Legislators who interpret their role as being in the legislature to represent a majority of voters' interest would be described as what type of representative?

This is the delegate type of representative. It takes into account simply the views of the constituency and nothing more. The views of the legislator, his or her gut instincts, and what might be best for the rest of the country are not part of the decision-making process. The people he or she is representing have the final say.