SAN FRANCISCO — Plaintiffs attorneys hope to make groundbreaking new law when they face off with social media titans Facebook and Zynga in two privacy class actions set for argument next week before the U.S. Court of Appeals for the Ninth Circuit.

But Kassra Nassiri of Nassiri & Jung and Adam Levitt of Grant & Eisenhofer appear to be facing an uphill battle. They’ve drawn two of the court’s more conservative judges, and last week the panel issued an order consolidating arguments in the two cases and shortening overall time from 60 minutes to 40.