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Modelling the individual and collective dynamics of the propensity to offend

Published online by Cambridge University Press:  23 June 2010

J.-P. NADAL ,
M. B. GORDON ,
J. R. IGLESIAS  and
V. SEMESHENKO
J.-P. NADAL
Affiliation:
Centre d'Analyse et de Mathématique Sociales (CAMS, UMR 8557 CNRS - EHESS), Ecole des Hautes Etudes en Sciences Sociales, 54 Bd. Raspail, 75270 Paris Cedex 06, France email: jean-pierre.nadal@ehess.fr Laboratoire de Physique Statistique (LPS, UMR 8550 CNRS, ENS, UPMC Univ. Paris 6, Paris Diderot Paris 7), Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France
M. B. GORDON
Affiliation:
Laboratoire TIMC-IMAG (UMR 5525), Université de Grenoble I, Domaine de La Merci, Jean Roget 38706 La Tronche, France
J. R. IGLESIAS
Affiliation:
Instituto de Física, Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre, Brazil
V. SEMESHENKO
Affiliation:
Departamento de Economía, Facultad de Ciencias Económicas, Universidad de Buenos Aires, Av. Córdoba 2122, 1120 AAQ Buenos Aires, Argentina
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Abstract

We introduce a general framework for modelling the dynamics of the propensity to offend in a population of (possibly interacting) agents. We consider that each agent has an ‘honesty index’ which parameterizes his probability of abiding by the law. This probability also depends on a composite parameter associated to the attractiveness of the crime outcome and of the crime setting (the context which makes a crime more or less likely to occur, such as the presence or not of a guardian). Within this framework we explore some consequences of the working hypothesis that punishment has a deterrent effect, assuming that, after a criminal act, an agent's honesty index may increase if he is caught and decrease otherwise. We provide both analytical and numerical results. We show that in the space of parameters characterizing the probability of punishment, there are two ‘phases’: one corresponding to a population with a low crime rate and the other to a population with a large crime rate. We speculate on the possible existence of a self-organized state in which, due to the society reaction against crime activities, the population dynamics would be stabilized on the critical line, leading to a wide distribution of propensities to offend in the population. In view of empirical works on the causes of the recent evolution of crime rates in developed countries, we discuss how changes of socio-economic conditions may affect the model parameters, and hence the crime rate in the population. We suggest possible extensions of the model that will allow us to take into account more realistic features.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 21 , Issue 4-5: Criminality , October 2010 , pp. 421 - 440
Copyright
Copyright © Cambridge University Press 2010

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