Both Ones and Eights are in the Instinctive Triad, both have strong wills, both are action-oriented, and both have strong notions about how to do things. However, Ones try to convince others to do the right thing (as they see it) from the standpoint of a moral imperative–because it is the right thing to do. They try to logically convince the other of the soundness of their views, but become irritated and less logical when others resists their reasoning. Eights, on the other hand, rely on their own self-confidence, and attempt to sway others by their gutsy convictions and sheer personal charisma. ("I don't know if it's the right way, but it's my way.") Ones try to convert those who resist them: Eights try to power through them.
The greatest misunderstanding between these two types involves their concern with justice, although the nature of their sense of justice can be quite different. Ones hold justice as an extremely important value–many judges, attorneys, advocates, and criminal prosecutors actually are Ones. Ones think a great deal about issues of providing suitable standards for human beings and about the specifics of how to administer a fair and equitable system. Ones at all Levels of Development refer to justice and think that they seek justice (no matter how skewed their interpretation of it may become). In any case, justice is a matter of principles–part of their idealism. They strive after justice and want to rectify injustices wherever they find them because, among other reasons, to do otherwise would be to fail to live up to their high moral standards and make them feel guilty.
In Eights, justice is more of a visceral response, a reaction to witnessing injustices occurring. Eights, generally speaking, do not walk around thinking about these matters, but if they saw a helpless person being harmed or bullied by others, without thinking about it, Eights would rush in to "level the playing field." For Eights, justice has little to do with abstract principles. Eights see themselves as protectors of others, and when they are healthy, they actually are. Eights are more likely to seek justice for "their people"–their family, friends, co-workers, ethnic group, and so forth. It is usually expressed in a concern that those in their care (or under their power and authority) be treated fairly. The cowboy marshal protecting the town against criminals and the union chief negotiating a just wage for the rank and file are examples of this more restricted concern for justice. With Eights, the sense of justice usually involves addressing an imbalance of power. This is quite different from the One who seeks to make sure that people are appropriately rewarded for good actions and punished for bad ones.
Of course, in their unhealthy manifestations, both types can be extremely unjust. Ones will still believe that they are being fair–the punishments they are meting out are for the good of the person being punished, or at the very least, for the good of society. Ones feel they need to rationalize their punitive activities. Eights do not. For unhealthy Eights, administering justice is simply meting out vengeance. ("You hurt me or my people, and I'll destroy you." "He ripped me off. Now he has to pay.") Needless to say, others may question the "justice" in either of these types' unhealthy behavior.
The confusion between Eights and Ones probably also stems from the fact that some Ones may misidentify themselves as Eights since they would like to have the authority and influence of Eights. They may also recognize that they have aggressive impulses and misidentify themselves as an "aggressive type," although they are really compliant to their ideals; the Eight is the true aggressive type par excellence. On the other hand, Eights almost never misidentify themselves as Ones, viewing Ones as lily-livered and bloodless–moral only because they are too weak to be strong. Although Eights themselves are unlikely to think they are Ones, other people sometimes misidentify Eights as Ones because they see them as reformers. But clearly, many natural leaders, including Eights, lead reforms when they are needed. Contrasting Ones such as Pope John Paul II, Ralph Nader, and Hilary Clinton with Eights such as Lee Iococca, Franklin Delano Roosevelt, and Barbara Walters gives a vivid sense of their differences.
perhaps this describes average 8s vs 1s? even then, I should relate to the 8 side at least a little bit. do people really view 8s as this hostile and animalistic?
I mean, MLK was an Eight! How do those stereotypes last so long? 
