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Journal ArticleDOI

Statistical physics of crime: A review

AbstractContaining the spreading of crime in urban societies remains a major challenge. Empirical evidence suggests that, left unchecked, crimes may be recurrent and proliferate. On the other hand, eradicating a culture of crime may be difficult, especially under extreme social circumstances that impair the creation of a shared sense of social responsibility. Although our understanding of the mechanisms that drive the emergence and diffusion of crime is still incomplete, recent research highlights applied mathematics and methods of statistical physics as valuable theoretical resources that may help us better understand criminal activity. We review different approaches aimed at modeling and improving our understanding of crime, focusing on the nucleation of crime hotspots using partial differential equations, self-exciting point process and agent-based modeling, adversarial evolutionary games, and the network science behind the formation of gangs and large-scale organized crime. We emphasize that statistical physics of crime can relevantly inform the design of successful crime prevention strategies, as well as improve the accuracy of expectations about how different policing interventions should impact malicious human activity deviating from social norms. We also outline possible directions for future research, related to the effects of social and coevolving networks and to the hierarchical growth of criminal structures due to self-organization.

Topics: Crime prevention (70%), Cultural criminology (64%), Organised crime (56%), Social responsibility (50%)

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Summary

  • This is particularly evident – even for microcriminality – in urban areas (in Europe and North America the percent of population living in urban areas is around 85%).
  • And the role of mathematical, statistical, and physical models has been steadily increasing.
  • Thus, the paper [6] appears to be extremely timely and useful.
  • Generally speaking, models are often more descriptive than predictive, in the sense that it is not expected that they predict e.g. the number of burglaries or car thefts that will occur in a given district over a given period of time.
  • Nevertheless, they can be instrumental in describing the mechanisms by which it can be foreseen that a concentration of crimes can appear in particular zones (hot spots), or the “contagion” that criminal behaviour can have on particular classes of individuals.
  • This description can in turn suggest how to contrast the phenomena.
  • Therefore, modelling the diffusion of criminal (or simply unlawful) behaviour in urban areas can be a tool that administrations and police authorities can use in order to choose optimal strategies to combat crime.
  • And this is particularly important in a horizon of budget cuts that impose the best use of the existing resources, optimization of strategies, logistics etc.
  • Of course “for complex phenomena as criminality (in its various guises), the goal is not to represent the whole reality, let alone generate precise predictions.
  • The enhanced understanding of “stylized facts” that characterise a system of interest by isolating elements of a theoretical model can shed new light on the subject and contribute to new insights into the more complex global picture.
  • With the aid of such models, one can then investigate the various effects implied by factors such as the severity of punishment, duration of imprisonment, different deterrence strategies, or the allocation of limited crime reduction resources in the most efficient way” [4].

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Physics of Life Reviews 12 (2015) 34–35
www.elsevier.com/locate/plrev
Comment
The role of mathematical modelling in modern criminology
Comment
on “Statistical physics of crime: A review” by
M.R. D’Orsogna and M. Perc
Mario Primicerio
Dipartimento di Matematica “U. Dini”, Università di Firenze, Viale Morgagni 67/A, 50141 Firenze, Italy
Received 2
December 2014; accepted 3 December 2014
Available
online 5 December 2014
Communicated by L.
Peliti
Criminality is a big challenge at several different levels. This is particularly evident even for microcriminality
in urban areas (in Europe and North America the percent of population living in urban areas is around 85%). It is
considered by sociologists among the most important indexes affecting the (perception of the) quality of life in a gi
ven
place.
Starting from the seminal paper by G. Beck
er [3], the study of crime and criminality from the point of view of
economics has been developed in several directions. And the role of mathematical, statistical, and physical models
has been steadily increasing. Thus, the paper [6] appears to be extremely timely and useful.
Generally speaking, models are often more descriptive than pr
edictive, in the sense that it is not expected that
they predict e.g. the number of burglaries or car thefts that will occur in a given district over a given period of time.
Nevertheless, they can be instrumental in describing the mechanisms by which it can be foreseen that a concentration
of crimes can appear in particular zones (hot spots), or the “contagion” that criminal beha
viour can have on particular
classes of individuals. This description can in turn suggest how to contrast the phenomena.
Therefore, modelling the dif
fusion of criminal (or simply unlawful) behaviour in urban areas can be a tool that
administrations and police authorities can use in order to choose optimal strategies to combat crime. And this is par-
ticularly important in a horizon of budget cuts that impose the best use of the existing (scarce) resources, optimization
of strate
gies, logistics etc.
Another feature of the models is the fact that they allow to perform simulations to mimic the response of the system
to changes of parameters, of external inputs or constraints. Of course “for complex phenomena as criminality (in its
various guises), the goal is not to represent the whole reality, let alone generate precise predictions. However, the
enhanced understanding of “stylized facts” that characterise a system of inter
est by isolating elements of a theoretical
model can shed new light on the subject and contribute to new insights into the more complex global picture. With the
aid of such models, one can then investigate the various effects implied by factors such as the severity of punishment,
dur
ation of imprisonment, different deterrence strategies, or the allocation of limited crime reduction resources in the
most efficient way” [4].
DOI of original article: http://dx.doi.org/10.1016/j.plrev.2014.11.001.
E-mail
address: primicer@math.unifi.it.
http://dx.doi.org/10.1016/j.plrev.2014.12.001
1571-0645/© 2014
Elsevier B.V. All rights reserved.

M. Primicerio / Physics of Life Reviews 12 (2015) 34–35 35
The review by M.R. D’Orsogna and M. Perc [6] shows how rich is the panorama of the methods that can be of
help.
A special attention is devoted to agent-based models in which the time-varying attractiveness of a given target (for
instance in burglary) is modelled, biasing the movement of a burglar over a grid simulating the city; the consequent
probability of occurrence of crime is evaluated, thus influencing in turn the attractiveness of the target. Possible
mean-field approximations are discussed, leading to models based on population dynamics and on reaction–dif
fusion
equations. Perhaps, from this point of view, the bibliography of the review could be successfully complemented with
the one that can be found in the paper by M. Gordon [7] and by the papers published in a special issue of EJAM [11]
in 2010.
Among the agent-based models, one could also include the methods based on cellular automata that can take into
account the influence that “neighbours” can have in the diffusion of unlawful behaviour (e.g. tax evasion), see for
instance [9].
Another important class of models is based on “space–time point processes”. These are particularly rele
vant to
the crimes that appear to be clustered in time and space, so that a methodology similar to that applied in studying
earthquake swarms and clusters can be used. This is a typical example in which a technique that has pro
ved efficient
in a context that is far from sociology and criminology appears to be successful not only in describing the occurrence
of an offence, but also, in some cases, to locate the home base of criminals.
It is well-kno
wn, and properly outlined in the paper, that evolutionary game theory has proved to be apt to model
some basic phenomena connected with crime and criminology, including the role of social control in discouraging
criminality: the category of “informants” plays a major role in the desirable transition from a criminal-controlled
society to an almost crime-free situation. And this is clearly described by an e
volutionary game with four possible
strategies (criminal, informants, guards, and “blinds”). Inspection games are another category of techniques that are
used in this context, although some counter-intuitive results could be obtained (see e.g. [1]).
An emer
ging line of investigation is also reviewed by the paper, with several hints of possible new areas of research:
the development of networks of criminality. The increasing interconnectivity of our societies suggests that, besides of
the classical cases of geographically localized networks such as street gangs, one could have to deal with or
ganized
criminal networks [8] that have a worldwide domain of action (drug dealers, money laundering [2,10] etc.); but another
topic that deserves further investigation concerns the way criminal or unlawful behaviour can proliferate just because
of the existence of social networks [5].
A final remark on the paper: the bibliograph
y is so rich that it would have been desirable that the references are
ordered by the alphabetical order of the first author, or by the date of publication.
References
[1] Andreozzi L. Rewarding policemen increases crime. Some more surprising results from the inspection game. Public Choice 2004;121:69–82.
[2] Araujo
RA. An evolutionary game theory approach to combat money laundering. J Money Laund Control 2010;13:70–8.
[3] Beck
er G. Crime and punishment: an economic approach. J Polit Econ 1968;76:169–217.
[4] Berestycki
H, Johnson SD, Ockendon JR, Primicerio M. Foreword to the special issue of EJAM on crime modelling. Eur J Appl Math
2010;21:271–4.
[5] Calvò-Armengol
A, Zenou Y. Social networks and crime decisions: the role of social structure in facilitating delinquent behaviour. Int Econ
Rev 2004;45:939–58.
[6] D’Orsogna
MR, Perc M. Statistical physics of crime: a review. Phys Life Rev 2015;12:1–21 [in this issue].
[7] Gordon
MB. A random walk in the literature on criminality: a partial and critical view on some statistical analysis and modeling approaches.
Eur J Appl Math 2010;21:283–306.
[8] McIll
wain JS. Organized crime: a social network approach. Crime Law Soc Change 1999;32:301–23.
[9] Meacci
L, Nuno JC, Primicerio M. Fighting tax evasion: a cellular automata approach. Adv Math Sci Appl 2012;22:597–610.
[10] Wa
lker J, Unger B. The Walker gravity model. Int Rev Law Econ 2009;5:821–53.
[11] http://journals.cambridge.or
g/action/displayIssue?jid=EJM&volumeId=21&seriesId=0&issueId=4-5.
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Starting from the seminal paper by G. Becker [ 3 ], the study of crime and criminality from the point of view of economics has been developed in several directions. Thus, the paper [ 6 ] appears to be extremely timely and useful. Therefore, modelling the diffusion of criminal ( or simply unlawful ) behaviour in urban areas can be a tool that administrations and police authorities can use in order to choose optimal strategies to combat crime. This description can in turn suggest how to contrast the phenomena.