Voting in a Stochastic Environment: The Case of Two Groups

TL;DR

This paper models voting dynamics in a society with two groups in a stochastic environment, deriving explicit formulas for group capital changes and analyzing voting rules to optimize group and societal benefits.

Contribution

It introduces a mathematical model of voting in stochastic environments with explicit formulas and evaluates claim thresholds for optimal group and societal outcomes.

Findings

Explicit formulas for group capital increments derived

Optimal claim thresholds identified for societal benefit

Analysis of voting rules under stochastic conditions

Abstract

Social dynamics determined by voting in a stochastic environment is analyzed for a society composed of two cohesive groups of similar size. Within the model of random walks determined by voting, explicit formulas are derived for the capital increments of the groups against the parameters of the environment and "claim thresholds" of the groups. The "unanimous acceptance" and "unanimous rejection" group rules are considered as the voting procedures. Claim thresholds are evaluated that are most beneficial to the participants of the groups and to the society as a whole.