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Emotional Modulation in Swarm Decision Dynamics

David Freire-Obregón

TL;DR

This work extends the bee equation into an agent-based model in which emotional valence and arousal act as modulators of interaction rates, effectively altering the recruitment and cross-inhibition parameters, and shows that emotional modulation can bias decision outcomes and alter convergence times by shifting effective recruitment and inhibition rates.

Abstract

Collective decision-making in biological and human groups often emerges from simple interaction rules that amplify minor differences into consensus. The bee equation, developed initially to describe nest-site selection in honeybee swarms, captures this dynamic through recruitment and inhibition processes. Here, we extend the bee equation into an agent-based model in which emotional valence (positive-negative) and arousal (low-high) act as modulators of interaction rates, effectively altering the recruitment and cross-inhibition parameters. Agents display simulated facial expressions mapped from their valence-arousal states, allowing the study of emotional contagion in consensus formation. Three scenarios are explored: (1) the joint effect of valence and arousal on consensus outcomes and speed, (2) the role of arousal in breaking ties when valence is matched, and (3) the "snowball effect" in which consensus accelerates after surpassing intermediate support thresholds. Results show that emotional modulation can bias decision outcomes and alter convergence times by shifting effective recruitment and inhibition rates. At the same time, intrinsic non-linear amplification can produce decisive wins even in fully symmetric emotional conditions. These findings link classical swarm decision theory with affective and social modelling, highlighting how both emotional asymmetries and structural tipping points shape collective outcomes. The proposed framework offers a flexible tool for studying the emotional dimensions of collective choice in both natural and artificial systems.

Emotional Modulation in Swarm Decision Dynamics

TL;DR

This work extends the bee equation into an agent-based model in which emotional valence and arousal act as modulators of interaction rates, effectively altering the recruitment and cross-inhibition parameters, and shows that emotional modulation can bias decision outcomes and alter convergence times by shifting effective recruitment and inhibition rates.

Abstract

Collective decision-making in biological and human groups often emerges from simple interaction rules that amplify minor differences into consensus. The bee equation, developed initially to describe nest-site selection in honeybee swarms, captures this dynamic through recruitment and inhibition processes. Here, we extend the bee equation into an agent-based model in which emotional valence (positive-negative) and arousal (low-high) act as modulators of interaction rates, effectively altering the recruitment and cross-inhibition parameters. Agents display simulated facial expressions mapped from their valence-arousal states, allowing the study of emotional contagion in consensus formation. Three scenarios are explored: (1) the joint effect of valence and arousal on consensus outcomes and speed, (2) the role of arousal in breaking ties when valence is matched, and (3) the "snowball effect" in which consensus accelerates after surpassing intermediate support thresholds. Results show that emotional modulation can bias decision outcomes and alter convergence times by shifting effective recruitment and inhibition rates. At the same time, intrinsic non-linear amplification can produce decisive wins even in fully symmetric emotional conditions. These findings link classical swarm decision theory with affective and social modelling, highlighting how both emotional asymmetries and structural tipping points shape collective outcomes. The proposed framework offers a flexible tool for studying the emotional dimensions of collective choice in both natural and artificial systems.
Paper Structure (18 sections, 6 equations, 2 figures, 2 tables)

This paper contains 18 sections, 6 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Agent States and Emotional Representation
  5. Bee Equation with Emotional Modulation
  6. Population fractions.
  7. Emotional Contagion
  8. Agent Decision Rules
  9. Initialization and Parameters
  10. Stopping Conditions and Metrics
  11. Experimental Setup
  12. Evaluation of Simulation Scenarios
  13. Analysis of Results
  14. Emotional Modulation and Classical Dynamics
  15. Scenario-by-Scenario Interpretation
  16. ...and 3 more sections

Figures (2)

  • Figure 1: Agent-based simulation of the bee decision-making model. Top: spatial distribution of agents on the grid, with blue representing commitment to option A, red to option B, and grey uncommitted individuals. Bottom: temporal evolution of the proportion of agents in each state ($\varphi_A$ in blue, $\varphi_B$ in red, and uncommitted $u$ in grey). The dynamics illustrate the gradual recruitment from the uncommitted pool towards both options and the role of cross-inhibition in shaping the relative growth of A and B.
  • Figure 2: Scenario 3: Snowball Effect. The plot shows the average trajectory of $\max(\varphi_A, \varphi_B)$, where $\varphi_X$ denotes the proportion of agents committed to option $X$, across simulation steps. The shaded area indicates the $95\%$ confidence interval. Starting from a perfectly balanced configuration, the system exhibits a gradual increase in the maximum commitment level until one option approaches complete dominance. This reflects a self-reinforcing recruitment dynamic: once an intermediate threshold of support is surpassed, the leading option continues to attract uncommitted agents at an accelerating pace.