do insects have a democratic-like system as humans do?
So far it has not been proven that insects have a democratic-like system as humans do. Insect societies have different forms of organization and decision making, often based on hierarchies, pheromones, and instinctual behavior.
What is the simplest animal with a democratic-like system?
The simplest animal with a democratic-like system is likely the honeybee. Honeybees have a social hierarchy in which decisions, such as the location of the hive, are made through collective behavior and consensus-building among the workers.