Otium is the Latin for leisure, and neg is to negate.
Negotium is then not-leisure: Business.
To negotiate is what is "done in the course of business".
A mentor who became a friend once gave me this advice: You cannot negotiate for both parties. It undermines at least you, and also the trust in the relationship.
I find the same true in leisure relationships: Advocate for your own needs, not the other's.