Miller's construction of Danforth, Parris, and Hale all seeking the same ends helps to bring out how politics makes strange alliances. While they all covet the same goal, they do so for different reasons. Miller makes it clear that this end is one out of fundamental self- interest. For Danforth, a confession validates the trial and its outcome. Danforth is aware that the rebellion in Andover as well as the lack of public faith in Salem in the trials and their outcome can be immediately re-authenticated with a confession. The confession brings more credibility to he and his trials. For Parris, the lack of public faith has led to a targeting of the Salem Minister. The popularity he enjoyed in the summer with the trial has now become something of a curse, as people blame him for the trial and the public resentment has been placed on his shoulders. Complete with a death warning, Parris needs the confession to resuscitate his public image. For Parris, a confession rehabilitates his sagging public perception. Hale recognizes that his own role in the trial was an unholy one. There is some level of "blood on his hands" and like a repentant Pilate, Hale seeks to make his own conscience clean. In obtaining a confession, Hale is able to save individuals. At the very least, a confession enables him to not have so much guilt on his own conscience as he can say that he brought someone "to the light." Hale recognizes that a confession is an embrace of a transcendental truth, something that motivated his participation in the Salem trials in the first place. For Hale, a confession saves himself from his own sense of guilt over his participation in the trials. For each men, a confession accomplishes specific ends. It is for this reason that Proctor refuses to "sign his name to lies." Proctor recognizes very clearly that his own confession is one manipulated by others to feed their own agenda. The reason for desiring the confession put aside, Miller develops the role that each man plays in trying to obtain a confession as one in which there is a fundamental use of human beings as a means to an end as opposed to treating men as an end in their own right.
Danforth: to keep his power and integrity that has. Add weight to all of the other trials (people he has already killed) so if more confess, then he's making himself look better as then he looks like he has hung people for a reason.
Hale: Wants Proctor to confess because he feels that if he doesn't then he is the reason for his death and he feels like a murderer. Use the quote in the book that links to McBeth! "blood on my head" So like he will always feel guilty for Proctor and his death. If Proctor confesses then it will be sinless and no point also Proctor would be lying so Hale feels bad.
Paris: If they don't confess then he will loose his face and his name. He is quite high up also and if they didn't confess then he could loose land/name. It will reflect badly on him. But if they confess then it will give Paris more power.
Overall they don't get what they want! They do get what they want because people & Proctor were hung. However they don't get what they were looking for because they wanted them to confess!