A good case can be made for changing Woodrow Wilson’s appealing slogan “Open covenants openly arrived at” to “Open covenants privately arrived at.” No matter how many people are involved in a negotiation, important decisions are typically made when no more than two people are in the room.
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A variation on the procedure of “one cuts, the other chooses” is for the parties to negotiate what they think is a fair arrangement before they go on to decide their respective roles in it. In a divorce negotiation, for example, before deciding which parent will get custody of the children, the parents might agree on the visiting rights of the other parent. This gives both an incentive to agree on visitation rights each will think fair.