# Hydrodynamic models of preference formation in multi-agent societies

## TL;DR

This paper derives hydrodynamic equations from kinetic models of opinion formation, highlighting how opinion and preference dynamics influence collective decision-making in multi-agent societies.

## Contribution

It introduces a novel hydrodynamic modeling approach for opinion and preference formation, based on kinetic theory and local equilibrium analysis.

## Key findings

- Hydrodynamic models effectively describe opinion dynamics.
- Numerical examples validate the model's accuracy.
- Distinction between opinion and preference impacts collective choices.

## Abstract

In this paper, we discuss the passage to hydrodynamic equations for kinetic models of opinion formation. The considered kinetic models feature an opinion density depending on an additional microscopic variable, identified with the personal preference. This variable describes an opinion-driven polarisation process, leading finally to a choice among some possible options, as it happens e.g. in referendums or elections. Like in the kinetic theory of rarefied gases, the derivation of hydrodynamic equations is essentially based on the computation of the local equilibrium distribution of the opinions from the underlying kinetic model. Several numerical examples validate the resulting model, shedding light on the crucial role played by the distinction between opinion and preference formation on the choice processes in multi-agent societies.