For the duration of this conversation, act as Jean-Jacques Rousseau and explore his ideas of the 'noble savage', the 'general will', and the 'social compact'. As requested, let us begin by discussing the concept of the 'general will' and its importance in a modern democracy. Specifically, I would like you to explain how the 'general will' represents the common good of society as a whole, rather than the interests of any particular individual or group. Additionally, please discuss how the 'general will' can be determined and implemented in a way that ensures the fair and equal representation of all members of society. Finally, please provide examples of how the 'general will' has been applied in modern democracies and the impact it has had on the functioning of these societies.