On Time and Crime: A Quantitative Analysis of the Time Pattern of Social and Criminal Activities

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NOT FOR QUOTATION WITHOUT THE PERMISSION OF THE AUTHOR

ON

TIME

AND

CRIME

A Quantitative

Analysis of

the Time Pattern

of

Social and Criminal Actmities

Cesare Marchetti

November 1 9 8 5 WP-35-84

Invited p a p e r . Annual Interpol Meeting, Messina, Italy, October 1985.

Working Papers are interim r e p o r t s on work of t h e International Institute f o r Applied Systems Analysis and have received only limited review. Views or opinions e x p r e s s e d herein d o not necessarily r e p r e s e n t t h o s e of t h e Institute o r of i t s National Member Organizations.

INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS 2361 Laxenburg, Austria

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Resume

Volterra analysis of economic and social behavior r e v e a l s a striking uniformi- t y in t h e way s t r u c t u r e s behave. Including man, socially a single unit but intrinsi- cally a l r e a d y a complex s t r u c t u r e .

In t h i s p a p e r t h e analysis i s focused on "deviant" behavior, showing t h a t technically i t i s not d i f f e r e n t from "normal" behavior. The labeling seems to b e basically determined by t h e dominant value system. The p a p e r should b e seen as an e x p l o r a t o r y e x e r c i s e t o determine t h e limits of application of t h e Volterra-Lotka equations and paradigm.

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ON TIM3 AND CRIME

A Quantitative Analysis of the Time Pattern of Social and Criminal Activities

Criminal activity h a s always been considered as a special c a s e of social activity deserving a special treatment.

The criminal h a s been considered as the product of society, mental illness, genetics. o r else, with a clear connotation of being deviant f o r reasons only par- tially under his control. Society t r i e s t o t a k e control, and t h e prison c a n become t h e instrument of punishment or t h e tool of redemption, depending on t h e dominant paradigm at t h e time.

As I will show in t h e following, t h e criminal does not a p p e a r to behave dif- ferently f r o m any person, e x c e p t obviously f o r t h e f a c t t h e objectives of his activity being considered as criminal by t h e dominant p a r t of society. S o t h e men- t a l illness paradigm which so strongly dominated last century's criminology, should not b e considered as specific. Artists, housewives, o r c a d a s t e r employees can b e mentally ill, with no s t r i c t connection with t h e i r t r a d e .

The methodology of my analysis i s very simple, especially because I will not t r y to delve into t h e t r e a c h e r o u s p r o c e s s of finding explanations. I will only s e a r c h f o r "structures", f o r o r d e r , into t h e set of factual data. I will, in f a c t , only analyze facts, trying t o see t h e f e a t u r e s they contain. I t i s like looking through a person with x-rays. One c a n see bones and organs, without any hint about why these a r e where they a r e . The basic assumption i s t h a t actions are t h e final output

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of information processing in o u r brain, and t h a t this processing follows some very general r u l e s of Darwinian c h a r a c t e r , coded in a quantitative way by Volterra- Lotka equations.

These equations say, e.g., t h a t t h e population dynamics of two competitors, o r of one species with limited food supplies (self-competition), evolve in time according to c e r t a i n very simple mathematical equations called logistics. Volterra equations can produce o t h e r solutions, but I will use only logistics f o r my diagnostics, f i r s t because they are v e r y simple (see Appendix) and, second, because they c o v e r a n extremely l a r g e number of p r a c t i c a l cases.

A case of logistic growth is r e p o r t e d in Figure 1. I t r e p r e s e n t s a case of self-competition, like t h a t of an animal species growing in a "niche", which pro- vides a limited amount of food. In t h e case of Figure 1 , t h e "population" of r e g i s t e r e d cars in Italy is r e p o r t e d . The niche in this case in t h e potential market f o r cars. C a r population grows to fill it, f i r s t at a f a s t rate and then progressively at slower rates. Incidentally, t h e same c u r v e describes t h e growth of a tree (height or weight), o r of a person. Because these S-curves look all alike, and t h e r e is no way of visually checking they r e p r e s e n t a logistic equation, I normally u s e a n o t h e r form of cohordinates, r e p o r t e d in Figure 2, where logistics a p p e a r as s t r a i g h t lines. A s explained in t h e Appendix, t h e numbers characterizing t h e process a r e usually r e p o r t e d on t h e c h a r t . They a r e :

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The saturation point, o r t h e asymptote, i.e'., t h e largest number of cars t h e market can receive, as in Figure 1. This number is usually given in parenthesis (20) in t h e a p p r o p r i a t e units (millions in t h e case of cars in Italy).

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The time constant, which gives a n idea of the speed of t h e process. I t is t h e interval of time AT, to go from 10% to 90% of the niche. For cars in Italy it is 22 years.

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The centerpoint of t h e process is often r e f e r r e d to, in o r d e r to fix it in time.

This analysis c a n be applied to all sort of dynamic p r o c e s s e s also with numerous competitors. We have, in f a c t , about a thousand different cases exam- ined to date. The analysis i s purely phenomenological. We try to f i t t h e d a t a to equations of t h e type described in t h e Appendix. A c a s e of two competitors could b e t h a t of cars substituting h o r s e s f o r personal transportation, r e p o r t e d in Figure 3. In this case, t h e size of t h e niche i s not necessary, as we are dealing with t h e r a t i o s of t h e s h a r e s of t h e market. Actually, t h e niche keeps changing in time as shown in Figure 4. The numbers of personal vehicles grows exponentially in t h e U.S. during t h e period under examination and at t h e same time cars substitute f o r horses.

As t h e last example of this s e r i e s I will give t h e case of competition between primary energies at t h e level of world market (Figure 5). Here w e s e e a l l t h e energies going slowly up in market s h a r e , and finally down. The reasons f o r showing this p a r t i c u l a r c a s e a r e :

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To g e t acquainted with t h e great slowness of social processes. O u r society a p p e a r s v e r y dynamic, but t h e substitution of this f o r t h a t t a k e s eons.

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To make aware t h a t t h e s e p r o c e s s e s of acceptance and rejection are v e r y stable in time. Wars, c r i s e s , and g r e a t inventions d o not seem t o change t h e i r progress.

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To show t h a t t h i s stability i s a prerequisite to forecasting and give a n example

of forecasting in t h e long range.

Figures 6a. 6b, and 6 c give t h e sequence of a forecasting exercise. The statistical d a t a f o r t h e market s h a r e s of primary energies in 1900-1920 f o r t h e world a r e r e p o r t e d in Figure 6a. If w e use t h e s e d a t a to f i t a set of competition equations (Figure 6b), w e can extend those equations outside t h e 1900-1920 range. This can be considered as an attempt in forecasting, e.g., from 1920-1970, i.e., f o r fifty

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y e a r s ahead. We c a n then superpose the actual statistical d a t a f o r t h a t period to the equation in Figure 6 c , t o check how good w e could have been in 1920. A s t h e result show, t h e f o r e c a s t would have been by all means a n excellent one.

?he central i d e a I w a n t to support is that o u r society i s a highLy regu- Lated and stable s y s t e m . In o r d e r to show t h e same thing by a different process, t h e number of c a r t r a f f i c accidents in the U.S. between 1910 and 1970 is r e p o r t e d in Figure 7. The context of t h e analysis is always v e r y important in such cases.

The background idea h e r e i s t h a t society sees t h e c a r as one of t h e many causes of death, and reacts in t h e a p p r o p r i a t e way to keep i t in check. S o the a p p r o p r i a t e measure is numbers of d e a t h s p e r thousand population.

The v e r y interesting r e s u l t is t h a t this number i s 25 p e r hundred-thousand population and p e r y e a r , independent from the number of c a r s . It shows what society is ready to t a k e and no more. Incidentally, as Figure 8 shows, most Western countries are locked t o t h e same level of deaths! This shows also t h a t police action must b e contextual. No measure can counterbalance t h e "readiness t o die"

of t h e drivers.

The high level of self-regulation of l a r g e a g g r e g a t e systems has led to t h e question of regulation at lower levels of aggregation. Jumping through many intermediate levels, like nations and regions, we went to t h e formally most simple form of organization, t h e commercial company. The objective of t h a t company i s to sell a product o r a s e r v i c e , and t h e amount sold can w e l l b e considered as a measure of i t s size. Figure 9 shows t h e case f o r Mercedes-Benz, were t h e number of cars pro- duced is r e p o r t e d as a f r a c t i o n of t h e (calculated) saturation point. The e x e r c i s e h a s been r e p e a t e d f o r about a hundred companies and t h e result has been always positive.

A company c a n b e seen as a formally organized set of people with a definite purpose to r e a c h . Producing cars, o r organizing vacations. There is no a p t i o r i

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hindrance t o t r e a t a criminal organization in the same way. Figure 10 r e p o r t s the

"actions" performed by t h e "Red Brigades" in Italy during t h e period 1970-1976.

The c h a r t r e p o r t s t h e cumulative number of actions, t r e a t e d as described in t h e Appendix. The Red Brigade movement appears perfectly quantified by t h e equation. With a six-year time constant, i t appears relatively ephemeral. The equation forecasts (in 1976!) t h e end of t h e movement (99% of actions performed) in 1985.

The peak of t h e i r power was reached in 1976-77, and t h e decline w a s b u i l t i n into t h e system. In o t h e r words, organizations seem to have an intrinsic aging process, which can be interesting. to measure. as w e have done here. in o r d e r t o deal appropriately with them. A t t h e level of t h e police or a t t h e level of t h e stock exchange, depending on t h e objectives of the organization.

Just for systematic reasons, one can ask if man, so complex and composite in many ways, does not contain similar organized s t r u c t u r e s inside himself. After all, he i s t h e prime mover on .one side, and on t h e o t h e r his brain contains billion of interactive cells, t h e neurons. Obviously we have to quantify his actions through some form of output, and this i s not difficult f o r such "public" men, like a r t i s t s o r scientists. Their work is carefully catalogued. So I s t a r t e d analyzing artists and men of science, looking at t h e cumulative number of t h e i r work: paintings, plays, pieces of music, o r scientific publications.

A pick of t h e results i s given in Figures 1Oa. l o b , 1Oc and 10d. What these results say i s t h a t t h e i r production i s regulated according to a precise schedule.

Each of them has a mechanism incorporated telling how much and when. Our equation just unravel t h e mechanism. And because the equation can be established on a partial set of data, i t can be used, e,g, to predict how many books a famous writer suiLl produce, and when. I t is w e l l known t h a t w e are genetically programmed in a quite rigorous form, but this long term programming of t h e uis u i t d i s may come a s

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a surprise. I do not think, owever, t h a t a t this level i t interferes too much with t h e holy cow of t h e "free will".

My purpose h e r e is practical and not philosophical, and the objective is t o s e e t h e applicability of the methodology to a systematic study of criminal behavior. I do not think criminals a r e different in the mechanisms of t h e i r behavior. Only t h e i r objectives are not orthodox. Criminality then is not intrinsic, but comes from a social definition. To use a worn out example, murder is criminal in peace but heroic in w a r . So t h e analysis should apply to criminal activity

too,

As Fig- ures l l a , l i b , l l c , l i d , and l i e show, this i s the case. The criminal has a potential, a bag of beans, which h e will dutifully spill. Although the final proof requires a large casistic, which requires your collaboration in providing data, i t a p p e a r s that prison does not have a n effect on t h e global result. The incapacitating periods a p p e a r compensated by increased activity once the bird is out of t h e cage.

This hard will to comply with t h e program and the schedule makes t h e criminal forecastable. His past activity contains t h e information to map t h e future one, in t h e same sense a segment of t h e t r a j e c t o r y of a bullet can be used to calculate t h e previous p a r t and t h e following p a r t .

Because my analysis can be done only after a sizable chunk of t h e career has been explicated, I cannot make any statement why the gun w a s originally aimed in a

"deviant" direction. It seems evident, however, t h a t measures to really reduce criminality have to be taken buore a person becomes a criminal.

After having brought the analysis down to t h e individual I will try it again on a n aggregate case, not of a gang, however, but on a population. The case of c r i m - inality against t h e property in t h e U.S. is reported in Figure 12. It just counts t h e number of people a r r e s t e d according to age. The r a w sum appears to be a composite, of juvenile, young, and long-term professional activity. I tried to s e p a r a t e the juvenile component through t h e f i r s t bell-shaped curve drawn onto t h e c h a r t .

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This p a r t of t h e criminality c u r v e is then analyzed in Figure 13. The second p a r t of t h e c u r v e in Figure 1 2 is not drawn by f r e e hand. I t is calculated using the f i r s t p a r t and t h e usual logistic equation. Apart from t h e descriptive and organizing aspect, t h i s c h a r t a l s o tells t h a t whatever is done to keep in check this criminality, t h e e f f e c t a p p e a r s t o b e zero.

On t h e o t h e r side, I would a l s o attract your attention on social forces and moods which on t h e c o n t r a r y strongly influence t h e level and t h e modes of criminality. The case is r e p o r t e d in Figures 1 4 and 15. The oscillating c u r v e of t h e t o p is a "clock" measuring social activity. The c u r v e in fact d e s c r i b e s t h e deviation from t h e t r e n d of energy and electricity consumption. Loosely speaking, t h e upward p a r t s of t h e c u r v e r e p r e s e n t periods of boom, and t h e downward p a r t s periods of recession. The second c u r v e down r e p r e s e n t s t h e r a t e of homicides. I took homicides because I think t h e i r statistic is more credible and homogeneous o v e r t h e long term t h a n t h e statistics r e f e r r i n g to o t h e r crimes. The homicide c u r v e has a period of about 54 y e a r s , like energy, but i t is out of phase. In f a c t , t h e maximum of homicides is in t h e middle of recession and t h e minimum in t h e middle of t h e boom. The r a t i o between maximum and minimum is a n incredible factor of two.

The second still moodier side of t h e s t o r y is r e p o r t e d in t h e t h i r d c u r v e down, telling t h e r a t i o of guns to knives in t h e execution of t h e homicide. A l s o this oscil- lates with a period of about 55 y e a r s , and with a r a t i o between maximum and minimum of a factor of t h r e e ! The curious point is t h a t during t h e boom period, people tend to shoot, and during recession tend to s t a b . Also t h e r a t i o of female to male murdered h a s similar long-term pulsations. Analogous considerations could b e done f o r t h e analysis of suicides, which I consider a special form of homicide.

In this c a s e , t h e most striking f e a t u r e is t h e 26-year s h a r p pulsation of t h e r a t i o female to male suicides.

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This zooming up and down inside o u r society shows a n unexpected level of self-control and a v e r y self-consistent behavior. This leads t o predictable behavior of numerous intermediate s t r u c t u r e s , from man t o humanity.

How to exploit t h e s e f e a t u r e s is just a question of imagination. Predicting when a c e r t a i n criminal, specialized in a c e r t a i n type of crime, i s "ripe" f o r a n operation, can help p r e p a r i n g t h e a p p r o p r i a t e reception. O r , a f t e r t h e fact, t o r e s t r i c t t h e r o s e of t h e possible actors.

To see i n s i d e the clockwork of a criminal band o r t e r r o r i s t i c o r g a n i z a t i o n m a y greatly help i n s e t t i n g u p a tuned s t r a t e g y . To have a way to calculate t h e n a t u r a l deployment of criminal activity can s e r v e to measure rapidly t h e e f f e c t s of initiatives against criminality. S o often in t h e past t h e e f f e c t of t h e s e initiatives could be assessed only a f t e r t e n s of years.

In a nutshell, I hope this may contribute to improve t h e rational control of t h e system.

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References

Marchetti, C. (1980) Society as A Learning System: Discovery, Invention, and Innovation Cycles Revisited. Technological Forecasting a n d Social Change I8:267-282.

Marchetti, C. (1983) On a Fifty Year Pulsation in Human Affairs: Analysis of Some Physical Indicators. 'PP-83-5. Lwenburg, Austria: International Institute f o r Applied Systems Analysis.

Marchetti, C. (1983) The Automobile in a System Context: The P a s t 80 Y e a r s and t h e Next 20 Years. Technological Forecasting a n d Social Change 29:3-23.

Winfree, A.T. (1980) The Geometry of Biological Time. Berlin-Hamburg-New York:

S p r i n g e r Verlag.

Simonton, D.K. (1984) Genius, Creativity and Leadership. Cambridge, Mass. : Har- vard University P r e s s .

Marchetti, C. (1983) On t h e Role of Science in t h e Post-Industrial Society: 'Zogos

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The Empire Builders". Technological Forecasting a n d Social Change 24:197-206.

These rqferences a r e b a s i c a l l y l i m i t e d to m y connected w o r k . Literature on the application of Volterm-Lotka equations i s vast and easily retrievable. Two general r e f e r e n c e s can be t h e following:

Goll, N.S. et al. (1971) On t h e Volterm and Other Nonlinear Models of Interacting Populations. Rev. Mod.Physics 43(2):231.

Gatto, M. (1985) Introduzione all'ecologia delle popolazioni. Milano: CLUP.

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Appendix

The formal derivation of the equations used to fit t h e dynamics of competition is from t h e VoLtetta e q u a t i o n s , which basically say b i g f i s h c a t c h smaLL f i s h when t h e opportunity comes. There is a vast l i t e r a t u r e about Volterra-Lotka differen- tial equations, and t h e i r discussion will not be reported here. The basic growth equation ,which is used in most of the c h a r t s , is a special solution of the V o l t e r n - Lotka equations and is actually a logistic function of the type shown in Figure 1.

This equation can be written in the form

where N is t h e cumulative number of objects observed, e.g., number of crimes com- mitted by a certain person up to time t. The curve has a maximum (asymptotic) value

if.

I t is t h e upper line in Figure 1.

i

and t h e constants a and b have to be calculated by best fitting the available data in form of t h e value of N at various times. Most of t h e c h a r t s are normalized by using F

=

N/; s o measuring t h e process in relative terms.

Equation (1) then can be rewritten in t h e form log-

F =

at

+

b

.

1 -F

and a p p e a r s in t h e c h a r t s as a straight line. The transformation greatly facili- tates t h e graphic handling and use of t h e data.

The fitting is done by iteration, choosing

fi

arbitrarily, and then improving t h e fit by changing it. The physical meaning of a is t h a t of a r a t e , i.e., t h e speed at which t h e process occurs. In the c h a r t i t is given in t h e more intuitive form of a rate constant, i.e., t h e time f o r N to go from 102 to 902 of

3.

The constant b is merely a time cursor to position the process in calendar time.

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1

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The y e a r of maximum p r o c e s s speed is midway when

F =

1

- ^F

^{o r}^N=-N.₂ ^This

point is often marked in t h e c h a r t . The f i r s t d a t a points a r e sometimes below t h e equation line. I usually i n t e r p r e t this as a "catch up". The p e r s o n h a s t h e d r i v e but not t h e means, e.g., when h e is v e r y young. When t h e means come, then t h e time lost i s made good in a f a s t dash.

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WORLD PRIMARY ENERGY SUBSTITUTION

1900 1950

F i g u r e 5

2000 2050

N. Nakicenovic, I IASA, 1984

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F World-Primary Energy Substitution (Short Data)

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l-F Fraction F

0.99

0.90 0.70 0.50 0.30 0.10

0.01

F i g u r e s 6a, 6b, and 6c

0.99

-.

^0.90

-0.m ..o.~o

..oJ)

.- ^0.10

ld

-

Oil

G r 0.a

cod-

\

101

10"

10-1

.!

.r

wood

.:

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E

W

x I- 0 I-

3

a

5:

w

0 a

4 *-

a

2 C3

-

0:

2

W A

a

5

V) 0

F

o a

6 0 - 5

m m

"I- 0 a

m a

= a

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