The option that can be used as a one-word substitute for "One who mediates in a deal or complex situation" is Option 4: Negotiator.

Option 1: Equaliser - An equaliser refers to something that makes things equal or balances them out. It does not specifically relate to mediating in a deal or complex situation.

Option 2: Solicitor - A solicitor is a legal professional who provides legal advice, prepares legal documents, and represents clients in legal matters. While solicitors may engage in negotiations, their role is broader and not solely focused on mediating in a deal or complex situation.

Option 3: Pacifier - A pacifier is an object, typically a nipple-shaped device, used to soothe or calm a baby. It is not directly related to mediating in a deal or complex situation.

Option 4: Negotiator - A negotiator is someone who facilitates discussions and agreements between parties involved in a deal or complex situation. They work to find mutually acceptable solutions and resolve conflicts. A negotiator is specifically associated with mediating and finding compromises in challenging situations, making it the most appropriate option in this context.