There are several synonyms for the phrase "vote nay" which means to vote against something. One popular synonym is "vote against," which has the same meaning, but is a more direct way of expressing opposition. Another option is to use the phrase "cast a negative vote," which can be helpful when discussing parliamentary procedures. Other synonyms include "reject," "oppose," "disapprove," and "veto." Each of these words conveys an element of dissent or refusal and can be used interchangeably with "vote nay" in most situations. Ultimately, the choice of synonym will depend on the context of the vote and the speaker's preference for a particular word.