The Optimal Majority Threshold as a Function of the Variation Coefficient of the Environment

TL;DR

This paper derives formulas for the optimal majority decision threshold and expected capital gains in a stochastic social decision model, showing how these depend on environmental variability and providing a constant rate of change at zero.

Contribution

It introduces explicit expressions for the optimal majority threshold and expected gains as functions of environmental parameters within the ViSE model.

Findings

Optimal majority threshold depends on environmental variation coefficient.

Maximum expected capital increment is explicitly characterized.

Rate of change of the threshold at zero is a constant: $(rac{ oot{2}{rac{2}{\pi}}}-rac{ oot{rac{\pi}{2}}{2}})$.

Abstract

Within the model of social dynamics determined by collective decisions in a stochastic environment (ViSE model), we consider the case of a homogeneous society consisting of classically rational economic agents (or homines economici, or egoists). We present expressions for the optimal majority threshold and the maximum expected capital increment as functions of the parameters of the environment. An estimate of the rate of change of the optimal threshold at zero is given, which is an absolute constant: $(\sqrt{2/\pi}-\sqrt{\pi/2})/2$.