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

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We present a new framework for modeling how agents make choices. This work clarifies when individual differences impact group behavior and introduces conditions for simplified analysis of agent dynamics.

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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.