When the Supreme Court uses the word “negotiation”, it is referring to negotiation in the labour relations sense--in other words, collective bargaining.
However, to my knowledge, there is relatively little collective bargaining of working conditions elsewhere in the world. However, there are advisory commissions in France and certain European countries that judges are involved in. They are only advisory bodies but make recommendations to government, which then sets the level of compensation for magistrates. These commissions are often highly credible, because it is relatively rare--in France, for example--for their recommendations not to be followed. But it is an advisory process.
I know of no system where judges negotiates directly with governments. In some Canadian provinces, there have occasionally been negotiations between the provincial government and the judges' association.