Final answer:
The statement about a mediator being akin to an invited guest who can be dismissed by the involved parties if desired is true. Mediators facilitate negotiations when informal methods fail and are subject to the parties' consent for their continued involvement in the bargaining process.
Step-by-step explanation:
A mediator in the context of bargaining or dispute resolution does indeed function much like an invited guest, with a significant caveat. The mediator's role is to facilitate communication and negotiate solutions between parties in conflict. Unlike a guest, however, a mediator is a neutral third-party whose involvement suggests that an informal approach to resolving the conflict has not been successful, and therefore, their presence is often governed by specific rules and agreements. While a mediator does not have the authority to enforce any decision, if one or both parties to a negotiation find that the mediator's services are no longer beneficial, they can decide to discontinue the mediator's involvement. So in that sense, the statement that a mediator can be required to leave if one or both bargaining parties no longer desire the mediator's continued involvement is true.
In the wider context of political negotiations, the dynamics can include persuasion, coercion, or even underhand tactics such as bullying or bribery, especially when parties hold significant power over others. A mediator's role in such scenarios can be particularly challenging, and their continued involvement would depend on the consent of the negotiating parties.