CCR5A

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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

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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,

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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

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,

(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

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(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

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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)

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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.

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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

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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,

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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

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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

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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)

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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

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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

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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

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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.

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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.

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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.

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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.

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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

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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:

[email protected].

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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

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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

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Figure 1. Observed States and expected States, 1900-2000.

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Figure 2. Observed "States" and expected “States," 1900-2000.