One appointment by two parties to settle a dispute

Arbiter
Mediator
Negotiator
Middleman

The correct answer is: Arbitrator.

An arbitrator is a neutral third party who is appointed by two parties to settle a dispute. The arbitrator will listen to the arguments of both parties and then make a decision that is binding on both parties.

A mediator is a neutral third party who helps two parties to reach a settlement. The mediator does not make a decision, but rather helps the parties to communicate and to find a solution that is acceptable to both parties.

A negotiator is a person who represents one party in a negotiation. The negotiator’s job is to get the best possible deal for their client.

A middleman is a person who acts as an intermediary between two parties. The middleman may be involved in a variety of transactions, such as buying and selling goods, or arranging for loans.

In the context of the question, the correct answer is arbitrator because an arbitrator is a neutral third party who is appointed by two parties to settle a dispute. The arbitrator will listen to the arguments of both parties and then make a decision that is binding on both parties.