Skip to main content
SpringerLink
Log in

Model-Based Demography: Towards a Research Agenda

  • Chapter
  • First Online:
Agent-Based Modelling in Population Studies

Part of the book series: The Springer Series on Demographic Methods and Population Analysis ((PSDE,volume 41))

Abstract

This chapter aims to contribute to the debate on the role of model-based approaches, such as agent-based modelling, in the future of demography. First we call attention to the developments of the discipline since the seventeenth century, and we describe its four successive paradigms related to the period, cohort, event-history and multilevel perspectives. We argue that these paradigms are complementary and that demography, since its beginnings, has subscribed to the classical scientific research programme launched by the promoters of modern science. Next, we examine how simulation modelling developing in population sciences recently, may help to respond to three main challenges: how to overcome complexity in social research; how to reduce its uncertainty; and how to reinforce its theoretical foundations. We sketch a model-based research programme for demography, looking specifically at interactions between various population systems. We then show how this approach might conform to the classical scientific research programme, in order to take advantage of its benefits.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Citations in this and in the next paragraph come from Bacon (1620), aphorisms 24, 39 and 40.

  2. 2.

    Induction is not taken in the sense of Mill (1843) and his followers, i.e. generalisation from particular facts. In Bacon’s sense, induction designates the complete research process (Sect. 2.4).

  3. 3.

    These fields were not so clearly defined at this time: scientists were working in different social or biological sciences and in statistics simultaneously.

  4. 4.

    Similarly, acknowledgement of the role of space in demography has led to the multi-regional perspective within the cohort paradigm (Rogers 1975), later extended to the multi-state case.

  5. 5.

    See Epstein (2008) for “sixteen reasons other than prediction to build a model”. Conte et al. (2012) highlight the capability of “generative” models to reproduce qualitative regularities observed in the real world (the stylised facts).

  6. 6.

    Burch (2003b) points to Nathan Keyfitz (1971) as the pioneer of the model-based demography.

  7. 7.

    Following Huneman (2014), we give these terms slightly different meanings than for example Thagard (1993, p. 6), for whom the weak simulation is “a calculating device drawing out the consequences of mathematical equations that describe the process simulated,” while a strong simulation “itself resembles the process simulated” (see also Brenner and Werker 2007).

  8. 8.

    For a discussion of the ABM documentation standards, and the ODD framework (“Overview, Design concepts and Details”), see Grimm et al. (2006), as well as Chap. 9 in this volume.

  9. 9.

    The problem here is not the empirical basis of such models – quite the contrary – but unrealistic mechanisms. Particularly problematic are Markovian assumptions of the lack of memory, where simulations are based on homogenous matrices of transition probabilities. Examples of micro-simulation models that allow for heterogeneous transition patterns or mechanisms, e.g. of partnership formation, include SOCSIM (http://lab.demog.berkeley.edu/socsim/).

  10. 10.

    After Franck (2002a), we interpret validation as a continuous process, rather than an achievable state.

  11. 11.

    Reverse engineering denotes today diverse research practices varying with the areas of application. We refer to its initial sense.

  12. 12.

    Bacon’s induction is regularly confounded with induction by philosophers in its usual sense of generalisation. Bacon wrote: “In establishing axioms, another form of induction must be devised than has hitherto been employed, and it must be used for proving and discovering not first principles (as they are called) only, but also the lesser axioms, and the middle, and indeed all. For the induction which proceeds by simple enumeration is childish; its conclusions are precarious and exposed to peril from a contradictory instance; and it generally decides on too small a number of facts, and on those only which are at hand” (Bacon 1620; aphorism 105).

  13. 13.

    Formulating and testing hypotheses is not wrong, in our opinion, as long as it is based on empirical observations. However, throughout the present chapter we plead for abandoning the hypothetical-deductive approach and for substituting it with the classical induction.

  14. 14.

    The property itself may not be generalized, of course.

  15. 15.

    The principles are traditionally named theories; this tradition goes back to Plato’s theoria, and reserves to the term theory the restricted sense of a corpus of principles. This is far from its present use describing as a ‘theory’ every sort of conceptual hypothesis, or model, or explanatory ‘mechanism’.

  16. 16.

    See for example the following definition of demography (IUSSP 1982): “the scientific study of human populations primarily with respect to their size, their structure and their development; it takes into account the quantitative aspects of their general characteristics”.

  17. 17.

    Plato, who was familiar with the concept of number developed by the Pythagoreans, developed at length the idea that measuring is judging, and that we ought to recourse to measures in order to act wisely in politics as well as in private life (see Bassu 2009, 2011).

References

  • Aalen, O. O. (1975). Statistical inference for a family of counting processes. PhD thesis, University of California, Berkeley.

    Google Scholar 

  • Ahlburg, D. A. (1995). Simple versus complex models: Evaluation, accuracy and combining. Mathematical Population Studies, 5(3), 281–290.

    Article  Google Scholar 

  • Alho, J. M., & Spencer, B. D. (2005). Statistical demography and forecasting. Berlin/Heidelberg: Springer.

    Google Scholar 

  • Alkema, L., Raftery, A. E., & Clark, S. J. (2007). Probabilistic projections of HIV prevalence using Bayesian melding. Annals of Applied Statistics, 1(1), 229–248.

    Article  Google Scholar 

  • Aparicio Diaz, B., Fent, T., Prskawetz, A., & Bernardi, L. (2011). Transition to parenthood: The role of social interaction and endogenous networks. Demography, 48(2), 559–579.

    Article  Google Scholar 

  • Axtell, R., Epstein, J., Dean, J., Gumerman, G., Swedlund, A., Harburger, J., Chakravarty, S., Hammond, R., Parker, J., & Parker, M. (2002). Population growth and collapse in a multiagent model of the Kayenta Anasazi in Long House Valley. Proceedings of the National Academy of Sciences of the United States of America, 99(suppl. 3), 7275–7279.

    Article  Google Scholar 

  • Bacon, F. (1620). Novum Organum. London: J. Bill. English translation: Spedding, J., Ellis, R. L., & Heath, D. D. (1863). The works (Vol. VIII). Boston: Taggard and Thompson.

    Google Scholar 

  • Bassu, S. (2009). Metretique, éthique et politique: le Protagoras et le Politique de Platon. Dissertatio, 29, 85–114.

    Google Scholar 

  • Bassu, S. (2011). Ordre et mesure, kosmos et metron de la pensée archaïque à la philosophie platonicienne. In S. Alexandre & E. Rogan (Eds.), Actes du colloque “Ordres et désordres”, Université Paris 1 and Université Paris Ouest, Nanterre-La Défense, 4–5 June 2010. Available via: Zetesis, vol. 2 [Online], https://f.hypotheses.org/wp-content/blogs.dir/3211/files/2015/04/2Bassu.pdf.

  • Bayes, T. R. (1763). An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society of London, 53, 370–418.

    Article  Google Scholar 

  • Bijak, J. (2010). Forecasting international migration in Europe: A Bayesian view (Springer Series on Demographic Methods and Population Analysis, Vol. 24). Dordrecht: Springer.

    Google Scholar 

  • Bijak, J., & Bryant, J. (2016). Bayesian demography 250 years after Bayes. Population Studies, 70(1), 1–19.

    Article  Google Scholar 

  • Bijak, J., Hilton, J., Silverman, E., & Cao, V. (2013). Reforging the wedding ring: Exploring a semi-artificial model of population for the United Kingdom with Gaussian process emulators. Demographic Research, 29(27), 729–766.

    Article  Google Scholar 

  • Billari, F., & Prskawetz, A. (Eds.). (2003). Agent-based computational demography. Using simulation to improve our understanding of demographic behaviour. New York: Physica-Verlag.

    Google Scholar 

  • Blayo, C. (1995). La condition d’homogeneite en analyse demographique et en analyse statistique des biographies. Population, 50(6), 1501–1518.

    Article  Google Scholar 

  • Boudon, R. (1977). Effet pervers et ordre social. Paris: Presses Universitaires de France.

    Google Scholar 

  • Brenner, T., & Werker, C. (2007). A taxonomy of inference in simulation models. Computational Economics, 30(3), 227–244.

    Article  Google Scholar 

  • Bullock, S., & Silverman, E. (2008). Levins and the legitimacy of artificial worlds. A Cross-Disciplinary Workshop “Epistemological Perspectives on Simulation”, Lisbon, 2–3 October 2008.

    Google Scholar 

  • Burch, T. (2003a). Data, models, theory and reality: The structure of demographic knowledge. In F. Billari & A. Prskawetz (Eds.), Agent-based computational demography. Using simulation to improve our understanding of demographic behaviour (pp. 19–40). Heidelberg/New York: Physica-Verlag.

    Chapter  Google Scholar 

  • Burch, T. (2003b). Demography in a new key: A theory of population theory. Demographic Research, 9(11), 263–284.

    Article  Google Scholar 

  • Casini, L., Illari, P. M., Russo, F., & Williamson, J. (2011). Models for prediction, explanation and control: Recursive Bayesian networks. Theoria, 26(1), 5–33.

    Google Scholar 

  • Charbit, Y., & Petit, V. (2011). Towards a comprehensive demography: Rethinking the research agenda on change and response. Population and Development Review, 37(2), 219–239.

    Article  Google Scholar 

  • Chattoe, E. (2003). The role of agent-based models in demographic explanation. In F. Billari & A. Prskawetz (Eds.), Agent-based computational demography. Using simulation to improve our understanding of demographic behaviour (pp. 41–54). Heidelberg/New York: Physica-Verlag.

    Chapter  Google Scholar 

  • Clark, S. J., Thomas, J. R., & Bao, L. (2012). Estimates of age-specific reductions in HIV prevalence in Uganda: Bayesian melding estimation and probabilistic population forecast with an HIV-enabled cohort component projection model. Demographic Research, 27(26), 743–774.

    Article  Google Scholar 

  • Conte, R., Gilbert, N., Bonelli, G., Cioffi-Revilla, C., Deffuant, G., Kertesz, Loreto, V., Moat, S., Nadal, J.-P., Sanchez, A., Nowak, A., Flache, A., San Miguel, M., & Helbing, D. (2012). Manifesto of computational social science. European Physical Journal Special Topics, 214(1), 325–346.

    Article  Google Scholar 

  • Courgeau, D. (2007). Multilevel synthesis. From the group to the individual. Dordrecht: Springer.

    Google Scholar 

  • Courgeau, D. (2012). Probability and social science. Methodological relationships between the two approaches (Methodos Series 10). Dordrecht: Springer.

    Google Scholar 

  • Courgeau, D. (2013). La mesure dans les sciences de la population. Cahiers Philosophiques, 135(4), 51–74.

    Article  Google Scholar 

  • Courgeau, D., & Franck, R. (2007). Demography, a fully formed science or a science in the making? An outline programme, Population-E, 62 (1), pp. 39–45. (La démographie, science constituée ou en voie de constitution? Esquisse d’un programme. Population, 62(1), 39–45).

    Google Scholar 

  • Courgeau, D., & Lelièvre, E. (1992). Event history analysis in demography. Oxford: Clarendon.

    Google Scholar 

  • Courgeau, D., Bijak, J., Franck, R., & Silverman, E. (2014). Are the four Baconian Idols still alive in demography? Revue Quetelet/Quetelet Journal, 2(2), 31–59.

    Article  Google Scholar 

  • Di Paolo, E. A., Noble, J., & Bullock, S. (2000). Simulation models as opaque thought experiments. In M. Bedau, J. McCaskill, N. Packard, & S. Rasmussen (Eds.), Proceedings of the 7th international conference on artificial life (pp. 497–506). Cambridge, MA: MIT Press.

    Google Scholar 

  • Doob, J. L. (1953). Stochastic processes. New York/Chichester: Wiley.

    Google Scholar 

  • Ducheyne, S. (2005). Bacon’s idea and Newton’s practice of induction. Philosophica, 76, 115–128.

    Google Scholar 

  • Durkheim, E. (1897). Le suicide. Paris: Alcan.

    Google Scholar 

  • Epstein, J. M. (2008). Why model? Journal of Artificial Societies and Social Simulation, 11(4), article 12. http://jasss.soc.surrey.ac.uk/11/4/12.html.

  • Franck, R. (Ed.). (2002a). The explanatory power of models. Bridging the gap between empirical and theoretical research in the social sciences (Methodos series, Vol. 1). Boston/Dordrecht/London: Kluwer Academic Publishers.

    Google Scholar 

  • Franck, R. (2002b). Computer simulation and the reverse engineering method. Conclusions of part II. In R. Franck (Ed.), The explanatory power of models (Methodos series, Vol. 1, pp. 141–146). Dordrecht/Boston/London: Kluwer Academic Publishers.

    Chapter  Google Scholar 

  • Geard, N., McCaw, J. M., Dorin, A., Korb, K. B., & McVernon, J. (2013). Synthetic population dynamics: A model of household demography. Journal of Artificial Societies and Social Simulation, 16(1), article 8. http://jasss.soc.surrey.ac.uk/16/1/8.html.

  • Godfrey-Smith, P. (2006). The strategy of model-based science. Biology and Philosophy, 21(5), 725–740.

    Article  Google Scholar 

  • Goldstein, H. (1987). Multilevel models in educational and social research. London: Arnold.

    Google Scholar 

  • Graunt, J. (1662). Natural and political observations mentioned in a following index, and made upon the bills of mortality. London: Tho. Roycroft.

    Google Scholar 

  • Grimm, V., Berger, U., Bastiansen, F., Eliassen, S., Ginot, V., Giske, J., Goss-Custard, J., Grand, T., Heinz, S., Huse, G., Huth, A., Jepsen, J. U., Jørgensen, C., Mooij, W. M., Müller, B., Pe’er, G., Piou, C., Railsback, S. F., Robbins, A. M., Robbins, M. M., Rossmanith, E., Rüger, N., Strand, E., Souissi, S., Stillman, R. A., Vabø, R., Visser, U., & DeAngelis, D. L. (2006). A standard protocol for describing individual-based and agent-based models. Ecological Modelling, 198(1–2), 115–126.

    Google Scholar 

  • Henry, L. (1959). D’un problème fondamental de l’analyse démographique. Population, 14(1), 9–32.

    Article  Google Scholar 

  • Hirschman, C. (2008). The future of demography. Asian Population Studies, 4(3), 233–234.

    Article  Google Scholar 

  • Holland, J. H. (1995). Hidden order. Reading: Addison-Wesley.

    Google Scholar 

  • Huneman, P. (2014). Mapping an expanding territory: Computer simulations in evolutionary biology. History and Philosophy of the Life Sciences, 36(1), 60–89.

    Article  Google Scholar 

  • Huyghens, C. (1657). De ratiociniis in ludo aleae. Leyde: Elzevier.

    Google Scholar 

  • Ibrahim, J. G., Chen, M.-H., & Sinha, D. (2001). Bayesian survival analysis. New York: Springer.

    Book  Google Scholar 

  • IUSSP [International Union for the Scientific Study of the Populations]. (1982). Multilingual demographic dictionary (2nd ed.). Liège: Ordina.

    Google Scholar 

  • Kennedy, M., & O’Hagan, T. (2001). Bayesian calibration of computer models. Journal of the Royal Statistical Society, Series B, 63(3), 425–464.

    Article  Google Scholar 

  • Keyfitz, N. (1971). Models. Demography, 8(4), 571–580.

    Article  Google Scholar 

  • Klüver, J., Stoica, C., & Schmidt, J. (2003). Formal models, social theory and computer simulations: Some methodical reflections. Journal of Artificial Societies and Social Simulation, 6(2), article 8, http://jasss.soc.surrey.ac.uk/6/2/8.html.

  • Kniveton, D., Smith, C., & Wood, S. (2011). Agent-based model simulations of future changes in migration flows for Burkina Faso. Global Environmental Change, 21(Suppl. 1), S34–S40.

    Article  Google Scholar 

  • Kuhn, T. (1962). The structure of scientific revolutions. Chicago/London: The University of Chicago Press.

    Google Scholar 

  • Laplace, P. S. (1774). Mémoire sur la probabilité des causes par les événements. Mémoires de l’Académie Royale des Sciences de Paris, Tome, VI, 621–656.

    Google Scholar 

  • Laplace, P. S. (1812). Théorie analytique des Probabilités (Vol. 2). Paris: Courcier Imprimeur.

    Google Scholar 

  • Levins, R. (1966). The strategy of model building in population biology. American Scientist, 54(4), 421–431.

    Google Scholar 

  • Lutz, W. (2012). Demographic metabolism: A predictive theory of socio-economic change. Population and Development Review, 38(Supplement), 283–301.

    Google Scholar 

  • Mannheim, K. (1928). Das Problem der Generationen. Kölner Vierteljahreshefte für Soziologie, 7(2), 309–330.

    Google Scholar 

  • Mason, W. M., Wong, G. W., & Entwistle, B. (1983). Contextual analysis through the multilevel linear model. In S. Leinhart (Ed.), Sociological methodology 1983–1984 (pp. 72–103). San Francisco: Jossey-Bass.

    Google Scholar 

  • McCulloch, W. S., & Pitts, W. H. (1943). A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics, 5(4), 115–133.

    Article  Google Scholar 

  • Mill, J. S. (1843). A system of logic, ratiocinative and inductive: Being a connected view of the principles of evidence, and the methods of scientific investigation (Vol. I). London: Harrison.

    Google Scholar 

  • Morgan, S. P., & Lynch, S. M. (2001). Success and future of demography. The role of data and methods. Annals of the New York Academy of Sciences, 954, 35–51.

    Article  Google Scholar 

  • Moss, S., & Edmonds, B. (2005). Towards good social science. Journal of Artificial Societies and Social Simulation, 8(4), article 13. http://jasss.soc.surrey.ac.uk/8/4/13.html.

  • NRC [National Research Council]. (2000). Beyond six billion: Forecasting the world’s population. Washington, DC: National Academies Press.

    Google Scholar 

  • Oakley, J., & O’Hagan, A. (2002). Bayesian inference for the uncertainty distribution of computer model outputs. Biometrika, 89(4), 769–784.

    Article  Google Scholar 

  • Pascal, B. (1665). Traité du triangle arithmétique, avec quelques autres traités sur le même sujet. Paris: Guillaume Desprez.

    Google Scholar 

  • Petit, V., & Charbit, Y. (2012). The French school of demography: Contextualising demographic analysis. Population and Development Review, 38(supplement), 322–333.

    Google Scholar 

  • Petty, W. (1690). Political arithmetick. London: Robert Clavel & Hen. Mortlock.

    Google Scholar 

  • Polhill, J. G., Sutherland, L.-A., & Gotts, N. M. (2010). Using qualitative evidence to enhance an agent-based modelling system for studying land use change. Journal of Artificial Societies and Social Simulation, 13(2), art. 10. http://jasss.soc.surrey.ac.uk/13/2/10.html.

  • Poole, D., & Raftery, A. E. (2000). Inference for deterministic simulation models: The Bayesian melding approach. Journal of the American Statistical Association, 95(452), 1244–1255.

    Article  Google Scholar 

  • Raftery, A. E. (1995). Bayesian model selection in social research. Sociological Methodology, 25, 111–163.

    Article  Google Scholar 

  • Raftery, A. E., Li, N., Ševčíková, H., Gerland, P., & Heilig, G. K. (2012). Bayesian probabilistic population projections for all countries. Proceedings of the National Academy of Sciences, 109, 13915–13921.

    Article  Google Scholar 

  • Rogers, A. (1975). Introduction to multiregional mathematical demography. New York: Wiley.

    Google Scholar 

  • Ryder, N. B. (1951). The cohort approach. Essays in the measurement of temporal variations in demographic behaviour. PhD thesis, Princeton University, New York.

    Google Scholar 

  • Silverman, E., & Bryden, J. (2007). From artificial societies to new social science theory. In F. Almeida e Costa, L. M. Rocha, E. Costa, I. Harvey, & A. Coutinho (Eds.), Advances in artificial life, 9th European conference, ECAL 2007 proceedings (pp. 645–654). Berlin/Heidelberg: Springer.

    Google Scholar 

  • Silverman, E., Bijak, J., & Noble, J. (2011). Feeding the beast: Can computational demographic models free us from the tyranny of data? In T. Lenaerts, M. Giacobini, H. Bersini, P. Bourgine, M. Dorigo, & R. Doursat (Eds.), Advances in artificial life, ECAL 2011: Proceedings of the eleventh European conference on the synthesis and simulation of living systems (pp. 747–754). Cambridge, MA: MIT Press.

    Google Scholar 

  • Silverman, E., Bijak, J., Hilton, J., Cao, V., & Noble, J. (2013). When demography met social simulation: A tale of two modelling approaches. Journal of Artificial Societies and Social Simulation, 16(4), article 9. http://jasss.soc.surrey.ac.uk/16/4/9.html.

  • Smith, S. K. (1997). Further thoughts on simplicity and complexity in population projection models. International Journal of Forecasting, 13(4), 557–565.

    Article  Google Scholar 

  • Tabutin, D. (2007). Whither demography? Strengths and weaknesses of the discipline over fifty years of change. Followed by a debate on the future of the discipline, by G. Caselli & V. Egidi, D. Courgeau & R. Franck, J. Hobcraft, & J. Hoem. Population-E, 62(1), 13–56.

    Google Scholar 

  • Thagard, P. (1993). Computational philosophy of science. Cambridge, MA: MIT Press.

    Google Scholar 

  • Whelpton, P. (1949). Cohort analysis of fertility. American Sociological Review, 14(6), 735–749.

    Article  Google Scholar 

  • Willekens, F. (2005). Biographic forecasting: Bridging the micro-macro gap in population forecasting. New Zealand Population Review, 31(1), 77–124.

    Google Scholar 

  • Willekens, F. (2012). Migration: A perspective from complexity science. Paper for the Complexity Science for the Real World workshop on migration, Chilworth. 16 Feb 2012.

    Google Scholar 

  • Xie, Y. (2000). Demography: Past, present and future. Journal of the American Statistical Association, 95(450), 670–673.

    Article  Google Scholar 

Download references

Acknowledgments

JB and ES acknowledge the Engineering and Physical Sciences Research Council (EPSRC) grant EP/H021698/1 “Care Life Cycle”. We thank Frans Willekens and Anna Klabunde for discussions and to the two anonymous reviewers for helpful suggestions. All the views and interpretations are those of the authors and should not be attributed to any institution with which they are affiliated. All the errors remain exclusively ours.

Author information

Authors and Affiliations

  1. Institut national d’études démographiques, Paris, France

    Daniel Courgeau

  2. Department of Social Statistics and Demography, University of Southampton, Southampton, UK

    Jakub Bijak

  3. Université catholique de Louvain, Louvain-la-Neuve, Belgium

    Robert Franck

  4. School of Computing, Teesside University, Middlesbrough, UK

    Eric Silverman

Authors
  1. Daniel Courgeau
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jakub Bijak
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Robert Franck
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Eric Silverman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jakub Bijak .

Editor information

Editors and Affiliations

  1. Centre for Sociological Research, University of Leuven, Leuven, Belgium

    André Grow

  2. Centre for Sociological Research, University of Leuven, Leuven, Belgium

    Jan Van Bavel

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Courgeau, D., Bijak, J., Franck, R., Silverman, E. (2017). Model-Based Demography: Towards a Research Agenda. In: Grow, A., Van Bavel, J. (eds) Agent-Based Modelling in Population Studies. The Springer Series on Demographic Methods and Population Analysis, vol 41. Springer, Cham. https://doi.org/10.1007/978-3-319-32283-4_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-32283-4_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32281-0

  • Online ISBN: 978-3-319-32283-4

  • eBook Packages: Social SciencesSocial Sciences (R0)

Publish with us

Policies and ethics

Search

Navigation