Party system classification A methodological inquiry

classifications. However, the most widely accepted criterion – the one normally
placed first on the list (Smith, 1989) – has always been the number of parties, often
defined in terms of their relative sizes. Traditionally, this approach draws a salient
distinction between two-party and multiparty systems which has long been recognized
as a theoretically fundamental divide (Daalder, 2002: 43–51), and then proceeds to
introduce several intermediate, supplementary or otherwise qualified types. Some
of the classifications, including the most influential one (Sartori, 1976), combine the
numerical/relative size criteria with different classificatory parameters, which is
increasingly viewed as a desideratum in party system research (Bardi and
Mair, 2008; Blau, 2008). But the number of parties is still important in such combina-
tions. The purpose of this study is not to propose a new taxonomy of party systems
nor to arrive at new substantive findings, even though some tribute will be paid to
both these aspects, but rather to develop a method that can be used for defining party
system types in operational terms, and distinguishing among them by a clear, parsimo-
nious criterion.

The primary motivation for this study stems from the fact that, given the pedigree of

classifying party systems by the numbers of parties, a surprising uneasiness remains
when we confront questions so simple that they have to be answered from scratch, such
as ‘how many two-party systems are there in the world?’ In my understanding, a satis-
factory answer to this question can be nothing else but a number. Yet too often the
answer takes a couple of pages and remains inconclusive (Mair, 1997: 204–5). Such
situations indicate a lack of method rather than a lack of knowledge. Hence, this study
is methodological, not theoretical or empirical. First, I briefly overview the existing clas-
sifications of party systems based on the numbers of parties and discuss methodological
tools that have been used, or can potentially be used, for classifying party systems, the
effective number of parties and the Nagayama diagram. Second, I introduce the new
method and explain its properties. For illustration, the method is applied to a comprehen-
sive set of post-World War II party systems. Several substantive findings produced by
the proposed method in its application to the data are discussed briefly.

Party system classifications, past and present

When using classifications of party systems based on the numbers of parties or their
relative sizes, many authors have introduced their own minor modifications to the estab-
lished models. Yet the lasting contributions of the past are few, and there have been sur-
prisingly few attempts to build on them in the past three decades (Wolinetz, 2006). The
classification of Duverger (1954), who identified two-party and multiparty systems as
major types, was important because he succeeded in placing this simple taxonomy high
on the research agenda of post-war political science. The second important step was by
Blondel (1968), whose contribution was not only to define the types identified by Duver-
ger in operational terms, but also to introduce a number of additional categories. The
basis for Blondel’s classification is the share of the vote jointly received by the two larg-
est parties in the legislative election. Two-party systems are those in which this exceeds
90 percent. For systems where it makes 75 percent of the vote or more, Blondel intro-
duces a new type of two-and-a-half party systems. All other systems are genuinely

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Party Politics 17(5)

540

multiparty, but they are divided into two types; those with and those without a dominant
party. These types are distinguished by the share of the vote obtained solely by the
largest party, the threshold being set at 40 percent.

A classification proposed by Rokkan (1970) differed from Blondel’s in two important

respects. First, Rokkan shifts the basis for party system classification from vote-shares to
seat-shares. Second, the Rokkan approach is centred not so much on the absolute
strengths of parties as on their relative strengths. The theoretical reason for these differ-
ences is that Rokkan much more explicitly relates party system properties to the patterns
of interaction among parties in their competition for office, and defines them in terms of
coalition-building. In the British–German ‘1 versus 1

þ 1’ party system, two large parties

alternate in power, occasionally in coalitions with third minor parties. In the Scandina-
vian ‘1 versus 3–4’ system, the largest party either rules alone or alternates with a more
or less formalized coalition of minority parties. The even multiparty systems, ‘1 versus
1 versus 1

þ 2 – 3’, are the home of fully fledged, multilateral coalition politics.

Some of the ideas embedded in Rokkan’s approach were elaborated in the seminal

work of Sartori (1976). From his perspective, parties are relevant only if, by merit of
their relative strengths on the legislative floor, they can influence coalition-formation.
Such potential can be either positive, in the form of being acceptable as coalition part-
ners (coalition potential properly), or negative, in the form of being able to undermine
coalition-formation (blackmail potential). The direction of the potential is defined by
the ideological distances among parties. This brings Sartori back to the two-
component classification of Duverger, with the two-party and multiparty systems
being the principal types, yet the second category is broken into two subdivisions
by the criterion of ideological distance. One of the innovations in Sartori’s work was
to identify a new type, predominant-party systems, characterized by continuous par-
liamentary domination of one political party. It has to be said that Sartori provides
no solid conceptual justification for singling out this particular type, noting instead
that ‘the predominant-party system actually is a more-than-one party system in which
rotation does not occur in fact’ (1976: 173). Apparently, here the basis for his classi-
fication is purely empirical.

While Sartori’s classification is often regarded as the most influential (Mair, 2002:

91–2), it has to be recognized that for those scholars whose research requires a more
differentiated view of party systems, and who need not focus so heavily on ideological
distances, it has little to offer. Modified versions of Blondel’s taxonomy remain wide-
spread. Using the percentages of legislative seats as a basis for his classification, Ware
(1996) outlines four main types: two-and-a-half party systems; systems with one large
party and several much smaller ones; systems with two large parties and several much
smaller ones; and even multiparty systems. An important attempt to build on Blondel’s
work was undertaken by Siaroff (2000), whose classification employs multiple quantita-
tive criteria: the number of parties obtaining more than 3 percent of seats (two, three to
five or more than five); the share of seats jointly obtained by the two largest parties
(95 percent or more, 80–95 percent or less); the seat ratio between the largest and the
second-largest party (greater or smaller than 1.6); and the seat ratio between the
second-largest and the third-largest party (greater or smaller than 1.8). The first criterion
distinguishes between two-party systems and all other systems, viewed by Siaroff as

Golosov

541

varieties of multipartism. Of these, two-and-a-half party systems are singled out by the
second criterion. The remaining moderate multiparty systems are those with one domi-
nant party, with two main parties and with a balance among parties. Extreme multiparty
systems are broken into three categories by the same rules, which makes for eight party
system types overall, seven of which are multiparty systems. The predominant-party sys-
tem is not in this scheme, but in a follow-up publication. Siaroff (2003: 271) includes it
as well, defined as a system in which the largest party gains at least 51 percent of seats,
and the seat ratio between the largest and the second-largest party is at least 1.8.

Obviously, in terms of operational thoroughness, Siaroff’s classification is best devel-

oped. It encompasses major advances in party system classification: it is centred around
seat-shares, not vote-shares; it counts parties by taking into account their relative sizes;
and it relates party system types to the patterns of coalition politics. No less obviously,
this classification goes too far in its enumeration of the minor types of multipartism,
which, to cite one example, leads Siaroff (2000: 71) into claiming that Belgium has gone
through six different party systems since World War II. The multiplicity and complexity
of the classificatory criteria are also a problem, especially given the fact that by the time
Siaroff developed his classification a parsimonious and apparently efficient numerical
criterion for classifying party systems was in place.

The effective number of parties is the number of ‘important’ parties in a given party

system. Conceptually, then, it is directly related to party system classifications discussed
above. Moreover, the fundamental approach that guides the reasoning beyond the effec-
tive number of parties is exactly the same as in many of these classifications: if only
important parties are to be counted, then their importance is the function of their relative,
not absolute, size. The difference is that the effective number of parties is expressed not
as a series of thresholds, but rather as a mathematical formula that yields a compact
numerical value for any given party constellation. Thus the effective number of parties
is a continuous measure. Its properties, irrespective of the specific mathematical form,
are thus: if all parties in the given party constellation are equal, then its value equals the
actual number of components, but if the components are not equal, then its value is
smaller than the actual number of components. In this way, the smallest components are
discounted. The effective number for a party constellation of two equal-size parties is
exactly two. It increases with the arrival of a third party, and the larger the third party
the greater the weight attributed to it by the effective number of parties. Apparently, this
provides us with a simple method by which to distinguish among the types that have
long been essential for party system classifications, two-party, two-and-a-half party and
multiparty (Lijphart, 1994: 67–9). The formula itself is constructed by applying
common-sense criteria of intuitive plausibility to the results of tests performed on
hypothetical and real datasets.

The Laakso–Taagepera effective number of parties (Laakso and Taagepera, 1979) has

been the most widely used measure in comparative research on political parties (Amorim
Neto and Cox, 1997; Lijphart, 1994; Ordeshook and Shvetsova, 1994). At some point,
this measure (N

) came very close to replacing all other methods of party system clas-

sification. Mathematically, the Laakso–Taagepera effective number of parties is defined
as 1 divided by the sum of squared vote-shares or seat-shares of all parties in the given
constellation:

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Party Politics 17(5)

542

In this formula, and in all formulae below, sigma stands for summation, with the lower
and upper bounds indicating its limits from the largest component (1) to the smallest (x),
while the components themselves (s

) are defined as absolute shares of the total.

This mathematical form is associated with a serious problem. N

does not differenti-

ate well between cases of one-party dominance and two-party constellations. For
instance, when the largest component is 70 percent of the total, and there are three minor
components of 10 percent each, N

equals 1.92, exactly the same as for a two-party con-

stellation in which the ratio between the largest party and the second party is 60/40. In
the world of the late 1970s, when Laakso and Taagepera proposed their index, instances
of predominant-party systems were rare. In the contemporary world, there are regions in
which predominant-party systems abound. This naturally renders the relevance of N

questionable (Bogaards, 2004). From a more methodological perspective, a continuous
measure is only good when it clearly differentiates among observations located close to
the ends of the theoretically defined continuum, which does not appear to be the case
with N

. In the recent literature, several attempts have been made to improve the effec-

tive number of parties by changing its mathematical form (Dunleavy and Boucek, 2003).
One of the proposed alternatives, N

, largely eliminates this shortcoming (Golosov,

2010). The values of the effective number of parties yielded by this measure for the
exemplary constellations above are more plausible; 1.51 for (0.7, 0.1, 0.1, 0.1) and
1.67 for (0.6, 0.4). The definition of N

is:

þ ðs

Þ s

This is not the end of the problem, however. As we have seen, party system classifica-
tions are heavily focused on the patterns of coalition politics. Therefore any numerical
criterion for such classifications has to distinguish clearly between the constellations
where the largest party takes a majority of seats and those where it does not. Irrespective
of its mathematical form, the effective number of parties cannot do that. In fact, it does
not have to, because its primary function is to register the levels of fragmentation. Con-
sider a predominant-party constellation (0.55, 0.25, 0.20). For this constellation N

2.47, which suggests a two-and-a-half party format, and N

¼ 1.94, which suggests

bipartism. Both categorizations are incorrect. Yet in this case it would be scarcely per-
missible for a measure of fragmentation not to register the presence of significant parties
beyond the largest one. There were proposals to adjust N

for the study of coalition pol-

itics by replacing proportions of seats in the formula with the Banzhaf voting power mea-
sures (Blau, 2008). However, such measures can only be supplementary because they
tend to eliminate the difference between predominant-party systems and two-party
systems.

Golosov

543

The Nagayama diagram, often referred to as the Nagayama triangle, is a two-

dimensional graphical representation of the space of electoral competition. It was used
mostly for analysing competition in single-member districts and proved to be quite
efficient (Likhtenchtein and Yargomskaya, 2005; Reed, 2001). The properties of the dia-
gram are systematically explained in Grofman et al. (2004). The x-axis is used to show
the absolute vote-share of the winning candidate, and the y-axis, that of the second-runner.
Because she never takes more votes than the winner, the feasible set of data points lies
within a triangle bounded by the x-axis and segments of the lines y

¼ x and y ¼ 1 – x.

By dividing the triangle into several segments, as shown in Figure 1, different patterns
of district contests can be identified.

Districts where the winner takes more than

50 percent of the vote fall within the BCD segment, and those where she does not fall
within the ABD segment. The BHFI segment contains very close races between two
major candidates: the CGFI segment, those in which the races are not very competitive
and the viable third candidates are absent, and the AEHI segment, those in which close
multi-candidate competition occurs. The EGI segment includes intermediate cases.
Thus the Nagayama triangle conveniently visualizes the patterns of district-level
competition.

But is it possible for the Nagayama triangle to be used for classifying party systems?

Of course, vote-shares of individual candidates can be replaced with legislative seat-
shares (Taagepera and Allik, 2006). Then the segments of the triangle obviously repli-
cate the types identified in the qualitative classifications of party systems. Yet such an
elegant solution is not feasible. First, as Grofman et al. (2004) correctly suggest, for the
graphical presentation of this kind to be efficient it has to allocate equal regions to all
theoretically important types. Indeed, it is imperative that the distribution of data points

Figure 1. The segmented Nagayama triangle. Source: Adopted with a minor modification from
Grofman et al. (2004)

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Party Politics 17(5)

544

across the available space be defined only by the data’s own properties, not by the con-
struction of the graph. While Grofman et al. demonstrate that this desideratum can be
satisfied when studying district contests, this is clearly not the case with party systems.
For instance, the region within which two-party constellations can be located, BFI, takes
only 4 percent of the overall space of the triangle. The second reason why the Nagayama
triangle does not fare well on classifying party systems is less apparent but probably
more important. Once the bounds of the diagram are established, we have to expect that
no points within the bounded space will be structurally empty. Yet, in fact, all points
along the x-axis of the Nagayama triangle, with the one exception of point C, are empty
by definition, simply because there can be no zero-size second component in a constel-
lation will the largest component be smaller than 1. Moreover, all points surrounding
the A vertex of the diagram, as well as those lying close to the x-axis, while not empty
in structural terms, are very likely to remain empty with any real-life dataset. This is
because there is a hidden parameter in the Nagayama triangle, that is, the number of
candidates or parties. The data point with x

¼ 0.1 and y ¼ 0.01 will not be empty only

if there are no less than 91 competitors, 90 of them receiving no more than 1 percent of
seats. Such structural zeros or near-zeros bias the graphic representation in favour of its
structurally non-empty segments.

The effective number of parties and the Nagayama triangle are good for doing what

they are meant to do. There is no better way of registering the levels of fragmentation in
the electorate than the effective number of parties, while the Nagayama triangle will
obviously remain in the toolkit of the students of district-level contests. It is clear, how-
ever, that none of them provides us with an adequate basis for party system classification.
Meanwhile, the lack of parsimonious operational definitions for party system types hin-
ders the existing qualitative classifications.

The new method for classifying party systems

The method of party system classification proposed in this study is informed by all three
streams of thought described above – the qualitative typologies, the effective number of
parties and the Nagayama triangle. The influence of the Nagayama diagram is funda-
mental, because it has to be credited for the very idea of representing types of competi-
tion as segments of a bounded two-dimensional space. Qualitative typologies help us
understand that for classifying party systems we have to focus on legislative seat-
shares, rather than on vote-shares, and define party sizes in relative terms rather than
in absolute terms. Both the Nagayama triangle and the qualitative typologies suggest that
the situations in which there are majority parties have to be clearly separated from those
in which there are not. One of the mathematical definitions of the effective number of
parties, N

, was instrumental in our finding a technical solution that satisfies all these

desiderata. In the Nagayama diagram, the coordinates of data points are absolute shares
of the total, while the relationships among party sizes are established by segmentation.
Yet it need not be so. The mathematical form of N

is such that the largest component is

always counted as 1, while all other components are weighted against the size of the larg-
est component and their own sizes. Therefore, taking the size of the largest component as
a constant, we can build a diagram with x-coordinates expressing the relative size of the

Golosov

545

second component, and y-coordinates the relative size of the third component. In other
words, the coordinates themselves can be indices, i.e. single numbers derived from more
than one quantity.

Such a solution is very close to one of the operational criteria developed by Siaroff

(2000); namely, the seat ratio between the largest and the second-largest party. Of
course, to make the index bounded, the inverse of the ratio has to be taken. Then the
x-coordinates can be defined as s

. The drawbacks of such an attractively simple

approach are discussed below. The optimal representation can be achieved by bringing
in an additional element, the share of seats jointly received by all parties from the fourth-
largest to the smallest, i.e. s

Thus the sizes of the second and third components are

weighted not only by the size of the largest component but also by this additional ele-
ment, one of the bounds being provided by entering s

into both the numerator and the

denominator of the equations:

þ s

;

þ s

Figure 2 shows the resulting graphical representation. I dub it the relative-size triangle
(RST). Indeed, similar to the Nagayama diagram, the feasible set of data points lies

Figure 2. The segmented relative-size triangle with some data points of significance

546

Party Politics 17(5)

546

within a triangle, the bounds of which are the x-axis (AC), the x

¼ 1 line (BC) and the y ¼

x line (AB). This determines the shape of the triangle.

Unlike the Nagayama diagram,

the one proposed contains no structurally empty points. All constellations with two par-
ties are located along the x-axis. Constellations with more than two parties can take any
point depending on the relative sizes of the parties, but not on their numbers. Another
advantage of the proposed graphical display over the Nagayama diagram is that it can
easily be segmented into equal-size regions corresponding to the theoretically important
types of party systems. The geometrical centre of any triangle is its centroid (G), the
point located at the intersection of its medians. The coordinates of the centroid are the
mean coordinates of the vertices, which makes it the true ‘average point’ of any triangu-
lar graphical representation. While intersecting at the centroid, the medians divide the
triangle into six equal-size segments. In order to define these segments in substantive
terms, we have to look at the equations describing the medians of the triangle, which are
y

¼ 0.5x for AF, y ¼ 1 – x for CE and y ¼ 2x – 1 for BD. These equations can be redefined

in terms of the sizes of the components. Consider the y

¼ 1 – x equation. Using the def-

initions of x and y provided above, we can write:

þ s

On removal of the redundant denominator and some other reductions, this can be
rewritten as: s

¼ s

þ s

, which can be achieved only if s

¼ 0.5.

Therefore all data points lying below the CE line represent the constellations in which

there is a majority party, the points above it, those in which there is not, and the points on it,
those where the majority party takes exactly half of the seats. The definitions of the six seg-
ments of the RST that stem from similar algebraic transformations are reported in Table 1.

Before defining the segments in substantive terms, it has to be clarified that in contrast

to the effective number of parties, the RST does not make numerically precise distinc-
tions among the degrees of party system fragmentation/fractionalization, which is espe-
cially visible with multipartism. For instance, it assigns all constellations in which more
than two of the largest components are of equal size to the same data point, B. Indeed, the
RST display is focused on the relative imbalances in size among the three largest parties.
Both aspects, fragmentation and imbalance, are important for characterizing entities that
consist of discrete components, and they do overlap empirically, but not to an extent that
would allow for developing a unified method of measurement (Taagepera, 1979). From

Table 1. Segments of the RST diagram defined by the sizes of the three largest components

Segment of the RST

AEG

> 0.5

< (s

þ s

)/2

> (s

– s

)/2

ADG

> 0.5

þ s

)/2

– s

)/2

CDG

0.5

> (s

þ s

)/2

< (s

– s

)/2

CFG

< 0.5

> (s

þ s

)/2

< (s

– s

)/2

BFG

< 0.5

þ s

)/2

– s

)/2

BEG

0.5

< (s

þ s

)/2

> (s

– s

)/2

Golosov

547

this theoretical perspective, the approaches embodied in the effective number of parties
and in the RST can be viewed as mutually complementary and used together whenever
appropriate. In particular, the effective number of parliamentary parties is indispensable
for characterizing multiparty systems irrespective of their placement on the RST diagram,
especially in those cases when it is important to distinguish systems with extreme or large
numbers of parties from those with three or four. Yet in those cases when it is important to
distinguish multiparty systems with one large party and several much smaller ones from
systems with two large parties and several much smaller ones, and/or to draw clear separa-
tion lines between multiparty systems and all other types, the effective number of parties
alone is insufficient and can be complemented with the RST. More importantly, the RST
diagram performs better than the effective number of parties on separating two-party sys-
tems from predominant-party systems, and on making distinctions within these types,
which enables it to serve as a basis for party system classification.

It would be incorrect, however, to assume that the fragmentation aspect is completely

unaddressed by the proposed method. The RST incorporates it by using the s

term in the

formulae for x and y. If they are defined as simple ratios s

and s

, such obviously

different-type combinations as (0.6, 0.2, 0.2) and (0.3 and 7 parties at 0.1) receive the
same scores, x

¼ y ¼ 1/3. Yet it is quite obvious that the first constellation should be

assigned to the predominant-party system type, while the second is an instance of multi-
partism, and separating these two types from each other is especially important given the
above-described property of the RST. With the s

term, the scores are quite different: for

the first constellation, they are still x

¼ y ¼ 1/3, but for the second, x ¼ y ¼ 3/4. In order

to understand the mathematical meaning of the s

term, it is useful to look at a hypothe-

tical constellation in which both s

and s

are infinitely small, close to zero. Taking into

account that for such constellations, s

þ s

1, the formulae for x and y reduce to s

Thus the values of s

are the lower theoretical limits of x and y values. For instance,

no constellation in which minor parties, starting with the fourth one, jointly take
50 percent of seats, can be placed below the EF line on the diagram irrespective of the
absolute sizes of the components, which promptly characterizes such constellations as
different from those with limited minor party presence.

For empirically oriented classifications, dubbed ‘extensional’ by Marradi (1990), the

only way to separate types from each other, provided that the criteria used for classifi-
cation are measurable, is to set cut-off points that satisfy the criteria of common sense.
Such arbitrary cut-off points are necessary for keeping the types mutually exclusive. In
‘intensional’ classifications, to which category the proposed method belongs, cut-off
points are not arbitrary because they are defined logically or, as in this particular case,
mathematically. The next step is to establish substantive correspondence between types
defined this way and the types empirically identified in previous research. The relation-
ships between some of the segments of the diagram and the major types identified in tra-
ditional qualitative typologies are not problematic, because they are defined by the
vertices of the triangle. The A vertex represents the constellation in which all seats are
taken by one party, which is perfect one-party dominance. The C vertex is the point
of perfect bipartism, because here there are only two equal-size parties. At the vertex
B, we find perfect multipartism, with constellations of more than two equal-size parties.
Then the quadrangular regions taking a third of the available space each, ADEG, CDFG

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Party Politics 17(5)

548

and BEFG, represent the predominant-party, two-party and multiparty constellations,
respectively. Each of them is divided by the segments of the median lines into two
equal-size subtypes. Their names could also be derived from the literature. But, to avoid
conceptual confusion stemming from the differences among the definitions proposed by
different authors, I give each of the subtypes a proper name derived from the structure of
the diagram. Each of the segments representing individual subtypes is adjacent not only to
a segment belonging to the same type, but also to a segment belonging to a different type.
The relative locations of the segments are substantively meaningful in the sense that they
reflect significant tendencies. For instance, both the AEG and ADG segments represent
predominant-party systems, yet in the former segment the multiplicity of challengers sug-
gests a tendency towards multipartism, while the latter gravitates towards a two-party for-
mat. Taking this into account, and with a little help from the vocabulary of natural science,
I define the subtypes as follows: polyvalent (AEG) and bivalent (ADG) predominant-party
systems; monovalent (CDG) and polyvalent (CFG) two-party systems; and bivalent (BFG)
and monovalent (BEG) multiparty systems. The structure of the diagram suggests that for
the data points located close to the vertices the differences between the subtypes become
blurred. Hence the additional segmentation of the RST, as shown in Figure 2, where small
triangles AHI, CJK and BLM indicate sectors within which the subtypes are not very con-
sequential for categorizing party constellations, while the types themselves are manifested
in full. At the same time, the data points around the centroid represent constellations

Figure 3. The RST display with the definitions of segments

Golosov

549

for which inter-type differences are blurred. At the centroid, we find the constellation (1/2,
1/3, 1/6) that, by the criteria set in Table 1, does not belong to any of the types. Figure 3
shows the RST diagram with the definitions of segments.

The above definitions of subtypes within the predominant-party and multiparty

categories are not problematic. True, the predominant-party systems have not been stud-
ied closely enough to be divided into subtypes, but they clearly ought to be. In fact, in the
classifications that do not include the predominant-party type, systems with many com-
parably small challengers normally fall into the category of multipartism, while systems
where there is only one visible challenger fall within the category of bipartism. In the
proposed classification, they are polyvalent and bivalent predominant-party systems,
respectively. The close analogues of monovalent and polyvalent multiparty systems can
be found in the classifications of Blondel (1968), Rokkan (1970), Ware (1996) and
Siaroff (2000). The former is the one in which the largest party has a strong advantage
over all others, including the closest challenger, but in the latter there is little distance
between the two largest parties, while all others are significantly smaller. Most proble-
matic, in terms of the previous qualitative classifications, is the two-party type. While the
constellations in the CDG segment are obviously two-party in the traditional sense of the
word, the CFG segment contains what have long been identified as two-and-a-half party
systems, and their placement into the wider two-party category leaves me in agreement
with Epstein (1964) and Rokkan (1970), but at odds with Sartori (1976: 186–90). Indeed,
unlike ‘pure’ two-party systems, two-and-a-half party systems yield coalitions. In the
structure of the RST, this is expressed very well by the differentiation between the two
segments.

Yet only two of the parties can head coalitions, and this suggests a significant

substantive proximity between the categories.

These formal definitions, of course, do not liberate me from the necessity to show

‘how it works’. While the analysis of the real-life data will follow, some hypothetical
constellations can be illuminating. They are selected to represent, at values of s

varying

from 0.25 to 0.75, situations in which there is the smallest possible difference between s

and s

; in which s

remains relatively large, while s

is significantly smaller but still quite

visible, s

¼ 0.25; in which s

¼ s

; and in which there are relatively large distances

between s

and s

and between s

and s

. The letter designators of the data points are

from Figure 2. For each of the constellations, I report two versions of the effective num-
ber of parties (N

and N

), all on the assumption that minor parties starting with s

are of

the same size as s

or take residual seats. Those cases which, as explained above, repre-

sent ‘pure’ types rather than subtypes, are indicated with asterisks in the party system
subtype column. When interpreting the data presented in the table, it is useful to take into
account that even if s

is large each of the individual components within this aggregate

quantity is equal to or smaller than s

An illustrative classification of the 1945–2005
democratic party systems of the world

Since party constellations are election results expressed in seat-shares by party, the data-
set for this study was constructed to include the results of all national legislative elections
held in democratic conditions in the course of the post-war period, from 1945 to 2005.

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Party Politics 17(5)

550

I judged the conditions to be democratic if, for the given election year in the given coun-
try, the DEMOC score of the Polity IV database was no less than 6.

The choice of Polity

IV was motivated by its chronological scope and by the fact that it is relatively indepen-
dent of election outcomes (Bogaards, 2007), so that predominant-party systems were not
discriminated against. The transitional score of –88 also qualified for inclusion if fol-
lowed by the score of 6 or larger for the next year, but not otherwise. In some cases when
legislatures were elected a year or two before independence and continued well into the
independence periods, such elections were included. The major exception from the rules
was Columbia in 1958–73 when, while qualifying as a democracy, it did not produce
meaningful election results. On the contrary, countries with severe suffrage restrictions
(such as South Africa and Rhodesia during their apartheid periods) were included. The
small countries not rated in the Polity IV database were nevertheless included on the con-
dition that their average Political Rights and Civil Liberties score, as defined by Freedom
House,

was 3.0 or less. The pre-1973 placements of small countries within the demo-

cratic or non-democratic categories were unproblematic. Of the West European

Table 2. Hypothetical party constellations on the RST diagram (Figure 2)

RST data point

Party system

subtype

0.75

0.25

1.60

1.33

0.75

0.20

0.05

1.65

1.36

PP*

0.75

0.125

1.68

1.37

0.75

0.125

0.0625

1.71

1.39

0.65

0.35

1.83

1.54

0.65

0.28

0.07

1.98

1.59

0.65

0.175

2.07

1.62

0.65

0.175

0.0875

2.13

1.66

MT*

0.55

0.45

1.98

1.82

0.55

0.36

0.09

2.27

1.91

0.55

0.225

2.48

1.94

0.55

0.225

0.1125

2.64

2.03

0.45

0.1

2.41

2.34

0.45

0.36

0.09

0.10

2.87

2.51

0.45

0.275

2.83

2.37

0.45

0.275

0.1375

3.17

2.54

BM*

0.35

0.3

2.99

2.90

0.35

0.28

0.07

0.30

4.43

3.87

0.35

0.175

0.30

4.35

3.51

0.35

0.175

0.0875

0.3875

5.19

4.05

(B)

MM*

0.25

4.00

0.25

0.20

0.05

0.50

7.69

6.90

MM*

0.25

0.125

0.50

6.40

5.36

0.25

0.125

0.0625

0.5625

8.53

6.89

Party system subtype abbreviations: PP

¼ polyvalent predominant-party system; BP ¼ bivalent predominant-party

system; MT

¼ monovalent two-party system; PT ¼ polyvalent two-party system; BM ¼ bivalent multiparty system;

¼ monovalent multiparty system

Golosov

551

micro-states, San Marino was included as of 1951, and all others as of international rec-
ognition in 1990–3. Several small countries of the Pacific were excluded because, while
qualifying as democracies, they have not had political parties and/or party-structured
assemblies. The data sources included a variety of print and online publications.

This data collection effort produced a set of 991 results of elections held in 136

countries throughout the period. All these constellations were plotted on the diagram and
ascribed to different party system subtypes. The results of the exercise were interesting in
themselves, but not for this study. Here, my focus is on party systems rather than on party
constellations. One of the clear operational differences between them is that party con-
stellations are single moment events, while party systems are continuous country-
specific patterns. Therefore they have to be identified by an additional effort. When
doing that, I acted on the premise that party systems are continuous, but they are also
changeable, which makes their existence in the course of 61 years possible but unlikely.
Then my first step was to divide all 991 observations into three chronologically defined
groups, 1945–65, 1966–85 and 1986–2005. These groups were sorted by country. From
each of the groups, I eliminated the countries in which there were fewer than three dem-
ocratic elections in the course of the given period,

and those in which such elections

were separated from each other by interruptions in democratic development or signifi-
cant instances of regime change.

This left me with 31 country-specific election

sequences for 1945–65, 41 for 1966–85 and 97 for 1986–2005. The problem with these
sequences was that not all of them could be safely assumed to represent specific party
system subtypes or even types. Significant continuities do exist, but they are not abso-
lute.

This made it necessary to bring additional differentiation into the population of

cases, which was done in two steps.

First, I identified as strongly homogeneous the sequences in which certain party con-

stellation subtypes were returned by majorities of elections, as weakly homogeneous
those in which certain party constellation types were returned by majorities of elections,
and as heterogeneous all other sequences. For each of the sequences, I established the
median point as the point with median coordinates on the RST diagram, and proceeded
to calculate average Euclidean distances between the actual data points in each of the
sequences and their median points.

Second, I judged as not belonging to any party

system subtypes those sequences in which such differences exceeded 0.333 for all cases,
0.236 for the weakly homogeneous and heterogeneous ones, and 0.167 for the heteroge-
neous ones only, the cut-off points being the Euclidean distances between the subtype
centroids of the RST diagram. For such instances, which turned out to be as many as
25, I crafted a separate category of fluctuating/evolving party systems. All the remaining
144 sequences qualified as belonging to this or that party system subtype by the location
of their median points. The resulting classification is reported in Table 3.

As presented in the table, the classification suggests several substantive inferences.

First, contrary to widespread opinion, two-party systems are not rare and unusual. In
1966–85, monovalent two-party systems were more widespread than any other subtype,
while in 1986–2005 they still made up 15.5 percent of the total. The least spread subtypes
are actually bivalent predominant-party systems, among which very small countries pre-
vail, and polyvalent two-party systems (or two-and-a-half party systems). Polyvalent
predominant-party systems used to be quite usual in the past, yet in 1986–2005 their

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Party Politics 17(5)

552

Table

The

classification

party

systems,

1945–2005

Party

System

Type

Subtype

1945–65

1966–85

1986–2005

Predominant-party

Polyvalent

Costa

Rica,

India,

Myanmar

(Burma),

Norway

Australia,

Botswana,

France,

India,

Japan,

Zimbabwe

(Rhodesia)

Canada,

Japan,

Mali,

Namibia,

South

Africa,

St.

Kitts

and

Nevis

Bivalent

Philippines

Barbados,

Gambia,

Jamaica,

Mauritius,

South

Africa,

Trinidad

and

Tobago

Bahamas,

Barbados,

Botswana,

Cape

Verde,

Jamaica,

Monaco,

St.

Vincent

and

Grenadines

Two-party

Monovalent

New

Zealand,

South

Africa,

United

Kingdom,

United

States,

Uruguay

Austria,

Canada,

Colombia,

Costa

Rica,

Fiji,

Greece,

Malta,

New

Zealand,

Spain,

United

Kingdom,

United

States

Argentina,

Australia,

Colombia,

Greece,

Guyana,

Honduras,

Liechtenstein,

Malta,

Mozambique,

Nicaragua,

Portu-

gal,

Taiwan,

Trinidad

and

Tobago,

United

Kingdom,

United

States

Polyvalent

Australia,

Austria,

Belgium,

Germany

Germany,

Ireland,

Venezuela

Costa

Rica,

Germany,

Ireland,

Paraguay,

South

Korea,

Spain,

Sri

Lanka,

Suriname

Multiparty

Bivalent

Finland,

France,

Iceland,

Luxembourg,

The

Netherlands,

Switzerland

Belgium,

Iceland,

Israel,

Italy,

Luxembourg,

Netherlands,

Portugal,

Switzerland

Austria,

Belgium,

Brazil,

Cyprus,

Czech

Republic,

Salvador,

Finland,

India,

Israel,

Latvia,

Luxembourg,

The

Neth-

erlands,

Poland,

Romania,

Ukraine,

Uruguay,

Venezuela

Monovalent

Brazil,

Denmark,

Ireland,

Israel,

Italy,

San

Marino,

Sri

Lanka,

Sweden

Denmark,

Finland,

Norway,

San

Marino,

Sweden

Benin,

Bolivia,

Chile,

Denmark,

Ecua-

dor,

Estonia,

France,

Iceland,

Italy,

Kiri-

bati,

Macedonia,

Madagascar,

Mexico,

Norway,

Panama,

Papua

New

Guinea,

Philippines,

Samoa

(West

Samoa),

San

Marino,

Slovak

Republic,

Slovenia,

Sweden,

Switzerland,

Vanuatu

Fluctuating/evolving

Canada,

Greece,

Japan

Cyprus,

Peru

Albania,

Andorra,

Bangladesh,

Belize,

Bulgaria,

Dominica,

Fiji,

Grenada,

Hungary,

Lithuania,

Mauritius,

Moldova,

Mongolia,

Zealand,

Pakistan,

Sao

Tome

and

Principe,

Solomon

Islands,

St.

Lucia,

Thailand,

Turkey

553

visibility faded.

This finding runs against the recent current of research on African

party systems, but note that most of them function in less than democratic conditions.
With the exception of 1966–85, the monovalent multiparty systems were almost always
a prevailing subtype, while the bivalent multiparty systems were continuously wide-
spread. However, there is little difference on this parameter between the most recent
stage and the immediate post-war period, which renders empirically irrelevant frequent
claims that we are entering the era of moderate multipartism. It has always been with us.
What is actually specific about the 1986–2005 period is the unprecedented spread of
fluctuating/evolving party systems. In the context of the massive arrival of new democ-
racies, however, this is not surprising. Of the 41 cases registered for the 1966–85 period,
26 (63.4 percent) were in place in the previous period, while for the 1986–2005 period,
the share of thus defined ‘old’ democracies declines to 39.2 percent, i.e. 38 of 97.

While all these findings might be interesting, for this study it is more important to

reveal the full potential of the proposed method, and from this point of view graphical
representations (Figures 4–6) are instrumental. The data points on the diagrams are the
median points for each of the party systems in Table 3, except the fluctuating/evolving
ones.

First, the diagrams allow for moving from a strictly categorical classification to a

nuanced analysis of the relative locations of individual party systems within their sub-
types. For instance, both India and Norway were polyvalent predominant-party systems
in 1945–65, which is registered in the table, but the diagram allows for estimating the

Figure 4. The party systems of the world, 1945–65 (see note 14 for country abbreviations)

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Party Politics 17(5)

554

difference. Second, the evolution of whole groups of party systems can be traced.
Denmark, Sweden and Norway are expectedly close to each other on all three diagrams,
but note their parallel yet still incomplete movement towards the vertex of perfect
multipartism. Third, being universal in scope, the diagrams make it possible to find
significant similarities among the party systems of countries that are rarely compared
to each other. Consider the relative locations of Spain, Sri Lanka and Paraguay in
1986–2005 (Figure 6). From a more methodological perspective, it should be noted that
the diagrams show how confidently this or that party system can be placed within a spe-
cific subtype. Indeed, many observers would find it doubtful that Switzerland changed its
party system subtype from 1966–85 to 1986–2005, as registered in Table 3. The graphi-
cal representation indicates that while the evolution was real the continuous location of
this party system very closely to the point of perfect multipartism makes its assignment
to the subtypes not very consequential. In a similar vein, the abundance of data points
closely grouped around the centroid in 1986–2005 can be viewed as additional evidence
of party system fuzziness during that period compared to the previous ones.

Conclusions

The output of this study is classification based on a parsimonious operational definition of
taxonomic units. While categorical by intention, it allows us to visualize intra-category

Figure 5. The party systems of the world, 1966–85 (see note 14 for country abbreviations)

Golosov

555

differences by individual observations being placed in a bounded two-dimensional space.
Not for nothing, the data requirements for the proposed classification are extremely limited
even in comparison with such popular one-dimensional measures as the effective number
of parties. This allows for comprehensive cross-national studies. And, after all, it answers
the question asked at the beginning of this article: how many two-party systems are
there in the world? For the period 1986–2005, the answer is 15 (two-and-a-half party
systems not included). Arguably, one remaining problem is that categorical variables
are not of great utility for quantitative political science. For instance, major achieve-
ments in research on electoral system effects were reached using the effective number
of parties as the dependent variable in multiple regression analysis. Yet everybody who
has ever engaged the index in this capacity is familiar with the difficulties stemming
from the fact that the values of the effective number of parties are almost never distrib-
uted normally. Besides, being unable to discriminate among theoretically important
party system types, the effective number of parties may yield unreliable results. If it
has been established that plurality systems are conducive to lower fragmentation, this
does not necessarily mean that they yield bipartism. Rather, they may be associated
with predominant-party systems. True or false, this hypothesis cannot be tested with
the effective number of parties. At the same time, recent advances in categorical data
analysis (Agresti, 2002) make it perfectly possible to use multiple categorical variables
with more statistical rigour than the continuous ones without violating the fundamental

Figure 6. The party systems of the world, 1986–2005 (see note 14 for country abbreviations)

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Party Politics 17(5)

556

assumptions of the technique employed. For this, a classification is needed, and my
concern in this study was to have it to hand.

Notes

I am grateful to the anonymous referees of the journal for criticism and comments. All errors of
fact and interpretation are entirely my own.

1. The segmentation presented in Figure 1 is the one proposed by Grofman et al. (2004), with

some minor simplification. At the same time, the authors suggest that different segmentations
are possible and sometimes desirable. If slightly modified, a simplified version of Siaroff’s
classification (2003) can be represented as a specific segmentation of the Nagayama triangle.

2. The mathematically correct yet clumsy notation for s

3. By further transformation of the coordinates, x

¼ 1 – (x þ y)/2 and y

¼ (x – y)/2, the triangle

can be rotated to assume a disposition identical to that of the Nagayama triangle, but I do not
see any substantive need for this.

4. For Siaroff (2003), two-and-a-half party systems have to be separated from both multipartism

and bipartism.

5. Available online at http://www.systemicpeace.org/polity/polity4.htm.
6. Available online at http://www.freedomhouse.org.
7. See Mackie and Rose (1991); Nohlen et al. (1999, 2001); Nohlen (2005); The PARLINE data-

base, available online at http://www.ipu.org/parline-e/parlinesearch.asp; and The Parties and
Elections in Europe database, available online at http://www.parties-and-elections.de.

8. Hence the choice of the 20-year time span, which was technical. Many legislatures are elected

for terms of more than four years, so a time span of less than 20 years could have removed
from the selection of cases some of the continuous democracies that simply held fewer than
three elections in the course of the period.

9. Such instances were determined on the basis of the existing scholarly conventions and

included the transition to the Fifth Republic in France, the demise of the apartheid system
in South Africa and the establishment of the Bolivarian Republic in Venezuela.

10. This was established by a log-linear analysis of continuities between party system subtypes

returned by consequential elections. The results of this analysis are not reported here.

11. In a two-dimensional space, the Euclidean distance between the points with coordinates (x, y)

and (x

, y

) is defined as

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
ðx x

þ ðy y

12. It might be tempting to ask whether such a complex procedure was necessary. The answer is

that some of the steps could be omitted, and I would find it commendable to omit them for
many research purposes. To trace the history of an individual party system, or to compare
sub-national party constellations in the same country, it would be sufficient just to draw dia-
grams. Yet, for the purpose of developing a comprehensive classification of the party systems
of the world, a fairly refined instrument was needed.

13. It has to be noted that, unlike some of the previous classifications, this one does not employ the

lack of alternation in power as a defining property of predominant-party systems. Therefore,
this category includes cases when elections returned overwhelming majorities to different par-
ties during the specified time span. Of course, the criterion of alternation in power can be used

Golosov

557

as a complementary tool, but also the proposed method can be adjusted to take this criterion
into account, say, by averaging party seat-shares for the given time span. This, however, goes
well beyond the purposes of this methodological exposition.

14. Country abbreviations are Internet domain name extensions: AR Argentina, AT Austria, AU

Australia, BB Barbados, BE Belgium, BJ Benin, BO Bolivia, BR Brazil, BS Bahamas, BW
Botswana, CA Canada, CH Switzerland, CL Chile, CO Colombia, CR Costa Rica, CV Cape
Verde, CY Cyprus, CZ Czech Republic, DE Germany, DK Denmark, EC Ecuador, EE
Estonia, ES Spain, FI Finland, FJ Fiji, FR France, GM Gambia, GR Greece, GY Guyana,
HN Honduras, IE Ireland, IL Israel, IN India, IS Iceland, IT Italy, JM Jamaica, JP Japan,
KI Kiribati, KN St. Kitts and Nevis, KR South Korea, LI Liechtenstein, LK Sri Lanka, LU
Luxembourg, LV Latvia, MC Monaco, MG Madagascar, MK Macedonia, ML Mali, MM
Myanmar (Burma), MT Malta, MU Mauritius, MX Mexico, MZ Mozambique, NA Namibia,
NI Nicaragua, NL Netherlands, NO Norway, NZ New Zealand, PA Panama, PG Papua New
Guinea, PH Philippines, PL Poland, PT Portugal, PY Paraguay, RO Romania, SE Sweden, SI
Slovenia, SK Slovak Republic, SM San Marino, SR Suriname, SV El Salvador, TT Trinidad
and Tobago, TW Taiwan, UA Ukraine, UK United Kingdom, US United States, UY Uruguay,
VC St. Vincent and Grenadines, VE Venezuela, VU Vanuatu, WS Samoa, ZA South Africa,
ZW Zimbabwe (Rhodesia).

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Author Biography

Grigorii V. Golosov is Professor of Political Science in the Faculty of Political Sciences and
Sociology of the European University at St. Petersburg and Project Director at the Center in
Support of Democracy and Human Rights Helix. He wrote Political Parties in the Regions of
Russia: Democracy Unclaimed (Lynne Rienner, Boulder, CO, 2004) and several other books, and
has published extensively on political parties and elections, including articles in Party Politics,
Comparative Political Studies, Europe–Asia Studies, International Political Science Review and
other journals.

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