mexico (2009, 2012), The Netherlands (2011), Portugal

(2011), Puerto Rico (2011), Romania (2009) and the United Kingdom (2011) bills were

introduced to reduce the number of national MPs.1 Many similar bills dealt with

reductions of regional and/or local MPs. At the same time, while old political regimes

crumbled because of inside pressures or were changed by external interference and new

ones were established in countries such as Afghanistan, Egypt, Iraq, Libya and Tunesia.

In these countries new assembly sizes had to be determined and the same question – how

many MPs do we need? – was asked. In both instances, the reform of existing assembly

sizes and the original design of new assembly sizes, an objective answer to that question

seems pretty difficult to give.

In many cases, political scientists ‘as electoral engineers’ (Farrell, 2011:191) have been

asked to comment or advise on the appropriate size (Lijphart, 1998). Typically, in such

cases political scientists point to the so-called ‘cube root law’ devised by Rein Taagepera,

which states that the number of seats in a given assembly approximates the square root of

its population (Taagepera, 1972; Taagepera and Shugart, 1989; Taagepera and Recchia,

2002; Taagepera, 2007). Taagepera and Shugart label this relation a law by because the

strong empirical connection is based on a deductive rational model. The empirical

argument is twofold: (1) when assembly sizes are originally designed, one can expect the

cube root law to hold, but (2) additionally -in the long term- ‘there should be a noticeable

trend toward larger assemblies’ (Taagepera and Shugart, 1989:179).2 However, so far this

second argument has not been examined rigorously in a longitudinal empirical test. As

1 The authors wish to thank Lidia Nunez for kindly allowing us to use this information. 2 Surely, ‘[a]ssemblies may fall below the predicted size because such nations are late in adjusting assembly size to increased population and literacy’ (Taagepera and Shugart, 1989:179), but in the long term one should see a trend towards increasing assembly sizes.

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such we do not know whether the relationship is a historical artifact or a genuine law.3

Our central question is therefore:

How is the change in population size over time related to change in assembly size over

time?

Our main argument is that our understanding of assembly sizes can be improved

substantially by differentiating between a design phase (when the assembly is put in

place) and a reform phase (when the size is adapted). This distinction stems from the

electoral systems literature where it is routinely made (Farrell, 2011). We find that the

‘law’ indeed works as expected in the design phase. For as far as assemblies are ever

designed, the context of design is well-suited for the fairly technocratic logic that

underpins the cube-root law since during design the political actors work under great

uncertainty, need to establish a legitimate system and have other more pervasive tools at

their disposal if they want to further their own self-interest. However, once a given

assembly size is agreed upon, adjusting this size is a different game where a political

logic dependent on the number of parties is more important than the earlier technocratic,

population logic.

We will proceed as follows: first we will discuss the theoretical framework and

distinguish between the design and reform phase. In the empirical section we will carry

out an Ordinary Least Squares regression analysis of population and assembly size of

countries that have democratized since 1950. Next, we will use a longitudinal analysis,

namely event history/survival analysis, to estimate whether population increases affect

the assembly size on a unique dataset covering 120 democracies (time frame: 1950 to

2010).

2. Theoretical framework

Arend Lijphart (1985, 3) once judged the study of electoral systems ‘the most

underdeveloped subject in political science.’ Since then studies on the topic have

3 In fact, this is actually what Taagepera (2007) himself suggests: ‘By now we have appreciable time series for growth in population and assembly size. In view of the importance of assembly size in affecting the number of parties, a thorough reanalysis would be desirable.’

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mushroomed. In the mid-1990s scholars started to look not only at the consequences of

electoral systems, but also at explanations of the origin and changes to these electoral

systems (Farrell, 2011:172). While the focus originally centered on major reforms of the

electoral formula, since the mid 2000s scholars adopted a more comprehensive approach

whereby other elements of the electoral legislation are studied (Leyenaar & Hazan,

2011:438), which opened up ‘a range of interesting questions’ (Farrell, 2011:172).

Nowadays, scholars also try to explain changes to such elements as ballot structure

(Jacobs & Leyenaar, 2011), gender quota (Celis, Krook & Meier, 2011), district

magnitude (Pilet, 2007) or electoral thresholds (Hooghe & Deschouwer, 2011). By doing

so, virtually all ‘major’ dimensions are now covered (Lijphart, 1994:10). There is one

exception though, and that is the assembly size. So far we still have very little insight in

how to explain changes to the assembly size. The little research trying to explain the size

of legislatures is mainly based on the cube root law. In what follows we will first discuss

this law and show why it is likely to only be partly true. Afterwards we offer a theoretical

framework encompassing broader insights from the broader literature on electoral system

design and reforms.

2.1 Assembly size, electoral systems and the cube root law

The core of the cube root law is that the size of a legislature is expected to be close to the

cube root of the population. Or more formally: S = (P)1/3, where S is the size of the

legislature and P the population size. The law consists of two elements: a theoretical,

deductive rationale and an empirical regularity (Taagepera and Shugart, 1989). The

theoretical argument is based on a ‘rational model’ starting from the assumption that

communication with constituents and other members of parliament is the most time-

consuming activity of representatives (Taagepera and Shugart, 1989:173).4 To minimize

the number of ‘communication channels’ an optimal assembly size can be calculated. As

Taagepera and Shugart (1989:179-182) elegantly show, this optimal size approximates

4 Though Taagepera and Shugart call the theoretical mechanism ‘rational’ most electoral reform scholars would call it a principled or technocratic argument based on the principles of representation and the quality of constituency service (Renwick, 2010: 39). Hence in what follows we will call the population size explanation the technocratic explanation. In the remainder of the paper, a ‘rational motivation’ will denote one where politicians maximize their power (Benoit, 2004).

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the cube root law of the population size.5 Crucially, however, if the cube root law is

genuinely a law, it should also hold in the future and as a consequence assemblies should

adjust to population growth (Taagepera and Shugart, 1989: 179). The empirical part of

the cube root law consists of simple cross-sectional analyses based on population and

assembly size data from 1965 (Taagepera, 1972) and 1985 (Taagepera and Shugart,

1989).6 Both analyses are ‘static’: they compare the sizes of legislatures and population at

one point in time.

There are three reasons why especially the empirical part of the law is vulnerable and can

be strengthened.

(1) The authors suggest that population size is causally related to assembly size. Only

population data from after the establishment the assembly are used (Taagepera, 1972;

Taagepera and Shugart, 1989), A key condition for establishing causality is that the cause

is measured before the effect and not simultaneously. In physics, the rigor of which

Shugart and Taagepera wish to replicate, the causal order is the 'acid test of success'

(Hoover 1993: 693). Taagepera and Shugart (1989: 176) themselves note that this is

problematic because ‘[a]ssemblies may fall below the predicted size because such nations

are late in adjusting.’

(2) The latter statement leads to a second concern, Taagepera and Shugart (1989) suggest

that the relationship between population and assembly size is dynamic in that countries

‘adjust’ their assembly size based on population growth. This would require a

longitudinal empirical test. However, only cross-sectional tests are provided based on

data from 1965 and 1985.

(3) In the final (best-fitting) model, population size is multiplied by literacy rates and

working age population (Taagepera and Shugart, 1989:179). This is not aligned with the

theory underpinning the cube root law, which is built on communication with all

constituents (i.e. the whole electorate) and suggests that other variables may influence the 5 Because communication channels is understood as the one-to-one interaction routinely associated with constituency service and does not consider one-to-many mass media communication, ‘strictly speaking the model only applies to single-member districts’, though Taagepera and Shugart (1989:181) suggest that other systems may also ‘assume a similar relationship.’ 6 Taagepera and Recchia (2002) replicated the relationship for Upper Houses around 2000; Taagepera (2007) also tested the law for the European capitals. In both cases, the fit is lower than with the national legislatures.

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relationship between population and assembly size. 7,8 All of this does not necessarily

mean that the cube root law is wrong, but suggests that further empirical analyses are

needed and it also suggests that other factors may be at play.9

Which other factors is, however, unclear. Somewhat strangely, so far the study of

explaining assembly sizes has remained understudied and fairly isolated from the rest of

the electoral reform literature. This is strange as Assembly sizes are clearly a part of

electoral systems. Lijphart (1994:12) notes that ‘if electoral systems are defined as

methods of translating votes to seats, the total numbers of seats available for this

translation appears to be an integral and legitimate part of the systems of translation.’

Indeed, the total number of seats available affects the proportionality of the overall

electoral system (Taagepera and Shugart, 1989:182-183; Lijphart, 1994:12-13; Colomer,

2004), especially at the lower end, where smaller assemblies have distinctly higher levels

of disproportionality (Farrell, 2011:158). If assembly size is a part of the electoral system,

one can expect that traditional explanations for changes of electoral systems can be

applied to assembly size as well. As such, it is a good starting point to look for other

factors that may explain changes in the assembly size.

2.2 Explanations of the original design of electoral systems

There are three reasons why the population size has a substantial impact when the

original assembly size is determined, namely uncertainty, legitimacy aspirations and the

relatively limited impact they have on seat shares.

When electoral systems are designed and the ‘original’ assembly size is laid out, this is

often done as part of a transition to democracy. Farrell (2011) distinguishes between three

waves of electoral system designs: a first wave when Western countries introduced

universal suffrage, a second when a substantial number of former colonies gained 7 In all fairness, all three are probably a remnant of data availability and the statistical state of the art at the time of the writing (1972 and 1989 respectively). Taagepera (2007:189) later on explicitly hinted at problems with data availability. 8 Taagepera (1972:385) actually explicitly included a term in his formula referring to unmeasured third variables in his earliest work on the topic. 9 In fact it may well be that the fit of the law is increased when the three problems are addressed.

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independence and a third one when a number of former autocratic countries became

democratic. During each of these waves the people deciding on the new electoral system

had to operate under a context of uncertainty. The context was uncertain because little

was known about the partisan preferences of the people, but also because typically a

substantial part of the electoral system was designed from scratch, which meant it was

hard to predict how the votes-seat translation would turn out. During each of those waves

the designers also had to establish a legitimate system that symbolized a new, more

democratic reality. Assembly sizes by their very nature have an impact on the

proportionality of the electoral system, but mostly when the assembly size is small: when

an assembly size is increased from one to two the impact is substantial, but when it

increases from 1000 to 1001 (or even doubles to 2000) the impact on the proportionality

is far smaller (Colomer, 2004). Given that during the electoral system design phase the

whole electoral system is under scrutiny of change, at these times the assembly size is

likely to be of relatively minor interest to self-interested politicians. As Jacobs and

Leyenaar (2011) have found, these three elements provide the perfect fertile soil for

principled or more technocratic arguments such as the population size. Hence we can

expect that:

Hypothesis 1. At the time of the original design, population size is associated with

assembly size according to the cube root law.

2.3 Explanations of the reform of electoral systems

However, it is one thing to design an electoral system for a newly established democracy;

it is quite another to change an electoral system for an existing one. Under such

circumstances fairly technocratic arguments such as the ‘optimal assembly size’ may be

less important. There is no research on explanations of changes in the assembly size:

typically researchers take a static view of assembly sizes. There is however an ever-

expanding body of literature dealing with changes to electoral systems in general, which

we will apply to the topic of assembly sizes. Specifically one can distinguish three

schools of thought in the field of electoral reform: the rational choice, institutionalist and

historical comparativist schools (Farrell, 2011; Leyenaar and Hazan, 2011).

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According to a first school, epitomized by Ken Benoit (2004), reformers are primarily

interested in increasing their vote shares. According to this model, electoral reforms will

occur when reformers have the ability (i.e. the required majority) to change the electoral

system to their benefit. The best example of such a reform is the French 1985 shift to PR

when the ruling French Socialist party was set to lose the upcoming election and wanted

to limit its losses (Renwick, 2010).

A second school, epitomized by Matthew Shugart (Shugart and Wattenberg, 2001;

Shugart, 2008) uses an institutionalist perspective and points to a combination of inherent

and contingent factors. The core of their argument is that electoral systems may have

inherent problems and produce systemic failures and anomalous outcomes. For instance,

majoritarian electoral systems can produce ‘wrong winners’ when that party with the

most seats was not backed by a majority of the voters such as the American presidential

election of 2000 where George W. Bush had more seats in the Electoral College but Al

Gore won the majority of the votes. Such problems often lead to calls for reform, and

incidentally to actual reforms.

A third school, epitomized by Alan Renwick (2010) and Gideon Rahat (2008), integrates

the two earlier ones and focuses on the broader picture using detailed case studies to

examine the actual processes that led to the reform. One of the key insights of the school

is that public opinion can have an impact on electoral reform through so-called ‘elite-

mass interaction’. In such cases, a minority of reformist politicians succeeds in

implementing electoral reform by mobilizing and/or using public dissatisfaction or even

outright public demand for reform (Renwick, 2010: 167).

To sum up, one can expect reforms when (1) reformers increase their seat shares by doing

so and/or (2) when the current electoral system fails to deliver (3) and/or when public

opinion is mobilized to back the reformers.

2.4 Applying electoral reform explanations to increases of the assembly size

How does this all translate to the study of assembly sizes? The more technocratic

reasoning outlined by Taagepera and Shugart fits best with the institutionalist school:

when the number of MPs is too low and when this shortage produces policy failures, the

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assembly size needs to be increased. Consistent with the simple reasoning outlined by

Taagepera and Shugart (1989) one can thus expect that:

Hypothesis 2a. A wider gap between the population size and the assembly size increases

the likelihood of assembly size enlargement.

Let us now move to the expectation that sees MPs as rational actors seeking to increase

their own benefit. As mentioned earlier assembly size has an impact on the

proportionality of the electoral system: increasing the assembly size typically affects the

district magnitude and thereby the effective electoral threshold. Enlargement of the

legislature therefore typically reduces the seat shares of the larger parties, unless some

form of compensation takes place. However, a bigger assembly size also reduces the

personal power of individual politicians, as they have to compete with an increased

number of other MPs e.g. for seats in the most prestigious parliamentary committees, the

ownership of topics that are most popular with the media and the important positions

within their own party. In sum, the power of individual politicians within the party is

reduced as the number of direct competitors increases. As such one can expect increases

in the assembly size when party leaders want to reduce the power of individual MPs or

when smaller parties in the parliament have the power to negotiate their way into a

coalition government, something which Colomer (2004: 3) calls the ‘micro-mega rule.’

Hence one can expect calls for expanding the assembly size when there are more smaller

parties in the parliament (especially when they enter office in a coalition government).

Under such circumstances, increasing the assembly size grants a relatively limited benefit

in terms of seat shares for the smaller parties, but bigger parties have the benefit of

weakening their MPs and increasing the power of the party leadership, especially in

proportional systems. Therefore we can expect that:

Hypothesis 2b. A higher number of parties increases the likelihood of assembly size

enlargement.

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What about the support of public opinion? If anything one can expect that citizens

typically do not demand more politicians. In fact, in many instances – especially in times

of economic crisis – a substantial portion of public opinion wants fewer MPs. In most

other instances one would actually expect attempts to reduce the assembly size. This is

indeed what Riera and Montero (2014) find in their study of bills on reductions of the

Assembly size at the regional level. In response to public dissatisfaction, regions

governed by a single-party majority wanted to reduce the assembly size (thereby reducing

the proportionality and their seat share), while in regions governed by a large party that

needed the support of a minor party introduced a bill that combined the reduction of the

assembly with a lowering of the legal electoral threshold to offset the loss of

proportionality. However, so far most of these reform proposals did not lead to actual

reductions. Hence, one can expect that if public opinion has any influence, it will be a

negative one.10

3. Data and method

3.1 Methods

This article combines two different analyses that look at the same data from different

perspectives. First, we carry out an analysis of the effect of population size on the design

of assemblies; that is: the first time these assemblies are ‘formed'. Here we use a bivariate

OLS regression with logged assembly size and population size in order to model the

power law relationship between the two variables. Second, we carry out a survival

analysis examining the effect of population growth on the likelihood of the enlargement

of the legislature. This technique is best-suited to examine factors influencing the

‘survival of cases’ (here: how long it takes before an assembly is enlarged). Additionally

it is also well-fit to carry out longitudinal analyses, something that is central in the cube

root law. As population size and the effective number of parties change over time, we

organized the data in the subject-period format to ensure the independent variables can

10 Unfortunately there are no longitudinal data on public dissatisfaction for a wide range of countries. As such including this variable would reduce the sample size dramatically. There are some data for economic performance, but even here data were only available for 55% of the observations, which seriously damages any analysis. Therefore we do not outline a hypothesis for this expectation.

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vary over time.11 As our dependent variable is measured per election we apply the

continuous-time models.12 Specifically, we will use a Cox regression in this analysis

given that we have no strong theoretical grounds to expect that the baseline hazard

function has any specific shape, which rules out parametric models. The advantage of

Cox regressions is that they are very flexible regarding the baseline hazard function. They

come at the cost introducing an additional assumption: the proportional hazards

assumption.13 To test whether this assumption is violated we use Schoenfeld residuals.

Lastly, as a country can experience multiple consecutive enlargements of the legislature,

this needs to be controlled for. These so-called repeated events will be accounted for in

the analysis by introducing shared frailties.

3.2 Pool of countries, controls and operationalizations

In the design analysis, the dependent variable is the size of the assembly; in the redesign

analysis, the dependent variable is the increase in size of assemblies. We obtain our

assembly sizes from Bormann and Golder (2013) who have a comprehensive data set of

the electoral system for every legislative election in democratic countries since the

Second World War. This includes the size of the assembly that is elected. It covers 134

democracies and a total of 1197 legislative elections. They select regimes that Cheibub et

al. (2010) have identified as democratic. This conception of democracy depends not only

on the existence of democratically elected institutions but also alternation of power. This

means that it is overly conservative: countries like South Africa, where the same party

has been democratically re-elected to power four times, is not democratic.

A key independent variable is the population size. We derive population sizes from the

United Nations (2013a), which offers authoritative estimates of population sizes in most

UN members and a number of territories. This data is available for the period 1950 and

2010. In the design analysis, we use population size as an independent variable. In the 11 This means we have values per election period nested in countries. 12 Using discrete-time models (i.e. logit regression) would produce biased estimates as the time intervals are not of equal length: some governments fall early, while others last longer; some countries allow a maximum length of four years, while other allow five; which is why continuous-time models are required here (Mills, 2011:188). 13 It is assumed that e.g. when the risk of democratic erosions in Country A is twice that of Country B, this risk ratio should remain more or less the same over time.

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reform analysis, we start by calculating the assembly size that one would expect (E[S])

based on the cube root law and the population of that country (P1/3).

E[S] = P1/3

The actual assembly size (S) is then subtracted from this expected assembly size. The

resulting number represents the seat gap (G) between the expected and the actual

assembly size. The higher the gap, the more likely an enlargement of the assembly

according to the Taagepera-Shugart model.

G = E[S]-S

The Argentinean legislature for instance counted 149 members in 1951. As there were

17,506,714 Argentines at the time, based on the cube root law we would expect 260 MPs.

The gap between the expected assembly size (260) and the actual assembly size (149) is

thus 111 seats.

In the reform analysis, we use a number of additional variables. Most importantly we use

the effective number of parties in the parliament to test our rational choice hypothesis.

The effective number of parties is included in the Bormann and Golder (2013) data set.

We also add three control variables, namely the number of years a country is democratic

and dummies measuring whether or not a country has a mixed member proportional

system, a single member district electoral system or not. In order to measure the years a

country is democratic we use the polity IV data set (Monty et al. 2014).14 The electoral

system is used as a control variable because multi-member proportional electoral

systems, like the German, tend to change the number of seats in assembly every election

due to the existence of overhang mandates (Überhangmandate). The single member

district dummy is included because the assembly size works differently in such political

systems (i.e. it is directly related to the number of districts; cf. Colomer, 2004).

14 This is obviously only relevant for countries that were already democratic before 1950.

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This means that our data comes with restrictions: the assembly data is available for 133

countries. However, no UN population data is available for 13 of these; because these

countries no longer exist (e.g. West-Germany), are a micro-state (e.g. Nauru) or it is not a

recognized UN-member (e.g. Taiwan). This leaves 120 states (these are listed in

Appendix 1). 81 states that are included by the UN dataset, but they are excluded from

the Bormann and Golder (2013), because they are not democratic or because they are not

independent states. The excluded countries are listed in Appendix 2. An overview of the

countries included in the design analysis is provided in Appendix 3. Lastly, the

descriptives of the variables in the reform analysis can be found in Appendix 4

4. Population size and the ‘design’ of assembly sizes

First we examine the design hypothesis. This proposes that during the design phase the

relationship between population size and assembly size follows the cube root law. The

technocratic model that Taagepera and Shugart (1989) formulated applies to the choices

made during the design of an assembly.

To this end we look at countries that formed their first assembly in the period 1950-2010

for which we have population and assembly size data. Appendix 3 lists 40 countries for

which have this data. These are all countries that became independent between 1950 and

2010 as well as Bhutan, which held its first elections in this period. Many other countries

democratized during this period, but the assembly size was not chosen ex nihilo during

the transition to democracy. There was an (elected) assembly in the autocratic phase. The

number of seats of this assembly was re-evaluated: these were cases of re-design not

design. A number of countries that became independent are not included in this list

because the Bormann and Golder (2013) do not include the first elected assembly.

We evaluate two models: first, the Taagepera-Shugart model, which holds that the

relationship between population size and assembly size follows the cube root law. For

this deductively determined estimate we can calculate an r-squared value; we can also

plot it (in Figure 1). As we do not estimate the coefficients deductively they do not come

with standard errors, however. The cube root law explains 78% of the variance of the

sizes of assemblies. As Taagepera and Shugart (1989) already observed, this prediction is

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poorer for countries with a small number of inhabitants than for countries with a large

number of inhabitants.

We can also take inductive approach, entering the logged population size as the

independent variable in a regression analysis to explain the logged assembly size. We can

see the model in Table 2: there are two crucial differences between Model 2 and Model 1.

There is an intercept that is significantly different from zero. This effectively means that

structurally the assembly sizes are almost 90% smaller than we would predict on basis of

the cube root law. At the same time however, the coefficient for logged population is

significantly higher: It is 0.46 (as compared to 0.33, that Shugart and Taagepera predict).

This implies that the relationship between assembly size and population size is much

steeper than the theory would propose. We can use Zelig to estimate the 95% confidence

intervals (Imai 2008, 2009). The lower offset and the higher coefficient mean that the

predicted values differ significantly between the Shugart-Taagepera model and our model

for all countries with less than ten million inhabitants. 85% of the countries in the

analysis fall within this region. The cube root law explains 78% of the variance of

assembly sizes. The inductive model has a higher explained variance and it explains 89%

of the variance of assembly sizes.

This analyses come with one major caveat: out of the 40 assemblies elected, 37 were

successors to local self-governing councils, either those preparing for home-rule in

decolonizing states (such as the Territorial Assembly that preceded the National

Assembly in the Republic of the Congo) or state councils in federal states (such as Czech

National Council that preceded the Chamber of Deputies). The fact that these are

successor parliaments is evident from the fact that countries do not immediately hold new

elections after they declare independence but elevate the existing regional council to

parliament and allow its term to expire before holding new elections. This means that

these councils are also actually not designed ex nihilo but that they are redesigns of

existing councils. Only three entities are not the direct successor of such as council: the

Bhutan National Assembly which was instituted for the first time, the German Bundestag,

which succeeded the West German Bundestag and the East German People's Chamber,

and the India Lok Shaba, which succeeded the Central Legislative Assembly which

administered both India and Pakistan. Of these three, the German Bundestag elected in

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1990 is a clear example of redesign, which meant to incorporate East Germany into the

West German political system. The Lok Shaba is arguably also a case of redesign, which

was meant to form an Indian political system without Pakistan. This leaves only Bhutan

in our data as a case of a parliament that was really brand new.

Table 1: Models for design hypothesis

Variable Model 1 Model 2 Intercept 0

(NA)-2.22***

(0.39)Populationa 0.33

(NA)0.46***

(0.03)R-squared 0.78 0.89N 40 40Dependent variable: logged assembly size *** > 0.01 > ** > 0.05 > * > 0.1 a Logged

Note: Derived from Model 1 and 2. Red line representing the Shugart-Taagepera model and blue line representing the Model 2 with a 95% confidence interval. 5. Population size and the reform of assembly sizes

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The 'static' analysis revealed that population size is clearly related to the assembly size

when these assemblies are first ‘designed’. But Taagepera and Shugart (1989:179) also

expected that assembly sizes would be ‘adjusted’ when population growth entailed that

population and assembly size are out of tune. Table 2 shows the results of the Cox'

regressions.

Starting with the control variables, it seems that the type of electoral system does not

matter: countries with mixed member proportional and single member district systems

are not more likely to expand their legislatures than countries with other electoral

systems.15 The number of years that a country is democratic, however, matters quite a lot.

Long-standing democracies are more likely to increase their assembly size than newly

established ones. New democracies often change their electoral systems quite frequently,

but they typically focus on other elements that have a more direct impact on seat shares

(Bielasiak & Hulsey, 2013). In newer democracies, parties apparently have other

priorities than changing the assembly size.

Based on the theory we would expect a positive and significant coefficient of our

population variable (cf. hypothesis 2a). The direction of the coefficient is indeed positive,

as we expected. However, the effect appears to be very small and is only marginally

significant (p = 0.056). Indeed, the hazard ratio coefficient indicates that holding the

other covariates constant, the likelihood of experiencing an enlargement of the legislature

increases by just 0.1% per one-unit increase in our population variable.16 Perhaps the

effect is underestimated because the range of that variable is very wide? Indeed a one-

seat change is very small given that the population variable ranges from -279.40 to

516.70. Figure 2 therefore shows the effect for the full range of meaningful values of our

population variable.17 It highlights that despite the wide range, the effect is very small.

Only when the expected assembly size is 130 seats larger than the actual one, does the

effect of the difference between the actual and expected assembly size become

marginally significant. Even then it is only significant at the 0.1 level (not shown in

15 We use the label ‘likelihood’ to describe hazards/risks/conditional probabilities, as this makes interpretations more intuitive. 16 A one-unit increase here signifies that the difference between the expected assembly size (based on the population size) and the actual assembly size increases by one seat. 17 Meaningful, as in: excluding the outlier values.

17

figure) and it is never significant at the 0.05-level. Countries with a gap of 170 seats are

just 20% more likely to experience an enlargement of the legislature than countries where

the assembly is just the right size according to the cube root law. As such, hypothesis 2a

cannot be corroborated.

The rational choice perspective suggests that assembly sizes should increase when the

effective number of parties increases. This seems to be the case. The p-value of the

parties variable is below the 0.01 threshold (p = 0.0095) and the effect is positive, as we

expected. The coefficient also suggests that the effect is more substantial: for every

additional party, the likelihood of an enlargement of the legislature increases by 3.5%.

Once again though, this number may be misleading, this time because the range of the

effective number of parties variable is more limited than for the population variable. To

put things in perspective, we therefore plotted the meaningful values for the effective

number of parties variable in Figure 3. It turns out that the effect is somewhat moderate

because in practice most countries have relatively few parties (between two and six to be

precise). A country with six parties is about 14% more likely to experience an increase in

the assembly size than a country with just two parties.18

18 We also carried out analyses including whether or not a country was in recession. Unfortunately, the number of observations then drops to just 663 and whole countries disappear as missing. For the sake of completeness, the results of this analysis are: after correcting for the fact that the variable has non-proportional hazards, the coefficients and p-values for our two main variables, the number of parties and the population size are very similar. The effect of the economic situation is absent at first, but becomes statistically significant and negative after six years of having the same assembly size.

18

Table 2. Models for the reform hypotheses

Model 1.

Controls only

Model 2.

Number of parties

Model 3.

Population

Model 4

Full model

Coef. (s.e.)

Haz. rat. Coef. (s.e.)

Haz. rat. Coef. (s.e.)

Haz. rat. Coef. (s.e.)

Haz. rat.

H2a. Population – assembly size gap (in seats)

0.0012 (0.0006)

1.001 0.0012 (0.0006)

1.001

H2b. Effective number of parties 0.0351 (0.0129)

1.036** 0.0343 (0.0132)

1.035**

Years democratic 0.0063

(0.0019)

1.006*** 0.0062 (0.0018

1.006*** 0.0062 (0.0020)

1.006*** 0.0070 (0.0020)

1.007***

Single Member District -0.0302

(0.1572)

0.09703 0.0115 (0.1603)

1.012 -0.0318 (0.1623)

0.09703 0.0065 (0.1657)

1.006

MMP 0.1730 (0.2484)

1.189 0.1847 (0.2480)

1.203 0.1520 (0.2873)

1.164 0.1673 (0.2869)

1.182

Events 235 230 217 213

Observations 1063 1001 950 922

LR test 63.18*** 63.34*** 63.18*** 65.41***

Schoenfeld residuals test (chi sq. value) 5.50 5.31 6.33 6.06

Generalized R2 0.42 0.44 0.44 0.47

***p<0.001, **p<0.01, *p<0,05 Note: All models include controls for number of past events by including shared frailties. Note2: Significant values for the Schoenfeld residuals would indicate that the effect of at least one variable changes over time. This is not the case for our variables, so no adjustments need to be made.

19

Figure 2. Effect of the population / assembly size gap19

Figure 3. Effect of the effective number of parties20

19 We used simulations to calculate the quantities of interest. To avoid distortion by outliers, the minimum/maximum value is always based on 1.5 times the inter-quartile distance. This number is subtracted from the Q1-value or added to Q3-value to determine the minimum and maximum X-values. 20 The number of parties is centered as hazard ratios always take 0 as the point of reference, a value that does not occur in our dataset.

20

6. Conclusion

This study set out to determine the relationship between population and assembly size.

We differentiated between two phases in which population size may play a role in

decision-making about assembly sizes: the first is when assemblies are designed for the

first time and second when assemblies are reformed, when their size is re-evaluated.

Statistically, we find a strong and significant effect of population size on assembly size in

the 'design phase'. The empirical patterns do not exactly fit the cube root law prediction,

showing a pattern that is closer to a 'root law' than a 'cube root law'. The crucial problem

however is that when critically reflect on the forty available cases of post-independence

or post-dictatorship assembly, only one (1) is an actual example of designed assembly

that does not have a predecessor. In the period 1950-2010, there are almost no examples

of countries that democratized or became independent without having some form of self-

governing council. This means that reform is much more important than design. Here we

find considerably less support for the hypothesis that growing population size is a reason

re-evaluate assembly sizes. This relationship is weak and barely significant. The

likelihood of change in assembly size is not predicted by discrepancies between the

population size and assembly size. The evidence presented here supports the hypothesis

that the number of parties matters for assembly size: the more fractionalized an assembly,

that is the more small parties there are, the more likely an assembly is to expand. The

reason is, we propose, that small parties benefit in terms of their seat shares when an

assembly expands. Practically, the size of the effect of the effective number of parties is

similar to the effect of population size. However, given that the effective number of

parties is a factor changes quite frequently and population growth is a long-term slowly

evolving process, the effective number of parties is more likely to play a role in real-life

debates about increasing the assembly size, than population size.

This leaves us with a puzzling observation: why do assembly sizes at particular points in

time actually match the population sizes of their respective countries, even though from

an empirical perspective population size does not play a major role in re-evaluating

assembly sizes? This study only surveyed the period 1950-2010, the relationship between

21

population growth and assembly size may actually have been set in the period before that.

After that 1950 the relationship continued to exist for the simple reason that the order of

magnitudes of the population sizes and the assembly sizes was set. For instance, the order

of magnitude of the size of the Irish parliament was set in 1922 to reflect the country's

population size then. Since then the population has increased and the size of the Dáil may

have been updated: but the population of Ireland did not increase ten-fold. The very

nature of the cube root calculation allows to absorb quite a lot of population growth.

Therefore the rough cube root law may still hold, reflecting earlier population sizes.

Second, in a similar line of argument the size of many self-governing regional or

territorial bodies that existed before countries became independent may have been set up

to reflect the size of the population in the region when they were first formed. Since then

the population did not change an order of magnitude. Therefore again the cube root law

may still hold, but it reflects much earlier population sizes. The same may also apply for

representative assemblies that were formed during autocratic phases. This does mean,

however, that cube root law is not a law: there is no direct causal relationship between the

current population sizes and the current assembly sizes. The existence of a statistical

relationship may only reflect a relationship between assembly and population sizes when

they were set up. We find no proof of continuous updating of these assembly sizes in the

period 1950-2010. In sum, present correlations between population and assembly size are

probably more of a historical artifact than a sign of an empirical law.

Future research may therefore want to expand their research in two directions: first, we

may want to look in more detail at the size of assemblies when they are actually designed

for the first time. This means that for Western democracies we would have to look at the

pre-War period. We would need to go back to as far as 930 for the Icelandic Althing. For

countries in Asia, Africa and Eastern Europe that, since the Second World War, have

become newly independent, we would need to look at the sizes of regional and territorial

self-governing bodies. And finally for autocracies, we would have to look at the size of

populations and assemblies for the first time at which assemblies were set up -

independent of the level of democracy in that country.

22

Second, future research may also want to provide a more elaborate longitudinal test of the

relationship between population and assembly size. For instance, in this study we could

not test the effect of public opinion, nor of factors that affect public opinion such a

country's economic performance. Given the lack of empirical support for the effect of

population size (from the institutionalist logic) and the relative small impact of the

number of political parties (rational considerations by MPs), the literature would indicate

that these kinds of explanations may be a third and more fruitful avenue.

23

7. Appendices Appendix 1: countries included

# Country Since 1 Albania 1992 2 Antigua and Barbuda 1984 3 Argentina 1951 4 Armenia 1995 5 Australia 1951 6 Austria 1949 7 Bahamas 1977 8 Bangladesh 1991 9 Barbados 1966

10 Belgium 1953 11 Belize 1984 12 Benin 1991 13 Bhutan 2008 14 Bolivia 1979 15 Brazil 1950 16 Bulgaria 1991 17 Burundi 1993 18 Canada 1953 19 Cape Verde 1991 20 Central African Republic 1993 21 Chile 1953 22 Colombia 1958 23 Comoros 1992 24 Congo 1963 25 Costa Rica 1953 26 Croatia 1992 27 Cuba 1950* 28 Cyprus 1985 29 Czech Republic 1990 30 Denmark 1950 31 Dominican Republic 1966 32 Ecuador 1952 33 El Salvador 1985 34 Estonia 1992 35 Fiji 1992 36 Finland 1951 37 France 1951 38 Georgia 2004 39 Germany 1990 40 Ghana 1979 41 Greece 1950

24

42 Grenada 1976 43 Guatemala 1950 44 Guinea-Bissau 1999 45 Honduras 1957 46 Hungary 1990 47 Iceland 1946 48 India 1951 49 Indonesia 1999 50 Ireland 1951 51 Israel 1951 52 Italy 1953 53 Jamaica 1962 54 Japan 1952 55 Kenya 1997 56 Kiribati 1982 57 Korea 1960 58 Kyrgyzstan 2007 59 Laos 1955* 60 Latvia 1993 61 Lebanon 1951 62 Liberia 2005 63 Lithuania 1992 64 Luxembourg 1954 65 Macedonia 1994 66 Madagascar 1993 67 Malawi 1994 68 Maldives 2009* 69 Mali 1992 70 Malta 1966 71 Mauritania 2006* 72 Mauritius 1976 73 Mexico 2000 74 Micronesia 1991 75 Moldova 1998 76 Mongolia 1992 77 Myanmar 1951 78 Nepal 1991 79 Netherlands 1952 80 New Zealand 1951 81 Nicaragua 1990 82 Niger 1993 83 Nigeria 1964 84 Norway 1953 85 Pakistan 1977 86 Panama 1952 87 Papua New Guinea 1977

25

88 Paraguay 1989 89 Peru 1956 90 Philippines 1953 91 Poland 1991 92 Portugal 1976 93 Romania 1990 94 Saint Lucia 1979 95 Saint Vincent and the Grenadines 1979 96 Sao Tome and Principe 1991 97 Senegal 2001 98 Serbia 2007 99 Sierra Leone 1962

100 Slovakia 1994 101 Slovenia 1992 102 Solomon Islands 1980 103 Somalia 1964 104 Spain 1977 105 Sri Lanka 1952 106 Sudan 1958 107 Suriname 1977 108 Sweden 1952 109 Switzerland 1951 110 Thailand 1975 111 Timor 2007 112 Trinidad and Tobago 1966 113 Turkey 1961 114 Uganda 1980* 115 Ukraine 1994 116 United Kingdom 1950 117 United States of America 1950 118 Uruguay 1950 119 Vanuatu 1983 120 Venezuela 1963

* only one case included

26

Appendix 2: countries excluded

# Country Reason of exclusion Included in 1 Afghanistan no democracy included in UN (2013a) 2 Algeria no democracy included in UN (2013a) 3 Andorra too small included in Golder (2013) 4 Angola no democracy included in UN (2013a) 5 Aruba not independent included in UN (2013a) 6 Azerbaijan no democracy included in UN (2013a) 7 Bahrain no democracy included in UN (2013a) 8 Belarus no democracy included in UN (2013a) 9 Bosnia and Herzegovina no democracy included in UN (2013a)

10 Botswana no democracy included in UN (2013a) 11 Brunei Darussalam no democracy included in UN (2013a) 12 Burkina Faso no democracy included in UN (2013a) 13 Cambodia no democracy included in UN (2013a) 14 Cameroon no democracy included in UN (2013a) 15 Chad no democracy included in UN (2013a) 16 Channel Islands not independent included in UN (2013a) 17 China no democracy included in UN (2013a) 18 Hong Kong SAR not independent included in UN (2013a) 19 Macao SAR not independent included in UN (2013a) 20 Côte d'Ivoire no democracy included in UN (2013a) 21 Curaçao not independent included in UN (2013a) 22 Czechoslovakia no longer exists included in Golder (2013) 23 Dem. People's Republic of Korea no democracy included in UN (2013a) 24 Democratic Republic of the Congo no democracy included in UN (2013a) 25 Djibouti no democracy included in UN (2013a) 26 Dominica too small included in Golder (2013) 27 Egypt no democracy included in UN (2013a) 28 Equatorial Guinea no democracy included in UN (2013a) 29 Eritrea no democracy included in UN (2013a) 30 Ethiopia no democracy included in UN (2013a) 31 French Guiana not independent included in UN (2013a) 32 French Polynesia not independent included in UN (2013a) 33 Gabon no democracy included in UN (2013a) 34 Gambia no democracy included in UN (2013a) 35 Guadeloupe no democracy included in UN (2013a) 36 Guam not independent included in UN (2013a) 37 Guinea no democracy included in UN (2013a) 38 Guyana no democracy included in UN (2013a) 39 Haiti no democracy included in UN (2013a) 40 Iran (Islamic Republic of) no democracy included in UN (2013a) 41 Iraq no democracy included in UN (2013a) 42 Jordan no democracy included in UN (2013a) 43 Kazakhstan no democracy included in UN (2013a)

27

44 Kuwait no democracy included in UN (2013a) 45 Lesotho no democracy included in UN (2013a) 46 Libya no democracy included in UN (2013a) 47 Liechtenstein too small included in Golder (2013) 48 Malaysia no democracy included in UN (2013a) 49 Marshall Islands too small included in Golder (2013) 50 Martinique not independent included in UN (2013a) 51 Mayotte not independent included in UN (2013a) 52 Montenegro no democracy included in UN (2013a) 53 Morocco no democracy included in UN (2013a) 54 Mozambique no democracy included in UN (2013a) 55 Namibia no democracy included in UN (2013a) 56 Nauru too small included in Golder (2013) 57 New Caledonia not independent included in UN (2013a) 58 Oman no democracy included in UN (2013a) 59 Palau too small included in Golder (2013) 60 Polynesia not independent included in UN (2013a) 61 Puerto Rico not independent included in UN (2013a) 62 Qatar no democracy included in UN (2013a) 63 Réunion not independent included in UN (2013a) 64 Russian Federation no democracy included in UN (2013a) 65 Rwanda no democracy included in UN (2013a) 66 Saint Kitts and Nevis too small included in Golder (2013) 67 Samoa not independent included in UN (2013a) 68 San Marino too small included in Golder (2013) 69 Saudi Arabia not independent included in UN (2013a) 70 Serbia and Montenegro no longer exists included in Golder (2013) 71 Seychelles no democracy included in UN (2013a) 72 Singapore no democracy included in UN (2013a) 73 South Africa no democracy included in UN (2013a) 74 South Sudan not existent yet included in UN (2013a) 75 State of Palestine not independent included in UN (2013a) 76 Swaziland no democracy included in UN (2013a) 77 Syrian Arab Republic no democracy included in UN (2013a) 78 Taiwan not independent included in Golder (2013) 79 Tajikistan no democracy included in UN (2013a) 80 Tanzania no democracy included in UN (2013a) 81 Togo no democracy included in UN (2013a) 82 Tonga no democracy included in UN (2013a) 83 Tunisia no democracy included in UN (2013a) 84 Turkmenistan no democracy included in UN (2013a) 85 Tuvalu too small included in Golder (2013) 86 United Arab Emirates no democracy included in UN (2013a) 87 United States Virgin Islands not independent included in UN (2013a) 88 Uzbekistan no democracy included in UN (2013a) 89 Viet Nam no democracy included in UN (2013a)

28

90 West Germany no longer exists included in Golder (2013) 91 Western Sahara not independent included in UN (2013a) 92 Yemen no democracy included in UN (2013a) 93 Zambia no democracy included in UN (2013a) 94 Zimbabwe no democracy included in UN (2013a)

29

Appendix 3: Countries included to test design hypothesis # Country Year

1 Antigua and Barbuda 19842 Armenia 19953 Bahamas 19774 Barbados 19665 Belize 19846 Bhutan 20087 Congo 19638 Croatia 19929 Czech Republic 1996

10 East Timor 200711 Estonia 199212 Germany 199013 Grenada 197614 India 195115 Jamaica 196216 Kiribati 198217 People's Democratic Republic of Laos 195518 Latvia 199319 Lithuania 199220 Macedonia 199421 Malta 196622 Mauritius 197623 Federated States of Micronesia 199124 Myanmar 195125 Nigeria 196426 Papua New Guinea 197727 Serbia 200728 Sierra Leone 196229 Slovakia 199430 Slovenia 199231 Solomon Islands 198032 Somalia 196433 Sri Lanka 195234 St. Lucia 197935 St. Vincent and the Grenadines 197936 Sudan 195837 Suriname 197738 Trinidad and Tobago 196639 Ukraine 199440 Vanuatu 1983

30

Appendix 4. Descriptives of the variables

Name variable Minimum Maximum Mean

Increase in assembly size 0 1 (235 observations) 0.20

Population size gap -279.40 516.70 32.29

Effective number of parties 1 52.42 3.55

Years democratic 0 201 43.34

Mixed member proportional 0 1 (55 observations) 0.05

Single member district 0 1 (287 observations) 0.24

Total N: 1197

31

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