Arguments and research studies examining whether people prefer arbitration or mediation to resolve a conflict between disputing parties are discussed, critiqued, and compared. In both mediation and arbitration a presumably neutral third party is involved, along with disputants, as an element of the dispute-resolution process. Mediation and arbitration differ primarily in terms of the role that is assigned to this third party. In mediation, disputants are actively charged with presenting information to each other and to the third party, while the third party is only allowed to propose or recommend a settlement. Under mediation, disputants have both high process control and high decision control. In arbitration, the disputants are in charge of the information to be presented, but the third-party decision maker has the authority to impose a decision after listening to the evidence. In arbitration, disputants have high process control but low decision control. The studies show that both voice (process control) and veto power (outcome control) are significant elements influencing people's feelings about the procedures they encounter. Current evidence is not sufficient to resolve the controversy. (RM)