Analytical Expression of the Expected Values of Capital at Voting in the Stochastic Environment

Details Analytical Expression of the Expected Values of Capital at Voting in the Stochastic Environment Analytical Expression of the Expected Values of Capital at Voting in the Stochastic Environment

2009-02-26

arxiv.org/abs/0902.4514v2

Automation and Remote Control, 2006, Vol. 67, No. 2, pp. 480-492. Original Russian text published in Avtomatika i Telemekhanik

Mathematics

Optimization and Control

13 pages, 5 figures, translated from Russian by M.A. Kasner

Scientific paper

10.1134/S000511790603012X

In the simplest version of the model of group decision making in the stochastic environment, the participants are segregated into egoists and a group of collectivists. A "proposal of the environment" is a stochastically generated vector of algebraic increments of participants' capitals. The social dynamics is determined by the sequence of proposals accepted by a majority voting (with a threshold) of the participants. In this paper, we obtain analytical expressions for the expected values of capitals for all the participants, including collectivists and egoists. In addition, distinctions between some principles of group voting are discussed.

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