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

TL;DR

This paper derives analytical formulas for the expected capital values of individuals in a stochastic group decision-making model involving egoists and collectivists, considering different voting principles.

Contribution

It provides the first explicit analytical expressions for expected capitals in a stochastic environment with diverse voting principles.

Findings

Explicit formulas for expected capitals of all participants.

Analysis of differences between voting principles.

Insights into social dynamics in stochastic decision environments.

Abstract

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.