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Politometrics: Quantitative Models of Political Institutions
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Summary and Keywords
Logical models and statistical techniques have been used for measuring political and
institutional variables, quantifying and explaining the relationships between them, testing
theories, and evaluating institutional and policy alternatives. A number of cumulative and
complementary findings refer to major institutional features of a political process of
decision-making: from the size of the assembly to the territorial structure of the country,
the electoral system, the number of parties in the assembly and in the government, the
government’s duration, and the degree of policy instability. Mathematical equations
based on sound theory are validated by empirical tests and can predict precise
observations.
Keywords: logical models, statistics, electoral system, political parties, federalism, policy change
“Politometrics” is a name for the application of mathematical forms and statistical
techniques for measuring political variables, quantifying and explaining the relationships
between them, testing theories, and evaluating institutional and policy alternatives. Its
main object is to promote studies that aim at a unification of the theoretical and the
empirical-quantitative approaches to political problems. Politometrics produces
probabilistic, empirically testable models of simple relationships that can make sense of
mountains of data. This type of study has long roots and old traditions, but they have
been revived and become newly appealing in a recent period in reaction to a disagreeable
breach in political science between inductive statistics and speculative formal models.
Politometrics: Quantitative Models of Political Institutions
Josep M. Colomer
Subject: Political Institutions, Quantitative Political Methodology Online Publication Date: Jan 2017
DOI: 10.1093/acrefore/9780190228637.013.500
Oxford Research Encyclopedia of Politics
Politometrics: Quantitative Models of Political Institutions
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A Search for Measurement, Explanation, and
Prediction
It’s interesting to note that the etymology of the word “statistics” is “the study of states,”
as it originated in data-based, causally oriented traditions of political analysis. Already in
the 17th century, William Petty developed a “political arithmetic,” which, in retrospect,
was seen as a search for “causal relationships between quantitative
variables” (Lazarsfeld, 1961; Petty, 1676/1899).
The necessary collaboration between quantitative empirical studies and explanatory
theory was remarked by August Comte in a seminal work published about 200 years ago:
“If it is true—he said—that every theory must be based upon observed facts, it is equally
true that facts cannot be observed without the guidance of some theory. Without such
guidance, our facts would be desultory and fruitless; we could not retain them: for the
most part we could not even perceive them” (Comte, 1822).
In this respect, political studies didn’t follow closely the methodological evolution of other
social sciences, but they were rather dominated by narrative historical or normative
juridical approaches for a very long time. “By the close of the 19th century none of the
developments in modern statistics had been incorporated in the political science
curricula of British or American colleges and universities.… The rapid developments that
took place in mathematical statistics after 1900 hand little impact on political
science” (Gow, 1985). There were some claims to building a science of politics that should
“consist of a body of verifiable and systematic knowledge, gathered by observation and
experiment” (Catlin, 1927). But still in the 1930s, Harold Gosnell confirmed that, while
“statistical studies depend upon qualitative descriptive analyses for fruitful hypotheses
and interpretations,” “political scientists have not only lagged far behind the economists
in the use of statistics but they have shown important resistance in some sections to
following this general direction” (Gosnell, 1933).
A rather isolated effort was the work by Lewis Fry Richardson on arms races and armed
conflicts (Richardson, 1949/1960). Initially a meteorologist, Richardson learned from the
problems of weather forecast that events, which seem to be governed by chance, are in
fact governed by laws and can be predicted if enough information can be processed. He
then changed subject and spent 20 years studying the causes of war. Richardson
quantified two basic, opposing components of interactions between states with rival
ambitions: mutual stimulation of armaments buildup and cooperation in the form of trade.
The solution of his equations determined the time course of the armaments expenditures.
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Richardson was able to obtain a good fit of the predicted time course for the armaments
race of the rival European blocs in the years preceding World War I and World War II.
He, however, acknowledged that “the equations are merely a description of what people
would do if they did not stop to think” (1960, p. 12). From the point of view of game-
theorist Anatol Rapoport, “Richardson’s quasi-deterministic view of international
relations is complementary to the strategic view, which assumes rationality in the pursuit
of ‘interests’ but leaves unanalyzed the genesis of the interests. The strategic view may
inquire how nations conduct (or would conduct, if they were rational) a diplomatic-
military game but says nothing about how the game got started, why enmities are built
up between some states and not between others, or, of course, why states behave so
frequently and so clearly against their own interests” (Rapoport, 1968).
These comments summarize the bulk of mutual criticisms that political scientists sitting
at separate tables have thrown to each other for several decades. Macro-structuralists
don’t explain the “mechanisms” of micro-behavior that produce interactions and
outcomes; micro-behavioralists and game-theorists take the structures and the
subsequent constraints on interactions for granted.
In the 1960s and early 1970s, “politometrics” appeared as a possible focal term for
theory driven, quantitative political science in parallel to biometrics, psychometrics, and
econometrics (and journals such as Pshycometrika, Econometrica, Sociometry,
Technometrics). The word “polimetrics” was possibly used for the first time by Hayward
R. Alker, Jr. at the International Studies Association (Alker, 1969). In his contribution to the
first encompassing Handbook of Political Science, he stated that “the key epistemological
ideal was the search for equations with manipulative, politically productive
significance” (Alker, 1975). As embedded in the so-called behavioralist period, the
endeavor focused then on the study of “intentional action,” including individual’s political
orientations, voting choices, and modes of political participation, for which some early
game theory models were also adopted.
More institution-oriented was the work of Ted R. Gurr, as presented in his book
Politimetrics. An Introduction to Quantitative Macropolitics (Gurr, 1972) (note the slightly
different spelling of the leading words in the works cited). In contrast to the above-
mentioned project, Gurr aimed at measuring and explaining regularities not on
micropolitics or individual behavior, but rather on macropolitics or structures, basically
“political groups, institutions, nations and international systems.” He emphasized that
scientific work requires that induction combine with and follow deduction. As he put it:
“All processes for gaining knowledge require us to make some initial assumptions
(axioms) and hypotheses (theorems) about the nature of social and political reality.… The
procedures of politimetrics are suited to testing all kinds of conjectures, however they
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are derived. The future of political science will be brightest if politimetrics becomes as
widely used for evaluating formal theories as it has been for testing ad hoc hypotheses.”
With this inspiration, Ted R. Gurr also initiated The Polity study, which profiles the
democratic and autocratic traits of all regimes worldwide from 1800 to the present and
has been further developed by some of his disciples (Gurr & Marshall, 2014).
A more advanced second part of Gurr’s book was published by Gordon Hilton with the
title Intermediate Politometrics (Hilton, 1976). From the first page, Hilton stated that
“while economics has econometrics, political science should develop politometrics. The
desire in political science—Hilton asserted—is to be able to produce ‘lawlike’
relationships between sets of variables.” In his extensive presentation of statistical
regression techniques, he postulated to develop, first, theoretical simple models and then
obtaining empirical estimators of the parameters. Most of Hilton’s examples and
applications went back to micro-behavioral problems, especially data analysis of voting
and congressional behavior, plus a few excursuses into international relations.
Thus, politometrics was conceived for a while as the name for the right development of
the scientific method for the study of politics in search of measurement, explanation, and
evaluation in the fields of both micropolitics and macropolitics.
Yet the word and part of its profile somewhat faded away. The APSA section in Political
Methodology tried to subsume “the fragmented history of quantitative political analysis”
and its “patchwork of names” under the bland label “political methodology” (King, 1991).
For a few decades, the expansion of political science witnessed a widening separation
between empirical uses of statistics techniques and theoretical formal modeling, the
breach that politometrics and similar ventures should bear to seal. While a focus on
micro-behavior had expanded the use of statistical techniques but neglected the role of
theoretical hypothesis, the return to the traditional political science focus on
macrostructures by the “new institutionalism” implied some loss regarding quantitative
specification and empirical validation of formal models.
In the first encompassing review of the state of the political discipline sponsored by the
American Political Science Association in the early 1980s, Christopher Achen sighted,
“More than anything else, what would help are formal theories with measurement models
built into them” (Achen, 1983). Ten years later, in the second edition of the survey, Larry
Bartels and Henry Brady registered some progress in a few areas, but “in the field as a
whole, there is still far too much data analysis without formal theory and far too much
formal theory without data analysis” (Bartels & Brady, 1993). In the third review, nine
years later, David Laitin pleaded for more interactions between statistics, formal
theorists, and fieldworkers, although he acknowledged that “this hoped for
interdependence is far more promise than reality” (Laitin, 2002). In the same volume,
1
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Charles Cameron and Rebecca Morton reviewed new efforts to link theory and data in
what they call “formal empirical (FE) work,” but the endeavor was presented, rather than
an achievement, as a “major challenge for the new century of political science” (Cameron
& Morton, 2002).
The more recent Oxford Handbook of Political Science series created new occasions to
replicate the pledge. In their overview of political methodology, Henry Brady, David
Collier, and Janet Box-Steffensmeier acknowledged that behavioralism’s “emphasis upon
methodology is a good one, but its weaknesses included a neglect of theory” (Brady et al.,
2009). The problem was also noted in the subfield of international relations, as “there has
been an overemphasis recently on tools at the expense of reflection about which
questions are more important for the human race and for the ecosystem” (Keohane, 2009).
In recent times, several initiatives increased awareness of existing methodological
confusions and insufficiencies and developed more explicit initiatives. The Empirical
Implications of Theoretical Models (EITM) project at the University of Michigan must be
highlighted. The EITM organizes annual summer institutes to train graduate students and
junior faculty in research strategies that integrate theoretical models and empirical
research. The program aims at promoting research in the subfields of American politics,
comparative politics, international relations, and political economy, although most of its
projects have dealt so far with building databases and values surveys and with the study
of attitudes and behavior, communication, entrepreneurship, elites and leadership, all
topics more characteristic of “behavioralist” traditional interests (Aldrich, Alt, & Lupia,
2008).
In a relatively recent review of the long-term evolution of American political science, Lee
Sigelman observed “growing attention to developing systematic methods for qualitative
research and to testing the empirical implications of formal models” (Sigelman, 2006). In
fact, like the Molière character who finds that he had been speaking prose all his life
without knowing that this is what he has been doing, many political scientists have been
trying to develop empirically testable theories and empirical studies in search of
interpretation—as aptly observed by Bernard Grofman (2007, note 44).
Specifically, I will review below some major results of the project of building
“quantitative logical models” with explanatory and predictive power that fit the
politometrics approach particularly well. An initial training in physics provided Rein
Taagepera with an outside point of view to existing political science, which helped
identify relative weaknesses and to point out fruitful ways to pursue further research. He
has also remarked the links between solid theory and practicability. On the one side, he
emphasizes the importance of thinking and imagining logical connections among
variables before using mathematical tools, as is more usual in other normal sciences. On
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the other side, he calls the attention about the necessary link between high scientific
rigor and practical relevance, against irrelevant ivory towers.
Rein Taagepera was awarded the Johan Skytte prize (which pretends to be the little
Nobel in political science), especially for his work on the relations between party systems
and electoral systems and the consequences for government stability (as culminating in
Taagepera, 2007). He, however, has also constructed and tested models for population
growth, arms races, and the importance of the issue of size to explain historical empires,
countries, cities, trade, and other relevant phenomena. The rest of this article focuses on
some of Taagepera’s recent authored, coauthored, or inspired “quantitative logical
models” dealing with macropolitics and, particularly, with quantifiable structural or
institutional variables such as population, seats, parties, territorial units, governments,
and policy. Many other contributions should be reviewed along these lines and connected
or compared with the findings presented below.
Quantitative Models of Political Institutions
Beginning with a major example of successful research can serve to illustrate not only
some interesting substantial contents of politometrics, but also some basic characteristics
of its methodological approach. The topic is classical: the relationships between party
systems and electoral systems.
First, the question was addressed with some reasonable hypothesis on interrelations and
causality. As expressed by Maurice Duverger since the early 1950s, the electoral system
effects can be formulated by two major “laws: 1) a majority vote on one ballot is
conducive to a two-party system; 2) proportional representation is conducive to a
multiparty system” (Duverger, 1950, 1951, as summarized in 1972).
Second, broad quantitative tests were applied to the hypotheses by using standard
statistical techniques. As found by Arend Lijphart, “the total amount of explained
variance [in the number of parties] is explained almost entirely by a single variable: the
effective threshold,” which is taken as a proxy for the electoral system and equals 75%/M
+1, being M the average magnitude or number of seats per electoral district. The
prediction was that “each percentage increase in the effective threshold reduces the
effective number of elective parties by 0.06.” Yet the quantification of the effects was
further neglected. It was retained only that “all of the coefficients of the regressions of
the dependent variables on the effective threshold … are statistically significant, usually
at the 1 per cent level” (Lijphart, 1994).
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Third, a quantitative logical model refining both Duverger’s hypothesis and Lijphart’s and
others’ empirics was produced. The number of parties, P, depends on the number of seats
of the assembly, S, and the number of seats to be elected in the district, M. This gives
way to the “seat-product.” According to Rein Taagepera: “When an assembly of S seats is
elected in districts of M seats, the most likely number of seat-winning parties P is:
This means that, with a large number of cases, we expect one-half of them to fall above
and one-half below the value P” (Taagepera, 2007; also Taagepera, 2001; Taagepera &
Shugart, 1993).
A further refinement was introduced regarding the measurement of the number of
parties. The “effective” number weights the absolute number of parties with their relative
size, according to the formula: , where p is each party’s proportion of all seats
(Laakso & Taagepera, 1979).
Obviously, the effective number of parties is usually lower than the absolute number, as
small parties count for much less than one. Therefore, with this fine-tuning the “seat-
product” must be raised to a higher root. It becomes:
where,
EP: Effective number of parties
S: Total number of seats in the assembly
M: Average district magnitude or number of seats per district.
(Taagepera, 2009).
As can be seen, the basic elements of this approach, as were accumulated by successive
research contributions on the specific problem, are accurate measurement of the
variables considered, logical hypotheses about their relations and deductive reasoning,
statistical treatment of empirical data, and mathematical design of the equation. Also, the
direction of the relationship or probabilistic causal explanation has been discussed, as
we’ll see later on.
The most important difference of the politometrics approach regarding previous
contributions is that models supported by quantitative measurements of the main
variables considered can define relationships and trade-offs among variables in terms of
“how much” one can depend on another and the expected variance of values. The
i
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equations need to include not only the sign and statistical significance of presumed
associations between different alternatives, but gradations of effects.
Following this orientation, several of the contributions reviewed below have produced
cumulative and complementary findings. They have contributed to a better understanding
of the choices and consequences of political institutions and the regularities that are
observed and can be predicted at several successive stages of the political process.
Focusing on major choices of democratic institutions, I review the following:
• First, the size of the assembly regarding the country’s population.
• Second, the relation between the size of the assembly, decentralized territorial
governments, and the electoral system.
• Third, the relation between the electoral system and the party system.
• Fourth, the relations between the party system, the size of the largest party, and the
number of parties in government.
• Fifth, the influence of the number of parties in government on the government’s
duration.
• Sixth, the effects of the number of parties in government on the degree of policy
instability.
These six basic relations can account for most major stages of a state-based political
process of decision-making, from the size of the country in population to the policy
outcomes. International and global institutional matters have also been explored.
Let’s proceed step by step. The following results are not presented in the chronological
order in which they were found, but by pointing out a succession of logical and
quantitative relations between major institutional variables.
Assembly Size
In order to estimate the size of a directly elected lower chamber of the assembly in a
democratic country, it was hypothesized that two motivations could counterweight each
other: broad representation of the population may require a high number of seats, while
communication between legislators and effectiveness in decision-making may be favored
by a low number.
Accordingly, it was found that the best approximation is to take the cube root of the
population. For most countries the number of inhabitants amounts to millions—that is,
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some figures with six zeroes—and so the cube root must be in the hundreds—or some
figure with two zeroes. The equation is:
where,
Pop: Population
S: Assembly size in seats.
The arrow indicates causal direction.
(Taagepera, 1972; Taagepera & Shugart, 1989).
For example, as Spain has about 45,000,000 inhabitants, the cube root of this number
closely approaches the 350 seats of its lower chamber of parliament (45,000,000 =
355). As Mexico has about 120,000,000 inhabitants, its lower chamber has 500 seats
(120,000,000 = 493). For most democratic countries, this is the best fit, as can be seen
in Figure 1.
Major deviations occur in two old democracies whose assembly sizes have been frozen for
a long period. The British House of Commons, which is the largest assembly of all
democratic countries (S = 659), is oversized regarding the country’s population and the
cube root law. In fact, it has maintained almost the same size as the so-called Imperial
Parliament established in the early 19th century (actually following the pattern of its
predecessors the parliaments of Britain and of England), apparently to give room to a
complex set of representatives from counties, boroughs, towns, universities, and other
types of districts. Formal proposals to reduce the size of the House of Commons have
been included in the government’s program for institutional reform since 2010.
In the opposite direction, the U.S. House of Representatives is undersized. During the
19th century, the size of the House was regularly increased to account for population
growth, but in spite of the increase in the country’s population it has remained frozen
since it was fixed at 435 seats in 1911. At that moment this was an almost exact fit with
the cube root of the population. Proposals to increase the number of seats in the House to
the cube root of the population have been repeatedly raised (see, e.g., Ladewig &
Jasinski, 2008; Lijphart, 1998). As we’ll see, however, other institutional devices have
compensated for the federal House’s relatively small size.
The size of the democratic assembly is also relatively low for very small countries with
less than one million inhabitants, such as some islands in the Caribbean or the Pacific
Ocean, as well as for regional or local legislatures. This might reflect these units’
1/3
1/3
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relatively high homogeneity and simplicity of political demands, as well as the relatively
lesser role of those assemblies within larger alliances, unions, or states.
A closely related topic is
the size of the second or
upper chamber. About
one-third of currently
existing democratic
countries have bicameral
parliaments, especially in
large, federal countries in
order to lend a voice to the
territorial units
The size of second
chambers in seats tends to
increase with increasing
population and, therefore,
with the size of the first
chambers just reviewed.
But when the second chamber represents the territorial units of a federal-like state, the
number of units also affects the size of the upper chamber. Every territorial unit elects at
least one seat, while larger units elect higher numbers of seats. In result, the number of
seats of the upper chamber is smaller than the number of seats of the lower chamber but
larger than the number of territorial units. The equation that best fits the empirical
observations equals the size of the second chamber to the geometric mean of the size of
the first chamber, S, and the number of territorial or “regional” units, R:
where,
S: Second chamber size in seats
S: First chamber of the Assembly size in seats
R: Number of Regions or territorial units.
(Taagepera & Recchia, 2002).
Click to view larger
Figure 1. Size of the Assembly in Seats.
2
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Federalism and the Electoral System
It was a traditional conjecture among political scientists that both federalism and the
electoral rules can favor institutional stability in large and heterogeneous countries.
Territorial governments could be considered as kinds of intermediate, aggregative,
nonideological “parties,” while political parties may play the role of aggregative, non-
territorial “administrations.” A large number of territorial political units in a federal
structure can be the basis for a large, aggregative “union,” while a large assembly based
on proportional representation and multipartism can also be aggregative because it can
lead to the formation of some broad government multiparty “coalition.” Both “union” and
“coalition” can keep a large and varied country together by using democratic means of
governance. For the same kind of reason, simple institutional configurations such as a
unitary state and plurality rule elections with a single-party winner can support durable
democracy in small and homogeneous polities, but they tend to be recipes for conflict and
democratic failure in large and heterogeneous countries.
Thus, it could be presumed that the territorial structure of the country and the electoral
system are institutional devices able to be exchanged with each other to some extent. Yet
different institutions may produce effects that cannot be exchangeable. It has been found
that different combinations of unitary or federal arrangements with majority or
proportional electoral rules can be appropriate for countries of different sizes.
Specifically, the larger the country, the more important is federalism in comparison to
proportional representation for the durability of democratic institutions. The equation is:
where,
Click to view larger
Figure 2. Size of the Second Chamber in Seats.
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S: Assembly size in seats
R: Number of territorial units or regions with elected assembly and political power
M: Number of seats of the average electoral district.
(Colomer, 2014A).
The placement of S in the function should not be confusing. Actually the model can
accept bidirectional lines of causality, as all variables are to some extent interdependent,
rather than independent or dependent. All the variables are manipulable and for each
country size there can be multiple equilibrium sets of democratic institutions. But each
institutional combination involves a certain trade-off between alternative elements.
The equation above shows that the larger the country, the more effective and durable
federalism can be, to the point of being compatible with very diverse electoral systems
for the lower chamber. Large federal countries include, for instance, proportional
Argentina, Brazil, Germany, and South Africa, as well as majoritarian Australia, Canada,
India, and the United States. In contrast, in medium-sized countries, a democratic regime
may rather rely upon proportional representation of multiple parties to obtain greater
endogenous support. In fact, proportional representation began to be adopted for
parliamentary elections in the early 20th century in a few medium-sized European
countries, such as Belgium, Finland, Norway, and Sweden, soon followed by Austria,
Denmark, Ireland, and Switzerland, and has spread widely among new democracies in
medium-sized countries across the world in recent decades.
Some examples of varied institutional combinations follow. Cases of small countries with
a unitary structure and a majoritarian electoral system are Botswana (where the model
predicts S = 62 and actually S = 63) or Jamaica (model S = 62, actual S = 60). Medium-
size countries with a unitary structure and a proportional representation electoral system
include Benin (M = 3.5, model S = 85, actual S = 83), Bulgaria (M = 240, model S = 241,
actual S = 240) or Estonia (M = 8.4, model S = 105, actual S = 101). Large countries
with a federal structure are compatible with varied electoral systems, whether
majoritarian (Australia, R = 8, model S = 175, actual S = 150), proportional (Poland, R =
16, M = 10.7, model S = 449, actual S = 460), or mixed (Mexico, R = 32, weighted M =
16.6, model S = 498, actual S = 500).
An extreme case is the United States, which has the maximum value of R in the world
(50) and the minimum value of M (1). The very high number of states somehow
compensates for the smallness of single-seat districts. According to the model, the House
of Representatives should have S = 438 seats; the very close actual value is 435, which,
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in spite of being undersized regarding the population, as mentioned above, makes a
satisfactory fit with the other two major institutional variables.
Which one of the multiple equilibrium sets of institutions exists largely depends on
actors’ strategies. If in a large country multiple territorial governments are established,
as it was from the very beginning in the United States, much political action tends to
focus on those local institutions; it is then less likely that multiple political parties will be
formed at the federal level, and as a consequence there will be less pressure to adopt a
large assembly and an electoral system of proportional representation. In contrast, in a
medium-sized, high-density country with a variety of economic interests or cultural
allegiances, such as, for example, the Netherlands, the formation of multiple political
parties may push for a sufficiently inclusive assembly elected by proportional electoral
rules, rather than for territorial governments. The relationships between institutional
variables are always established through the intermediation of collective action.
If the existing institutional regime fits an equilibrium solution, it can provide incentives
and constraints for actors to behave in ways that can reinforce its stability. This can also
explain the success or failure of some recent attempts of institutional reforms. Several
initiatives to introduce proportional representation rules failed in federal countries,
mainly in Canada and the United States, while successful reforms in the same direction
took place in unitary countries, like New Zealand and Japan.
The Electoral System and the Party System
We have already presented the main politometric finding on this classic political science
topic, the “seat-product”:
More recently, the direction of causality was also discussed. Duverger’s laws were
broadly understood as if the number of parties were dependent on the electoral system.
Yet, although he didn’t elaborate much on it, he had already pointed out the reverse
effect: “It is also clear that the relationship between electoral and party systems is not a
one-way phenomenon; if a one-ballot vote tends toward a two-party system, a two-party
system also favors the adoption of a single ballot voting system” (Duverger, 1972).
Stein Rokkan went further: “In most cases it makes little sense to treat electoral systems
as independent variables and party systems as dependent. The party strategists will
generally have decisive influence on electoral legislation and opt for the systems of
aggregation most likely to consolidate their position” (Lipset & Rokkan, 1967).
A more explicit hypothesis regarding the actors’ motives and choices was presented.
According to the “Micro-mega rule,” the large prefer the small and the small prefer the
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large. This postulates that a few large parties may tend to prefer small assemblies, small
electoral districts, and small thresholds (the smallest being plurality rule, which does not
require anyone), in order to exclude others from competition, while multiple small parties
tend to prefer large assemblies and large districts with proportional representation in
order to enter the system and have an influence within (Colomer, 2004).
Statistical calculations were developed in order to give the reversal hypothesis empirical
support. It was found that the probability of change from plurality or majority rule in
single-seat districts to proportional representation in multi-seat districts is higher than
50% when the effective number of parties is higher than four (Colomer, 2005).
But the reversed quantitative logical model above presented was also validated. The
electoral system, summarized by M, can be derived from the number of parties, whose
leaders and members are likely to be the designers and choosers of the electoral system,
and from the number of seats in the assembly, which is a structural variable depending
on the country’s population:
The equation also shows that the number of previously existing parties, which is the
result of human collective action, is more influential than the structurally determined size
of the assembly for the choice of the electoral system.
Number of Parties in Government
The number of parties with seats in the assembly is clearly related with the number of
parties in the cabinet. There is an obvious direct relation between the two variables in
parliamentary regimes, as either there is a majority party in the assembly or a multiparty
coalition is formed in support of the prime minister. But the relation is also highly
relevant in presidential regimes. When the president’s party does not have an absolute
majority of seats, multiparty coalitions tend to be formed in similar ways as in
parliamentary regimes, with the only restriction that the president’s party must be a
coalition partner (as long as the president’s party is the largest party, the two processes
work in a very similar ways).
There is a long tradition of both formal models and empirical studies of coalition
formation in parliaments and congresses (Laver & Schofield, 2003; Pereira & Melo, 2012).
But the quantitative approach can be very simple. The average number of parties with
seats in democratic assemblies is about six, while the average number of parties in
governments is about two. The best fit is given by the equation:
where,
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P: Number of parties with seats
PG: Number of parties in government.
More sophisticated is the
calculation of the relative
size of the largest party,
which may also determine
whether the government is
going to be formed by one,
two, or a higher numbers
of parties. The reasonable
hypothesis is that the
larger the number of
parties, the smaller the
seat share of the largest
party. The best fit was found with the equation:
where,
P: Number of parties with seats
p: Seat-share of the largest party.
(Taagepera, 2007, ch. 8)
For example, in an assembly with 4 parties, it should be expected that the largest party
would have about 50% of the seats and most likely be able to form a single-party
government. For the world average value of 6 parties, the largest party would have 40%
of the seats and most likely be able to form a majority coalition with only one junior
partner, as is actually the average empirical observation.
Cabinet Duration
The advantages and drawbacks of the duration of cabinets has been debated. For some,
short-lived cabinets are unlikely to provide effective policy-making and may over the
longer run affect the legitimacy of the political system. For others, overly durable
cabinets imply executive dominance and may go stale. For any of the normative
judgments, nevertheless, it may be interesting to be able to explain and predict the
duration of cabinets in parliamentary regimes.
Click to view larger
Figure 3. Size of Government in Parties.
1
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A cabinet may be considered to last as long as its partisan composition does not change
and the prime minister remains the same. With this criterion, the total range of mean
cabinet durations for 35 countries observed extends from 1.5 years (in Finland) to 40
years (in Botswana). In order to explain this variance, several studies have focused on
either structural factors (including rules for appointing and dismissing governments,
electoral volatility, party system polarization, and other elements) or the effects of
unpredictable, critical events. But those studies have not offered specific quantitative
predictions (See reviews by Grofman & van Roozendaal, 1997; Laver, 2003).
A quantitative logical model drawing from some of the findings above reviewed has
focused on the number of parties with seats. It is assumed that the higher the number of
parties, the more potential for channels of conflict, which can lead to party shifts among
those initially sharing or supporting a coalition cabinet. It’s not only the number of
parties in the coalition that counts, as parties in the opposition can also have ways to
affect its duration. The relative sizes of the parties may also be relevant, as, for example,
party systems with a large, dominant party may have more durable cabinets. This leads to
take the effective number of parties as, as reported above; it weights the number of
parties by their relative sizes. The best fit was found for the equation:
where,
C: Cabinet duration in years
EP: Effective number of parties with seats.
(Taagepera, 2002, 2007, ch. 10).
Again, this means that the actual duration has an equal probability of being above or
below 42 years/EP . For every specific case, the deviation from the prediction of the
model leaves room for other explanatory, whether structural or eventful factors
mentioned above.
2
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Policy Change
Policy change or instability has been valued differently by different authors depending on
whether they praise more clear-cutting electoral promises and executive effectiveness or
broad consensus in decision-making. Several studies have considered whether policy
instability can depend on a variety of economic, social, political, and institutional factors,
but no quantitative measurement was provided. (See, e.g., Lijphart, 1999; Persson &
Tabellini, 2003; Schmidt, 1996). Following the politometrics approach, the degree of policy
change or instability was modeled and quantified in relation to the number of parties in
government. Since the relationships between the number of parties in government and
other variables, such as the number of parties with seats and the electoral system, are
well established, as we have seen above, it was possible to simplify the question into only
two variables.
Actually, it was traditionally observed that single-party governments, such as those
formed in the United Kingdom for several decades, tend to produce very high levels of
policy changes and reversals, whereas multiparty coalition governments, such as the ones
in Switzerland or Israel, tend to produce a high degree of stability and little policy
change. In order to quantify this relationship, policy change was measured on the basis of
the data for policies and preferences of parties and governments in a few dozen countries
since World War II produced by the Party Manifesto project (Budge et al., 2001; Kim &
Fording, 2002, 2010; Klingemann et al., 2006). As they are standardized on a scale of 0–100,
they permit intra-country, cross-country and long-term comparisons. For each country,
policy change is measured as the average difference between the government’s policy
scores in each pair of successive elections.
There is a strong negative correlation between the number of parties in government and
the degree of policy change. The fewer parties in government, the more changes, and
vice versa. An equation with quantitative values indicates that in comparison with the
Click to view larger
Figure 4. Cabinet Duration in Years.
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high levels of policy instability in certain systems with single-party governments, such as
the United Kingdom (which is about 30% of the policy-ideology spectrum); a series of
two-party coalition governments, such as those in Germany, can reduce policy instability
to about half (so about 15%); while three, four or more parties in government, as in
Israel, the Netherlands or Switzerland, reduce policy instability to about one-third (10%).
This is summarized by the equation:
where,
PG: Number of parties in government.
Ch: Average percentage of policy change between two successive elections,
which is calculated by the difference between the weighted average of policy positions of
each government for all k election-years t: .
(Colomer, 2012).
Analogous calculations for
the separation-of-powers
system of the United
States gave a provisional
estimate of policy change
of 7%, which somehow
confirms the so-called
gridlock, deadlock, or
paralysis effect of a regime
with institutional “checks
and balances” and
frequent situations of
divided government.
Institutional Design
The package of accumulated politometric findings also suggests indirect relations
between different variables, which can be used for forecasting probable effects of
institutional changes and for supporting institutional advice and design.
Click to view larger
Figure 5. Policy Change.
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For example, from the measurement of cabinet duration one could move backward to its
directly or indirectly causal variables, first to the number of parties with seats and the
size of the largest party; then to the factors of the seat-product, that is, the electoral
district magnitude and the size of the assembly in seats; and from the latter to the
country’s population. In the notation given above, the chain would be:
In this presumed causal chain, the mean cabinet duration is directly connected to the
number of parties and more and more indirectly to the other variables. Hence one should
expect the electoral system, as operationalized with S and M, to be less precise than the
number of parties in predicting the cabinet duration. But this is the relationship that
matters for institutional engineering. According to the model it can be predicted, for
example, that doubling the electoral district magnitude would reduce the mean cabinet
duration by about 20% (Taagepera & Sikk, 2010).
Another example is the hypothetical formation of a worldwide elected assembly, which
could work for check and accountability of the global institutions. As it is estimated that
the world population in 2025 will be about 8 billion, the size of a world assembly in seats,
according to the cube root law, should be about 2,000.
For the number of territorial units, as the size of the countries is so hugely varied, a
possible arrangement could be to count both states and regions in federal-like countries.
Rounding numbers, there are in the world about 200 states and about 500 political
regions (including 50 states in the United States, 26 in India, and so on), which would
make about 700 territorial units.
Then the equation that relates the size of the assembly, the number of regional or
territorial units and the average district magnitude produces M ≈ 3. This could
reasonable imply a combination of single-member districts and medium-size multimember
districts.
Then the size of the upper chamber would be about 1,000, certainly smaller than the size
of the lower chamber and larger than the number of territorial units.
(adapted from Colomer, 2014B).
The politometric models here recollected can provide a parsimonious and consistent
explanation of the variety of combinations of some basic institutional alternatives in
durable democratic countries. In future research, additional variables could be added to
refine the models, including, in particular, the density of the population and
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measurements of its economic and cultural heterogeneity, which could qualify the size of
the country in population that has been taken so far as a proxy of social complexity. Other
institutional variables may refer to the relations between presidents and assemblies,
which may involve a gradation of relative powers, checks, and balances. (For an early
attempt to measure separate institutional powers with quantitative values, see Shugart &
Carey, 1992.) The models should also provide predictive capacity able to support forecasts
and practical advice, especially for the success of attempts at constitutional reforms, new
democratizations, or state-, nation-, and federation-building.
Methodological Discussion
The pertinent presumption for all the previously reviewed works is that the political
outcomes of human interactions can produce regularities amenable to being captured by
mathematical formulas similar to those used by physicists or by economists. Political
scientists may expect a set of relevant postulates, if they are captured by a few stylized
formulas, to be the foundations of a deductive method of inquiry. Well-modeled
hypothesizes, if expressed as mathematical relationships between well-defined variables,
can be subjected to empirical testing, and are capable of being used to develop specific
predictions. This should open doors toward theoretically driven, empirically grounded
political analysis.
To make further progress and develop cumulative scientific knowledge, politometric
models should fulfill a few specific methodological traits that have been briefly mentioned
on the way in the above review. They include a small number of measurable variables,
logical hypothetical relationships, varied forms of mathematical equations, results
focused on the numerical values of quantitative coefficients, and directionality of causal
relationships.
First, a simple and relevant equation should include a small number of well-defined
variables. Physics works with a few, clearly defined, precisely measurable variables, such
as distance, time, mass, energy, temperature. Economics, on its own, operationalizes
population, product, money, employment, trade. Politometrics, in turn, needs to focus on
measurable parameters such as arms, votes, seats, parties, offices, governments, policy
distance, ethnic distance, and so on.
Second, the format of the functional relationship must be established on logical grounds,
which usually requires assumptions regarding actors’ motives and choices. As in physics,
economic theorems are not generalizations induced from experience, in contrast to still
common uses in political science. They postulate logical hypothetical relationships among
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variables that should enable us to explain and predict observations. Economists began
following this path several generations ahead of mainstream political scientists, but a few
decades ago they still encountered difficulties and objections that were similar to those
faced more recently within political science.
Third, the mathematical equations that establish relations among variables may have a
nonlinear form, but include multiplication, division, power or derivative (or have an
additive linear format for the logarithms of the variables). Most basic equations in mature
sciences are not linear and very few are simply sums; nonlinear forms of equations are
also widely used in economics (Colomer, 2007; Crease, 2004). Warnings regarding the
narrowness of the traditional linear, additive regression model were raised in economics
several decades ago (see Malinvaud, 1970). Similar alarms regarding the possibility of both
finding spurious linear relationships or overlooking true nonlinear relationships were also
raised in political science (McGregor, 1993). This is also a current concern in psychology
(Nisbett, 2015).
Fourth, quantitative coefficients should be taken seriously. Further progress with new
data and observations should not start from scratch or focus only on statistical
significance, but start from the quantitative results of previous analyses.
Fifth, the directionality of the relationship should be specified (perhaps using “arrows”
instead of “equal” signs, as in some equations above). This is because the mechanisms
that can explain relationships between structural or institutional variables typically
include human action with some intentional direction. Human decisions may alter any of
the variables and make it exogenous or independent, as was discussed regarding the
reverse relationship between electoral systems and party system, and it is valid for any
choice of institutional formulas.
Certain warnings that were already raised in economics should also be taken into
account. In particular, it has been argued that the depth and precision of scientific
knowledge acquired in physics may not be achieved in the social sciences for two
reasons. One has to do with the range of validity of theorems. Kenneth Arrow remarked
that while physical laws are “true for all time,” economics (and for that matter, political
science) is more constrained by given circumstances. Accordingly, each historical or
contemporary episode should “be interpreted as the application of general principles to
unique contexts” (Arrow, 1985). Economists and other social scientists typically suspect
that the human world changes more than the natural one, thus imposing more
constraining territorial and temporal limits on the validity of hypotheses and postulates
that should be specified.
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Nevertheless, it can be observed that the laws of physics are also valid only under
specified conditions. Galileo’s law of falling bodies, for instance, implies an idealized
“perfect vacuum,” but to measure and predict each specific episode, the resistance of air
or “friction” and other circumstances have to be estimated. Actually, physical laws do not
predict the future in an unconditional sense. They merely say that if certain conditions
are fulfilled, then certain outcomes can be expected. Whether this implies a difference of
degree or of quality in the kind of knowledge that can be developed in the natural
sciences and in the social sciences, is something open to discussion. To use Arrow’s own
comparison, it is likely that the social sciences should be able to develop, in proportion,
more “geology” than “physics” or “chemistry,” that is, more study of specific events than
standard laws. But no geology is feasible without solid foundations in physics and
chemistry, as the study of business or public administration should be based on solid
economics and political science.
A second objection is that in the social sciences there is a greater degree of influence of
the observer on the subject being observed. Specifically, knowledge of economic
phenomena may itself become an economic variable, since people with such knowledge
can change the economic situation to which they refer. Again, influence of the observer
on the observed has also been claimed for any science using laboratory experiments,
since observation always means interaction. In quantum mechanics, for instance,
“seeing” particles requires bombarding with photons, which does not affect large objects,
but alters subatomic particles. It is clear, nevertheless, that this objection is more
relevant to the development of testable postulates and predictions in the social sciences.
An implication is that the “mechanisms” or decisions likely to be made by human beings
given specific constraints and incentives may also be specified in order to account for
expected outcomes—as developed in game theory, prospect theory, and related
approaches.
None of this diminishes, however, the potential for the development of politometrics.
With the above-mentioned properties, mathematical equations based on sound theory can
be validated by empirical tests, and can predict precise observations. They can provide
not only knowledge and understanding of political phenomena, but also the best
foundations for applied research in fields such as public administration, policy-making,
electioneering, diplomacy, conflict resolution, and others with a wide professional
projection.
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Notes:
(1.) There has been some hesitation about the exact conformation of the appropriate
names for the approach. As the name for a subfield of political science or polito-logy,
polito-metrics is derived from the Greek roots “politika” and “metrics” or measurement.
This is analogous to the use of econo-metrics as derived from “oikonomus” or economics
and “metrics.” In contrast, the previously used name polimetrics would be analogous to
the nonexisting and narrower ecometrics; and, in addition, “poli” could be confused with
“poly” or “many” (see self-revision and discussion by Alker, 1996). Other uses include a
numerical Computation Laboratory at Ohio State University that was named Polimetrics
from 1969 to 1996, when it was renamed the Political Research Lab. A related book title
is Daniel T. Osabu-Kle, Introduction to Polimetrics (1997). Polimetrics has also remained
as the name for quantitative-oriented courses in Arizona State, Virginia State, Carleton,
and other universities.
The distinction between micro- and macropolitics, which is, of course, imported from
micro- and macroeconomics, was adopted for volumes 2 and 3 of the Handbook of
Political Science edited by Greenstein and Polsby (1975) and promoted as an
organizational criterion by Harry Eckstein, whose colleagues at the University of
California, Irvine, have kept it for their core courses (Grofman, 2005).
Josep M. Colomer
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Department of Government, Georgetown University