In The Crucible, what does Reverend Parris want Judge Danforth to do?
The Reverend Parris is a man obsessed by the idea that there exists a faction in Salem who wants to get rid of him. He is paranoid about his position and sees a threat against him in almost every corner. He has been struck by this delusional belief even before he came to Salem. The good Reverend therefore wishes to protect his status and will do everything in his power to side-track any suspicion against him.
After the Reverend had discovered his daughter, Becky, and his niece, Abigail Williams, dancing in the woods, his daughter fell into a deep fit. This lead to rumours of witchcraft being spread around Salem. Since the origins of this rumour were found to be in his own household (his slave Tituba had been implicated for encouraging the girls to indulge in the summoning of spirits), he was intent on deflecting all suspicion and rumour away from himself and direct it elsewhere.
It is for these reasons that the Reverend meddled in the court's affairs during the witch trials. He became a sort of lay-prosecutor and would advise Judge Danforth, whether he needed his input or not, to such a degree that the Judge at one point lost patience with him. The Reverend especially feared John Proctor, one of the leading citizens of Salem, since he had been incessantly criticised by him for being materialistic and using the parish to profit himself. Reverend Parris, therefore, pointed out all John's wrongdoings during the trial for he wanted Judge Danforth to find John Proctor to be found guilty of witchcraft. In this way, he would be rid of one of his fiercest opponents.
When John was arrested and imprisoned, Reverend Parris further beseeched the judge to get a written confession from John. This would then be publicly displayed so that others could see that the much-respected (and feared) John Proctor had admitted to being a witch. Such a publicly displayed confession would dishearten the Reverend's enemies and discourage them from challenging him any further.
Added to this, the Reverend had claimed that there had been threats against his person and the confession would provide him the protection he so desperately sought. He felt that a faction existed which was out to ruin him and he believed that John Proctor was its ringleader. With him out of the way, the faction would collapse.
The Reverend used the same reasoning with regard to Rebecca Nurse. She too, had been critical of him and was also John Proctor's good friend. It would please the Reverend tremendously if she were out of the way and confessed.
The desperate Reverend's plan, however, did not reach fruition, for neither John or Rebecca executed written confessions. John had initially declared his guilt and signed a confession (to Rebecca's horror) but then decided to tear it up to save his name. Both went to the scaffold, innocent, without giving the Reverend what he wanted.
It is acutely ironic that not long after the fever and disruption of the trials had died, the Reverend was voted out of office. He left Salem and was never heard of again.