A party is an organization or individual involved in an interaction. In Confrontation ManagerTM, parties are defined as belonging to missions rather than to the individual options boards where they appear. Thus, though you can add a party at interaction level, you can't delete it except at mission level.
A party added to an options board should be a group that will consult separately about whether or not to implement its stated intentions when the time comes for intentions to be implemented. For example, the US decision in 1920 not to join the League of Nations, after having campaigned for it, meant that it was a separate party. As in this case, a party will generally be made up of subparties (the President, Congress, etc.) that decide its preferences, beliefs, position, etc., through their internal interactions.
In OedipusDecisionMaker a party is called a character.