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February 2015 Resource dependent branching processes and the envelope of societies
F. Thomas Bruss, Mitia Duerinckx
Ann. Appl. Probab. 25(1): 324-372 (February 2015). DOI: 10.1214/13-AAP998


Since its early beginnings, mankind has put to test many different society forms, and this fact raises a complex of interesting questions. The objective of this paper is to present a general population model which takes essential features of any society into account and which gives interesting answers on the basis of only two natural hypotheses. One is that societies want to survive, the second, that individuals in a society would, in general, like to increase their standard of living. We start by presenting a mathematical model, which may be seen as a particular type of a controlled branching process. All conditions of the model are justified and interpreted. After several preliminary results about societies in general we can show that two society forms should attract particular attention, both from a qualitative and a quantitative point of view. These are the so-called weakest-first society and the strongest-first society. In particular we prove then that these two societies stand out since they form an envelope of all possible societies in a sense we will make precise. This result (the envelopment theorem) is seen as significant because it is paralleled with precise survival criteria for the enveloping societies. Moreover, given that one of the “limiting” societies can be seen as an extreme form of communism, and the other one as being close to an extreme version of capitalism, we conclude that, remarkably, humanity is close to having already tested the limits.


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F. Thomas Bruss. Mitia Duerinckx. "Resource dependent branching processes and the envelope of societies." Ann. Appl. Probab. 25 (1) 324 - 372, February 2015.


Published: February 2015
First available in Project Euclid: 16 December 2014

zbMATH: 1308.60103
MathSciNet: MR3297775
Digital Object Identifier: 10.1214/13-AAP998

Primary: 60J05 , 69J85
Secondary: 60G40

Keywords: almost-sure convergence , Borel–Cantelli lemma , capitalism , communism , complete convergence , Controlled branching processes , extinction criteria , Galton–Watson processes , laissez-faire society , Lorenz curve , mercantilism , order statistics , society structures , stopping times

Rights: Copyright © 2015 Institute of Mathematical Statistics


Vol.25 • No. 1 • February 2015
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