Download - CCR5A
Is a World 1
Running Head: A POPULATION-PRESSURE ALTERNATIVE
Is a World State Just a Matter of Time? A Population-Pressure Alternative
Robert Bates Graber
Truman State University
Is a World 2
Abstract
Previous efforts to forecast political evolution have been atheoretical extrapolations, time
itself the only independent variable. A mathematical population-pressure theory of
political evolution is summarized, and applied to two new time series for 20th-century
polities—one for the number of states as traditionally identified, a second for the number
of “states” when the League of Nations and the United Nations (but not their members)
are considered autonomous political units. The number of states unexpectedly increased
in proportion to global population density ( , for population in billions);
the number of “states,” however, as theoretically expected, decreased in proportion to it (
). A future population of, say, 10 billion accordingly is predicted to
consist of 342 states and 6 “states.”
KEYWORDS: League of Nations, mathematical prediction, political evolution,
population-pressure theory, United Nations, world state,
Is a World 3
Is a World State Just a Matter of Time?
A Population-Pressure Alternative
Attempts to predict the political future seldom have been scientific. The few
exceptions have lacked definite theoretical motivation, being instead essentially
mathematical extrapolations of trends observable in the past (Hart,1948; Naroll, 1967;
Marano, 1973; Carneiro, 1978. (For summaries see Roscoe, this issue; for a new
contribution see Peregine, Ember, & Ember, this issue). This paper will present a
population-pressure theory of political evolution, then use the theory to predict the
political future—first ahistorically, then historically based on two new time series for the
number of autonomous political units in the 20th century.
A Population-Pressure Theory
Anthropologists have noted a general connection between a population's material
circumstances and its tendency to undergo political evolution. The circumstances
conducive to political evolution have been classified by Carneiro (1970) as
environmental circumscription, social circumscription, and resource concentration.
Carneiro proposed that the mechanism through which these circumstances brought about
political evolution, from villages through chiefdoms to states, was competition over
scarce resources—ultimately, conquest warfare or the threat thereof.
A mathematical theory inspired by Carneiro's work emphasized sheer population
density rather than warfare (Graber, 1995). The most convenient mathematical expression
of this theory with which to begin is
Is a World 4
,
(1)
where N denotes the number of autonomous polities composing a population P inhabiting
a total area A. The dot denotes the proportional or percent growth rate (rigorously, the
derivative, with respect to time, of the natural logarithm). For purposes of this paper, a
non-negative population-growth rate will be assumed.
Suppose we imagine a growing population able to expand freely into a
productive, homogeneous, uninhabited environment. In such an ideal case it would seem
reasonable to assume that the area inhabited would expand in proportion to the
population growth. In this case area would increase at the same proportional rate as
population ( ), so we can replace in Equation (1) with to get , or
(for ). (2)
Here we see that the number of autonomous polities theoretically will increase at the
same proportional rate as population. (The mean number of people per society, of course,
must in this case remain constant.) The initial populating of Earth by small bands must
have approximated this idealization, as does the recent process of population growth,
village splitting, and territorial expansion of the Yanomamö in the Amazon Basin
(Chagnon, 1974).
If, however, material circumstances fully inhibit the territorial expansion of a
growing population, area will increase not at all. Hence the growth rate for area will not
equal that for population, as before; rather, it will equal zero, in which case we can
replace in Equation (1) with zero to get , or
Is a World 5
(for ). (3)
Now the number of autonomous polities theoretically will not increase but rather will
decrease at the rate at which population is increasing. (See Graber, 1995 for proofs that
in this case the mean number of people per society will increase just twice as rapidly as
population, and in proportion to its square.) While this case lacks the degree of empirical
support enjoyed by the former case (i.e., of uninhibited expansion), its theoretical
predictions have been shown plausible over a fairly wide range of archaeological and
historical applications (Graber, 1995, pp. 67-73, 151-152). It is, moreover, entailed by
what is apparently the simplest mathematical form for a general population-pressure
theory of political evolution. For these reasons it seems worthwhile to consider its
implications for the political future of humanity.
Several additional formulas will prove useful. In the case of uninhibited
expansion, the number of polities theoretically increases in proportion to population;
therefore, for an interval from initial time 1 to terminal time 2,
(for ). (4)
If population, say, has doubled, so also will have the number of polities. In the case of
fully inhibited expansion, however, the number of polities theoretically changes not in
direct but rather in inverse proportion to population:
(for ). (5)
In this case a doubling of population, making the right side equal 2, entails a halving of
the number of polities since, for the left side to equal 2, , which is now in the
Is a World 6
denominator, must equal just half the numerator ( ). Cross-multiplying and reversing
Equation (5) calls attention to an interesting entailment: constancy of the population-
polity product ( ).
Inasmuch as the readily habitable portions of Earth evidently have been inhabited
for nearly 10,000 years (Cohen, 1977), the situation since that time may be approximated,
for the world as a whole, as one of fully inhibited expansion. It is to Equation (5), then,
that we presumably must look in order to deduce theoretical predictions. In particular, we
might wish to predict how many people will be needed to forge the current number of
polities into a single unit ("world state"). To obtain the needed formula we first solve
Equation (5) for :
(for ).
(6)
Setting at unity yields an elementary world-state formula,
(for ), (7)
according to which the factor of population increase needed to generate a world state
(P2/P1) is simply the number of currently-existing autonomous political units (N1).
We might also wish, however, to predict how many polities there will be should
population reach a certain level. For this purpose we solve Equation (5) for :
(for ). (8)
Is a World 7
A tripling of population, then, theoretically would be attended by political fusions
sufficient to reduce the total number of polities to one third of the original number.
Predicting the Political Future
Ahistorical Predictions
Population needed for a world state. Use of Equation (7) to project the population
at which the world will be politically unified requires estimating the population of, and
the number of autonomous polities in, the world at present. The US Census Bureau
estimates world population at just over 6.25 billion; relatively reliable sources estimate
the number of nations at 193 (the 191 members of the UN, as well as Taiwan and Holy
See). Substituting these values for and in Equation (7) gives a first result: P2 =
6.25 × 109 × 1.93 × 102 = 1.21 × 1012.
A population this size—1.21 trillion—would contain nearly two hundred people
for every one alive today. This is a number far larger than envisioned by conventional
demographic projections; far larger, too, than appears sustainable on the fossil-fuel
foundation of industrialization as we know it. Yet enormous as a hypothetical 193-fold
increase may sound, it evidently is only around one third as large as the actual factor of
increase since the end of the Pleistocene (taking 10 million as the terminal-Pleistocene
estimate [cf. Cohen, 1977, pp 53-54]). Furthermore, technological and social innovations
that would make human reproduction far cheaper than it now is are not entirely
unimaginable. Under conducive conditions, human populations have sustained annual
growth rates, for several decades, of 3%; at this (discrete) rate, a 193-fold increase occurs
in only 178 years.
Is a World 8
Population needed for a world “state.” If the prediction remains somewhat
implausible, may it be because we have counted polities incorrectly? Supranational
polities—first the League of Nations, then the United Nations—seem to be playing a
gradually larger role in world affairs, notably in the form of military “peacekeeping
operations” (United Nations, 2000, pp. 298-302). Are such polities to be counted, and if
so, how? It will not do simply to add “1” (for the UN) to the 193, since we want the units
enumerated to be mutually exclusive. The solution, though perhaps seeming extreme, is
clear: We must consider all 191 member nations to compose a single autonomous
political unit, Taiwan a second, and Holy See a third. Using quotation marks to remind
ourselves of the heterodox nature of this count, let us call it an enumeration not of states
but of “states.” According to this “states” count, then, political unification of the entire
world would require, according to Equation (7), only a threefold increase in population;
deleting Holy See, which is in several respects anomalous, would reduce the theoretically
required population increase to a doubling. These predictions also seem rather
implausible, not only in view of specific facts such as Holy See’s having no desire to
become a regular member of the UN, but also because, with so few remaining “states,”
the prediction becomes quite sensitive to whether a particular entity is included or
excluded.
It might be supposed, however, that the rather unconvincing nature of this first set
of predictions is rooted in problems with the very concept of autonomous political units:
the apparent heterogeneity of the entities—especially the “states”—enumerated, or the
artificiality of treating autonomy (independence) as simply present or absent rather than
Is a World 9
as a matter of degree. Scientists, however, are free to formulate whatever concepts we
find useful—a principle christened by one philosopher the autonomy of the conceptual
base (Kaplan, 1964, p. 79). Use of the autonomous-political-unit concept already has
proven, at the very least, provocative (Carneiro, 1978); the suggestion that it be discarded
(e.g., Modelski & Vellut, 1968, p. 954) seems therefore premature.
A problem perhaps more important—and certainly more tractable—lies in the fact
that these initial predictions result from having hastily applied the theory to current
estimates of population and number of polities, making no use of any information about
the trajectories by which these variables reached their current values. But a whole
century's worth of such information has accumulated; perhaps taking it into account will
help yield predictions of greater credibility.
Historically Informed Predictions
Table 1 displays the number of autonomous political units, both States and
“States” of the 20th century, as of the end of every fifth year. The States series presented
derives from work by Russett, Singer, and Small (1968), Wyckoff (1980), and Bauer
(1998); the "States" series, from comparison of the States inventories with membership
lists for the League of Nations (Walters, 1975, pp. 64-65) and for the United Nations
(2000, pp. 289-297). (The States figures here differ modestly from those previously
published [Graber, 1995, p. 140, Table 7.2], having been corrected for recently-unearthed
errors involving Ireland and Viet Nam.)
The identification of politically autonomous units as such of course has been more
difficult than one would like. The criteria are a blend of emic and etic (Harris 1969,
Is a World 10
1979): “At any given time, an entity was classed as independent if it enjoyed some
measure of diplomatic recognition [emic] as well as effective control over its own foreign
affairs and armed forces [etic]” (Russett et al., 1968, p. 934).
Why begin with the year 1900? After noting considerations of data availability,
especially for the world beyond the Western powers, Russett et al. (1968, p. 933) added
that
the coding problem is markedly eased by the turn of the century, by which time
the unification of Germany, Italy, and Russia had been completed, almost all of
the Indian subcontinent had come under the British Raj, and Africa had been
largely carved up by the colonial powers. An earlier starting date would not only
have necessitated a dramatically longer list [italics added], but one with a far
greater likelihood of error and ambiguity.
Viewed anthropologically, the need for a “dramatically longer list” were we to try to
begin much before 1900, far from being only a source of problems for data quality and
coding, reflects the crucial fact that autonomous political units, globally, were still
deproliferating, as they apparently had been doing for millennia (Carneiro, 1978). This
long period of deproliferation apparently ended—indeed, reversed—around 1900.
Carneiro (1978) suggested that the reversal began only with decolonization after
World War II, and that when “viewed against the enormous reduction in autonomous
political units that has occurred over the last three millennia, this reversal appears as little
more than a small back-eddy in an onrushing current” (1978, p. 220). But what appeared
to Carneiro in the 1970s as a three-decade “back-eddy” with one particular historical
Is a World 11
cause now appears as a century-long process not so much caused by as expressed through
several diverse historical events, including not only decolonization after mid-century, but
balkanization decades before, and Soviet disintegration decades after.
The proliferation of States. Figure 1’s line for the States series is rather flat until
1940, after which it rises sharply in a nearly linear fashion; indeed, the number of states
increased quite regularly, for sixty years, at a rate of very nearly 2.35 states per year. This
proliferation of States is an entirely unexpected phenomenon theoretically inasmuch as
the inhabited area of Earth has not changed appreciably in the 20th century. This
proliferation may have been due in part to the League of Nations and, especially, to the
United Nations—an interesting possibility for future investigation. In any case, it is easy
to see that the overall factors of increase, for population and for States, are similar; this
raises the possibility—less expected, if anything, than the proliferation itself—that the
proliferation inexplicably has proceeded proportionally with population growth.
How well does this theoretically unexpected proliferation fit, so to speak, with
theoretical expectations for proliferation? To find theoretically expected values for
number of States N for various levels of population P, we must solve Equation (4) for N2:
(for ). (9)
Letting initial values be 1.65 for population (in billions) and 55 for States,
. (10)
The Expected States column of Table 1 has been generated using this formula.
(The world-population estimates for 1900, 1910, 1920, 1930, and 1940 are rounded from
Is a World 12
values in United States, n.d.-a; estimates for 1905, 1915, 1925, 1935, and 1945 have been
interpolated assuming five years of discrete growth at the annual rate for the decade. The
estimates for 1950 and thereafter are rounded from values in United States, n.d.-b.)
Figure 1 suggests a surprisingly good fit for the entire century. Regressing
States on population yields adjusted R2 of .95 and an ostensibly significant t ratio (20.38).
There is, however, evidence of two problems that often plague the use of time-series data
to test theoretical models: heteroscedasticity and autocorrelation. These are known to
render ordinary-least-squares (OLS) results reliable neither for identifying non-
randomness nor for assessing the strength of the relationship.
Econometric analysis, however, allows correction of the problems.
Transformation of both variables using generalized least squares (GLS; see Gujarati,
1992, pp.365-372), followed by logarithmic transformation, yields a regression
apparently free both of autocorrelation (p > .05, critical-runs test; Durbin-Watson d =
1.82 [p > .05]) and of heteroscedasticity (Spearman rank correlation coefficient rs = .29, p
= .20 [two-tailed]). (The GLS application used a Theil-Nagar ρ estimate of .692, and a
Prais-Winsten factor of .722.) The relationship appears, after all, to be rather strong:
Though adjusted R2 has dropped from .95 to .74, the latter value indicates that population
alone explains nearly three fourths of the variation in States. The relationship is not only
quite strong, but highly nonrandom (t = 7.53, p < .001). The equation that results from the
econometric refinement is
. (11)
Is a World 13
It should be noted that this differs but little from Equation (10), and that the exponent is
very close to the theoretically expected value of unity. The closeness of this fit is as
striking as the relationship itself is puzzling. Possibly ethnic identities tend to diversify in
proportion to population growth, and prove sufficiently forcible, in the proliferation of
polities, to account in part for the observed relationship.
To put this result to predictive use we must assume something about future
population change. Population forecasts are highly sensitive to assumptions about
fertility. As likely as any, perhaps, is the United Nations Population Division's "medium
fertility variant,” which explicitly estimates nearly 9 billion people by 2050, and suggests
a leveling off at around 10 billion by around AD 2100 (United Nations, 2003).
Substituting 10 for P in Equation (11) predicts a stabilized number of States, around AD
2100, of 342. This should be compared with the straightforward result of 333 produced
by Equation (10), that is, without econometric refinement.
The deproliferation of “States.” Figure 2 shows a sharp drop representing the
formation of the League of Nations in 1920; upheaval around mid-century; and a rapid
approach to unity after 1990. Counting “States” rather than States, then, the apparent
20th-century “reversal” disappears: Deproliferation continued, disguised in the form of
federations so (apparently) weak that it seldom—if ever—occurred to anyone to consider
them seriously and systematically as autonomous political units alongside the traditional
(non-member) states with which they coexisted.
Is it possible that this deproliferation has been an inverse function of density
increase? Let us begin by reconsidering Equation (8). According to this formula, as we
Is a World 14
have seen, the number of autonomous polities will decrease in proportion to population
increase. Clearly, the straightforward theoretical expectation, for every value N2 of
"States" after 1900, will be the initial number of "States" (55) times the reciprocal of the
factor by which population has increased. The initial population P (1.65 billion), like the
initial number of "States," will be constant; substituting these into Equation (8) for N1 and
P1 gives
. (12)
This formula generates the Expected "States" column in Table 1.
Figure 2 suggests a rather poor fit. The theoretical predictions are clearly
outstripped by the actual deproliferation after 1920, though they nearly catch up in 1990.
Regressing "States" on the reciprocal of population does yield adjusted R2 of .67, but
neither this, nor the ostensibly significant t ratio of 6.41, can be taken at face value; as
was the case with States, analysis of residuals produces clear evidence of both
autocorrelation and heteroscedasticity. GLS transformation, followed by squaring (to
avoid loss of four negative values) and taking logarithms again yields a regression
apparently free both of autocorrelation (p > .05, two-tailed critical-runs test; d = 1.94 [p >
.05]) and of heteroscedasticity (rs= .11, p = .63 [two-tailed]), with adjusted R2 of .34. (The
GLS application used a Theil-Nagar ρ estimate of .684, and a Prais-Winsten factor
of .730.)
To be stressed are the facts that (1) the foregoing econometric corrections result in
a large decline, in adjusted R2, from .67 to .34—meaning that one third rather than two
thirds of the variation in “States” is actually explained by population; but (2) the inverse
Is a World 15
relationship between population and “States” nevertheless proves highly significant (t =
3.37, p = .003 [two-tailed]). Perhaps this is as much as should be expected. The number
of “States” is modest, after all, both absolutely and relative to the number of States; it
changes much more abruptly, too, than does population. The extent to which this
abruptness is operating as a suppressor variable deserves future investigation. It seems
quite likely, too, that in testing the explanatory power of population alone (a strategy
dictated by the theory being tested), an unknown—but possibly large—number of
relevant variables have been omitted.
The econometrically refined equation is
, (13)
which, while differing more from unrefined Equation (12) than Equation (11) did from
Equation (10), remains quite similar. According to Equation (13), a population of 10
billion will bring the number of “States” to nearly six (5.82); the analogous prediction,
using unrefined Equation (12), is just over nine (9.08). It should be noted that while the
econometric refinement for States left the exponent at 1.018, this one for “States” leaves
it at 1.186. The deproliferation of “States,” then, unlike the proliferation of States, has
been somewhat more sensitive to density increase than theoretically expected; in both
cases, however, political evolution’s observed functional relationship—whether direct or
inverse—to population density has been, as theoretically expected, to approximately the
first power of the latter.
Conclusion
Is a World 16
The prediction that a stable population of 10 billion will be divided into around
six “States” may appear patently unrealistic inasmuch as there were fewer “States” than
that already by AD 2000. However, the fact that the mechanism of “States”
deproliferation has been voluntary federation rather than conquest warfare suggests that
what is most realistic is to expect not a definite reduction to a single autonomous unit, but
rather a fluid situation in which a relatively comprehensive global system’s universality is
chronically compromised by one or a few anomalous units (e.g., Holy See), and by
occasional new polities not yet admitted, or old ones withdrawing for one reason or
another. (The League of Nations experienced several withdrawals, the United Nations,
one [Indonesia, 1965-1966].) Indeed, the predicted increase in number of States entails a
fairly steady supply of nascent polities that for various reasons may experience a time lag
between what Russett et al. called “politically effective” independence on one hand, and
suprastate membership on the other.
The implausibility of the ahistorical results motivated resort to history, and the
theoretically unexpected proliferation of States in turn motivated construction of the
“States” series. Whether this represents laudable interaction between deduction and
induction, or just special pleading, the reader will have to decide. As to the quality of the
predictions: Time will tell.
Is a World 17
References
Bauer, K. L. (1998). An update of and follow-on to the standardized lists of
political units by Theodore Wyckoff (1980) and Bruce Russett, J. David Singer,
and Melvin Small. Unpublished manuscript, Truman State University, Kirksville,
MO.
Carneiro, R. L. (1970). A theory of the origin of the state. Science, 169, 733-738.
Carneiro, R. L. (1978). Political expansion as an expression of the principle of
competitive exclusion. In R. Cohen & E. R. Service (Eds.), Origins of the state:
The anthropology of political evolution (pp. 205-223). Philadelphia: Institute for
the Study of Human Issues.
Chagnon, N. A. (1974). Studying the Yanomamö. New York: Holt, Rinehart and
Winston.
Cohen, M. N. (1977). The food crisis in prehistory: Overpopulation and the origins of
agriculture. New Haven, CT: Yale University Press.
Graber, R. B. (1995). A scientific model of social and cultural evolution. Kirksville, MO:
Thomas Jefferson University Press.
Gujarati, D. (1992). Essentials of econometrics. New York: McGraw-Hill.
Harris, M. (1968). The rise of anthropological theory: A history of theories of culture.
New York: Thomas Y. Crowell.
Harris, M. (1979). Cultural materialism: The struggle for a science of culture. New
York: Random House.
Is a World 18
Hart, H. (1948). The logistic growth of political areas. Social Forces, 26, 396-408.
Kaplan, A. (1964). The conduct of inquiry: Methodology for behavioral science.
Scranton, PA: Chandler.
Marano, L. A. (1973) A macrohistoric trend toward world government. Behavior Science
Notes, 8, 35-40.
Modelski, G., & Vellut, J. (1968). [Communication on Russett, Singer, & Small].
American Political Science Review, 62, 952-955.
Naroll, R. (1967). Imperial cycles and world order. Peace Research Society: Papers, VII,
Chicago Conference, 1967 (pp. 83-101).
Russett, B. M., Singer, J. D., & Small, M. (1968). National political units in the twentieth
century: A standardized list. American Political Science Review, 62, 932-951.
United Nations. (2000). Basic facts about the United Nations. New York: Author.
United Nations. (2003). World population prospects: The 2002 revision. Highlights. New
York: Author.
United States. (n.d.-a). Historical estimates of world population. Retrieved February 17,
2002, from http://www.census.gov/ipc/www/worldhis.html.
United States. (n.d.-b). Total midyear population for the world: 1950-2050. Retrieved
February 17, 2002, from http://www.census.gov.ipc/www/worldpop.html.
Is a World 19
Walters, F. P. (1975). A history of the League of Nations. London: Oxford University
Press. (Original work published 1950 under the auspices of the Royal Institute of
International Affairs)
Wyckoff, T. (1980). Standardized list of national political units in the twentieth
century: The -Singer-Small list of 1968 updated. International Journal of Social
Science, 32, 833-846.
Is a World 20
Author Note
Robert Bates Graber, Professor of Anthropology and Sociology, Division of
Social Science, Truman State University.
An earlier version of this paper was presented at the first meeting of the Society
for Anthropological Sciences, held at the Drury Inn and Suites in New Orleans on
November 22-23, 2002. For assistance of several kinds I thank David Capps, David
Gillette, Amber Johnson, Peter Peregrine, John Quinn, Jim Roscoe, and Jane Sung.
Neither the analyses nor the conclusions necessarily represent the views of any of them.
Correspondence concerning this article should be addressed to Robert Bates
Graber, Division of Social Science, Truman State University, Kirksville, MO. E-mail:
Is a World 21
Table 1
Population, Observed and Expected States and "States,” 1900-2000
Year Population Observed Expected Observed Expected
(billions) States States “States” “States”
1900 1.65 55 55.0 55 55.0
1905 1.70 57 56.6 57 53.4
1910 1.75 58 58.3 58 51.9
1915 1.80 57 60.1 57 50.3
1920 1.86 72 62.0 27 48.8
1925 1.96 74 65.4 22 46.3
1930 2.07 72 69.0 20 43.8
1935 2.18 73 72.7 18 41.6
1940 2.30 60 76.7 29 39.5
1945 2.42 69 80.8 23 37.4
1950 2.56 82 85.2 25 35.5
1955 2.78 89 92.7 16 32.6
1960 3.04 112 101.3 16 29.9
1965 3.35 131 111.5 17 27.1
1970 3.71 142 123.6 18 24.5
1975 4.09 157 136.3 16 22.2
1980 4.46 166 148.6 15 20.4
1985 4.86 170 161.8 14 18.7
Is a World 22
1990 5.28 171 176.1 15 17.2
1995 5.69 192 189.7 8 15.9
2000 6.08 192 202.7 4 14.9
Is a World 23
Figure 1. Observed States and expected States, 1900-2000.
Is a World 24
Figure 2. Observed "States" and expected “States," 1900-2000.