Modélisation de phénomènes collectifs Jean-Pierre...

Modélisation de phénomènes collectifs

Master Humanités Numériques et ComputationnellesApproches quantitatives et modélisation mathématique en SHS

http://www.lps.ens.fr/~nadal/Cours/HN

Jean-Pierre Nadaljpnadal@ehess.fr

Centre d’Analyse et de Mathématique Sociales

&

Laboratoire de Physique de l’ENS

Contagion, diffusion

Different approaches

2

I. Threshold modelsChoice under social influence:« positive externalities »« bandwagon property »« strategic complementarity »« mimetism »

Willingness to join/adopt higherif others do the same

agent i adopts/joins if:

idiosynchratic willingness to adopt+ an amount which increases with the number of ‘neighbours’ who are

adopting> Cost

‘neighbours’: social network: friends, colleagues,…

T. C. Schelling« Micromotives and Macrobehavior » (Norton & Cy, 1978)traduction française : « La tyrannie des petites décisions » (PUF, 1980)

Model : « The dying seminar »

M. GranovetterThreshold models of collective behavior, American Journal of Sociology, vol. 83, no. 6, pp. 1360–1380, 1978

Same model, context of riot contagion

J.-P. Nadal et M. B. GordonPhysique statistique de phénomènes collectifs en sciences économiques et sociales, in Mathématiques et Sciences Humaines, n. 172, 2005

http://journals.openedition.org/msh/2969

To join or not to join a riot,to adopt or not to adopt a given behavior…

II. Event history approachEconometric analysis

example: Diffusion of innovation

Goal:finding correlations betweenthe adoption of an innovation at a given time and given place,and the adoptions at previous times at other locations, taking into account some characteristics of these events.

J. M. Box-Steffensmeier, B. S. Jones, Event History Modeling: A Guide for Social Scientists, Cambridge University Press, 2004

D. Courgeau & E. Lelievre , The Event History Approach in Demography, Population: An English Selection Vol. 3 (1991), pp. 63-79 https://www.jstor.org/stable/2949132?seq=1#page_scan_tab_contents

D. J. Myers, Racial rioting in the 1960s: An event history analysis of local conditions. Am. Sociol. Rev., 1997 http://users.cla.umn.edu/~uggen/myers_asr_97.pdf

See also literature on: « survival analysis », Cox model.

III. Epidemiological modellingDynamics of sales of new productsF. M. Bass, A New Product Growth for Model Consumer Durables, ManagagementScience, Vol. 15(5), 1969reprinted in Vol. 50(12), 2004, as one of the « 10 most influential titles of this journal » (seealso Comments by F M Bass in this issue).

Diffusion of first namesB. Coulmont, V. Supervie and R. Breban, The diffusion dynamics of choice: From durable goods markets to fashion first names, Complexity, 2016 https://doi.org/10.1002/cplx.21748

Riot contagionS. L. Burbeck, W. J. Raine, and M. A. Stark, The dynamics of riot growth: Anepidemiological approach,Journal of Mathematical Sociology, vol. 6, no. 1, pp. 1–22, 1978

L. Bonnasse-Gahot et al, Epidemiological modeling of the 2005 French riots: aspreading wave and the role of contagion,Scientific Reports, 2018 https://doi.org/10.1038/s41598-017-18093-4

Epidemiological modelling

Diffusion of new goods

F. M. Bass: Dynamics of sales of durable goods (Manag. Sci., 1969)

N = number of sales

p = innovation coefficient(likelihood that someone will start using the product because of media coverage)

q = imitation coefficient(likelihood that someone will start using the product because of word-of-mouth)

K = market size (carrying capacity)

Fashion goods - Social diffusion

Diffusion of first names

G. Desplanques, Les enfants de Michel et Martine Dupont s'appellent Nicolas etCéline, Economie et statistiques, 1986http://www.persee.fr/doc/estat_0336-1454_1986_num_184_1_2421

S. Lieberson & E. O. Bell, Children's First Names: An Empirical Study of Social Taste,American Journal of Sociology, 1992https://www.jstor.org/stable/2781457?seq=1#page_scan_tab_contents

B. Coulmont, V. Supervie and R. Breban, The diffusion dynamics of choice: Fromdurable goods markets to fashion first names, Complexity, 2016.https://doi.org/10.1002/cplx.21748

Fashion first names

INSEEClassement des prénoms en France depuis 1900https://www.insee.fr/fr/statistiques/3532172

Fashion first namesB. Coulmont, V. Supervie and R. Breban, 2016.

Recall the Bass model:

with here:

N = number of individuals with the considered first name

p = innovation coefficient(likelihood that someone will make the choice because of media coverage)p = 0 in the case of first names.

q = imitation coefficient

K = maximum number of bearers (carrying capacity)

𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑

= 𝑞𝑞𝑞𝑞(1 − 𝑑𝑑𝐾𝐾

) ‘logistic model’

Fashion first namesB. Coulmont, V. Supervie and R. Breban, 2016.

𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑

= 𝑞𝑞𝑞𝑞( 1 − 𝑑𝑑𝐾𝐾

) logistic model

simplest epidemiological model:

‘micro’ justification: « behavioral game », choice of a fashion name vs any other nameAt a given time: undecided, or choice already made

‘ chicken game’: cost for having chosen the same name

random binary interactions

Adoption of a fashion name with a probability proportional to the relative advantageof choosing a fashion name over a non-fashion name per consulted individual

(adopters of the fashion first name)

Fashion first namesB. Coulmont, V. Supervie and R. Breban, 2016.𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑

= 𝑞𝑞𝑞𝑞 (1 − 𝑑𝑑𝐾𝐾

) logistic model

Data: French, Dutch and US nationwide databases

American names:Diane (black)Seymour (red)

French names: Philippe (black) Francisco (red)

Dutch names: Ingrid (black) Moniek (red)

Fashion first namesB. Coulmont, V. Supervie and R. Breban, 2016.

𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑

= 𝑞𝑞𝑞𝑞 (1 − 𝑑𝑑𝐾𝐾

) logistic model

Riot contagion

English Hunger riots, 1766, 1801

Riot contagion

English Hunger riots, 1766

Riot contagion

S. L. Burbeck, W. J. Raine, and M. A. Stark,“The dynamics of riot growth: An epidemiological approach,”Journal of Mathematical Sociology, vol. 6, no. 1, pp. 1–22, 1978

Riot contagionS. L. Burbeck, W. J. Raine, and M. A. Stark,“The dynamics of riot growth: An epidemiological approach”Journal of Mathematical Sociology Vol. 6, no. 1, pp. 1–22, 1978

Riot contagionL. Bonnasse-Gahot et al, Epidemiological modeling of the 2005 French riots: aspreading wave and the role of contagion, Scientific Reports, 2018

See specific file.

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