When Does Population Diversity Matter? A Unified Framework for Binary-Choice Dynamics.

Area of Science:

• Complex Systems
• Agent-Based Modeling
• Statistical Mechanics

Background:

• Existing models often simplify agent behavior, potentially overlooking the impact of individual diversity on collective outcomes.
• Understanding the interplay between individual preferences and emergent group dynamics is crucial in various fields.

Purpose of the Study:

• To introduce a unified modeling framework for binary-choice dynamics incorporating individual preferences.
• To systematically analyze the conditions under which individual-level diversity influences collective dynamics.
• To compare annealed (time-varying preferences) and quenched (fixed preferences) dynamics.

Main Methods:

• Developed a flexible modeling framework for agent state updates based on preference-driven mechanism selection.
• Analyzed the mathematical relationship between annealed and quenched dynamics under varying preference distributions.
• Identified a specific constraint on transition probabilities for the equivalence of the two dynamics.

Main Results:

• The proposed framework integrates diverse existing models of binary-choice dynamics.
• A key constraint on transition probabilities was found to equate annealed and quenched dynamics.
• When this constraint holds, quenched dynamics simplify to a one-dimensional system, precluding oscillations.

Conclusions:

• The framework offers a systematic way to determine the relevance of individual diversity in collective behavior.
• The identified constraint provides a condition for simplifying complex agent-based models.
• This work advances the understanding of emergent phenomena in systems with heterogeneous agents.