Liberty Valance and Tom Doniphon show constant tension throughout the film because they are both alpha male cowboys who strive to be the top cowboy in town. Rance Stoddard is also plays an important role in the western town. His Eastern moral of the law conflict with both the alpha male cowboys. Stoddard, who lives by the law, is in disbelief about how the Western people settle their disputes. He eventaully turns to their side because he is a favorable candidate to represent them in Capital City, so should settle his dispute their way.
Matheson would assess both the alpha males as typical hardboiled western characters. They both have the anti-social qualities that Matheson talks about in the text. Liberity Valance never has any type of social interaction with the people of town unless he is playing cards or having a drink. He doesn't even live in the town but only comes with his two side-kicks to take care of business.
Tom Doniphon on the other hand shows the qualities of being damanged and isolated. Matheson says on page 896, "There is very little difference between Doniphon and Liberity Valance. Both men settle their problems in the same fashion...Doniphon may wear a white hat in The Man Who Shot Liberty Valance, but like Valance, he too exhibits a highly antisocial and disordered personality." Doniphon has blood on his hands and doesn't want Stoddard to be in the same situation or die. This is the reason that he kills Liberty Valance, while Stoddard is in a stand-off with him. Tom has seems to isolate himself from the people of town by drowning his sorrows at the bar and being agressive with anyone who gets in his way. However, Tom has a way to take charge and be one of the towns people when he needs to. He shows this when they are casting their votes from who should represent their territory in Capital City. Tom Doniphon was able to take order and carry out the law. Tom Doniphon respects the laws of the East but knows that the way of settling disputes out West is differnt. This is the reason that Doniphon wants Stoddard to be elected and help bring change to the West.