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The Theorem of the envelopment of societies for resource-dependent populations , also named Bruss-Duerinckx theorem, is a mathematical result on the behavior of populations which choose their society form according to only two hypotheses, namely those which are seen as most "natural": * Hypothesis 1 (H1): Individuals want to survive and see a future for their descendants, * Hypothesis 2 (H2): The average individual prefers a higher standard of living to a lower one, where H1 is supposed to precede H2 in the case of incompatibility of H1 with H2. Here populations with a society structure are modeled by so-called resource-dependent branching processes (RDBPs). The objective of RDBPs is to model different society structures and to compare the advantages and disadvantages of different societies, with the focus being on human societies. A RDBP is a discrete time branching process (BP) in which individuals are supposed to have to work in order to be able to live and to reproduce. The population decides on a current society form by a policy, that is a prescription of rules how available resources are to be distributed among the individuals. Policies may change over the generations by the interaction of individuals. ==Adapting the model to reality== To model a human society, a RDBP incorporates apart from an initial state (number of ancestors at time 0) individual demands for resources (standard of living), creation (production) of new resources for the next generation (including non-consumption and heritage of resources), a policy to distribute resources, and a control option for individuals interacting with the society. For simplicity the reproduction in a RDBP is modeled as being asexual, but the option to replace the mean reproduction rate by the so-called ''average reproduction rate'' of mating units (see Galton-Watson processes and ref. 1984) allows to show that the main results given below are not affected by this simplification. Formally, a RDBP is a stochastic process defined on the non-negative integers which is a BP defined by * an initial state ; * a law of reproduction of individuals (asexual); * a law of individual creation of resources; * a law of individual resource demands (claims); * a policy to distribute available resources to individuals which are present in the population * a tool of interaction between individuals and the society. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Bruss–Duerinckx theorem」の詳細全文を読む スポンサード リンク
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