In some cities, purchases of new voting machines slowed the balloting as voters labored to apply the new technology to the state’s notoriously long ballot. “All over the state, we saw a lot of late openings attributed to technology issues,” said Anthony Gutierrez, the executive director of Common Cause Texas, which helped run a hotline that flagged voting problems. “People were used to voting on the same machine for two decades, and there was going to be some training time required.”