Justice Sonia Sotomayor and Jones Day’s Michael Carvin sharply differed Tuesday on how to determine racially discriminatory voting rules during a complex and sometimes combative argument in a major voting rights case before the U.S. Supreme Court.

In the combined cases Brnovich v. Democratic National Committee and Arizona Republican Party v. Democratic National Committee, the justices reviewed a ruling by the U.S. Court of Appeals for the Ninth Circuit that struck down two state voting rules under Section 2 of the Voting Rights Act: the state’s out-of-precinct policy in which the state discards all ballots cast by voters in the wrong precinct, and its criminal law barring the collection of early ballots by most third parties.