# Nonlinear Opinion Dynamics with Tunable Sensitivity

arXiv: https://arxiv.org/abs/2009.04332 · HTML: https://mlsanity.com/paper/2009.04332/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Sep 2020.

## Built on by (most cited first, 6 of 6)

- [Active Uncertainty Reduction for Safe and Efficient Interaction Planning: A Shielding-Aware Dual Control Approach](https://mlsanity.com/paper/2302.00171/) (2023)
- [Behavior-Inspired Neural Networks for Relational Inference](https://mlsanity.com/paper/2406.14746/) (2024)
- [Mixed Strategy Nash Equilibrium for Crowd Navigation](https://mlsanity.com/paper/2403.01537/) (2024)
- [Resolving Oversmoothing with Opinion Dissensus](https://mlsanity.com/paper/2501.19089/) (2025)
- [Decentralized Reinforcement Learning for Multi-Agent Multi-Resource Allocation via Dynamic Cluster Agreements](https://mlsanity.com/paper/2503.02437/) (2025)
- [Sampling-Based Coordination-Informed Multi-Objective Multi-Robot Reinforcement Learning](https://mlsanity.com/paper/2606.30893/) (2026)

## Abstract (arXiv)

We propose a continuous-time multi-option nonlinear generalization of classical linear weighted-average opinion dynamics. Nonlinearity is introduced by saturating opinion exchanges, and this is enough to enable a significantly greater range of opinion-forming behaviors with our model as compared to existing linear and nonlinear models. For a group of agents that communicate opinions over a network, these behaviors include multistable agreement and disagreement, tunable sensitivity to input, robustness to disturbance, flexible transition between patterns of opinions, and opinion cascades. We derive network-dependent tuning rules to robustly control the system behavior and we design state-feedback dynamics for the model parameters to make the behavior adaptive to changing external conditions.} The model provides new means for systematic study of dynamics on natural and engineered networks, from information spread and political polarization to collective decision making and dynamic task allocation.