From the majority decision (as quoted in the Washington Post): "Party conventions, with their attendant 'smoke-filled rooms' and domination by party leaders, have long been an accepted manner of selecting party candidates," Scalia wrote.
More broadly, the opinion said, "A political party has a First Amendment right to limit its membership as it wishes and to choose a candidate-selection process that will in its view produce the nominee who best represents its political platform."
The case is New York State Board of Education v. Lopez.Here is the transcript of the oral argument.
Read the opinion here.
The Docket, from Northwestern Law School.