Voting Originated Social Dynamics: Quartile Analysis of Stochastic Environment Peculiarities
- PDF / 1,601,689 Bytes
- 19 Pages / 612 x 792 pts (letter) Page_size
- 26 Downloads / 156 Views
TIMIZATION, SYSTEM ANALYSIS, AND OPERATIONS RESEARCH
Voting Originated Social Dynamics: Quartile Analysis of Stochastic Environment Peculiarities V. M. Maksimov∗,a and P. Yu. Chebotarev∗∗,b ∗
∗∗
Moscow Institute of Physics and Technology, Dolgoprudny, Russia Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia e-mail: a [email protected], b [email protected] Received December 16, 2019 Revised April 29, 2020 Accepted May 25, 2020
Abstract—The model of voting originated social dynamics in a stochastic environment (the ViSE model) is considered. Within this model, the influence of the heaviness of distribution tails on the effectiveness of egoistic and altruistic strategies in terms of maximizing two criteria, the average capital increment and the number of non-bankrupt participants, is investigated. Homogeneous societies and four types of distributions used to generate proposals (Gaussian, logistic, Student’s with 3 degrees of freedom, and symmetrized Pareto distributions) are studied. To assess the effect of tail heaviness, all distributions are unified by quartile using scatter. Such an approach can be used to compare the heavy-tailed distributions that are commensurable by density with other distributions under consideration on an interval containing 90% of observations. Keywords: ViSE model, social dynamics, dynamic voting, stochastic environment, pit of losses, egoism, altruism, heavy-tailed distributions DOI: 10.1134/S0005117920100069
1. INTRODUCTION The main assumptions of the ViSE (Voting in Stochastic Environment) model, suggested for analyzing the utility of collective decisions, are as follows [1, 2]. Society initially consists of n participants (also called agents). Each participant is characterized by the current value of his capital (debt, if negative), or utility. The vector of nonnegative initial capitals of all participants is given. In each step m = 1, . . . , M, a proposal is put to the vote, and the participants vote, guided by certain strategies, for or against it. A proposal is the vector of algebraic capital increments of all participants. The proposals approved through an adopted voting procedure are implemented. One of the variants of the model assumes the elimination of the bankrupt participants, i.e., the participants whose capital has become negative (the extinction mode). The dynamics of the participants’ capital can be analyzed to compare voting strategies and collective decision procedures, in order to choose the optimal ones among them in terms of maximizing an appropriate criterion. By assumption, each proposal is generated in a stochastic way: its components are the realizations of random variables, in the simplest case, independent and identically distributed, with a given mean μ and a given standard deviation σ. Therefore, the proposals put to the vote can also be called the proposals of a stochastic environment, or the proposals of the environment. This environment is favorable if μ > 0; neutral if μ = 0; and unfavorable if μ < 0. Let
Data Loading...
