Collective decision making with a mix of majority and minority seekers

TL;DR

This paper models how populations with mixed majority and minority seekers reach consensus or polarization depending on their proportions, revealing phase transitions and the impact of contrarian behavior on collective decision-making.

Contribution

It introduces a model combining opinion dynamics with game-theoretic incentives, analyzing the effects of majority and minority seekers on collective outcomes.

Findings

For less than half majority seekers, the population self-organizes into a stable majority-minority split.

When the majority seekers exceed half, the population tends toward a balanced, polarized state.

Near the threshold, the population state is most distant from the optimal collective decision.

Abstract

We study a model of a population making a binary decision based on information spreading within the population, which is fully connected or covering a square grid. We assume that a fraction of the population wants to make the choice of the majority, while the rest want to make the minority choice. This resembles opinion spreading with "contrarian" agents, but has the game theoretic aspect that agents try to optimize their own situation in ways that are incompatible with the common good. When this fraction is less than 1/2, the population can efficiently self-organize to a state where agents get what they want -- the majority (i.e. the majority seekers) have one opinion, the minority seekers have the other. If the fraction is larger than 1/2, there is a frustration in the population that dramatically changes the dynamics. In this region, the population converges, through some distinct phases, to a state of approximately equal-sized opinions. Just over the threshold the state of the population is furthest from the collectively optimal solution.