Supreme Court Justice Stephen Breyer said oral arguments cause him to change his view of a given case at the high court nearly half the time.

Breyer told Law360 that by the time the justices arrive at oral arguments, they have a point of view about the cases, but remain open to the opposing side.

"I would say oral argument changes the way you look at a case fairly often," Breyer said in an interview with Law360. "If you said 40 or 50 percent of the time, that might be a ballpark. To change your mind from A to B, is less often, 10 percent of the time or 15 percent, something like that."

Breyer also said that he thought public support and public perception of the court matters "very, very much" to the effectiveness of the U.S. court system.

"That doesn't mean your decisions have to be popular — to the contrary," Breyer said. "You only have a rule of law if courts are willing to protect people who are very unpopular. Hamilton made this very clear. The Constitution is there for the least popular person as much as for the most. And so you must have support for that principle in the country, which is very hard to get."