The service is defying critics and stepping up identification requirements to tackle fake accounts.
Kody Brown and his wives will appeal the decision, their lawyer said.
The Fundamentalist Church of Jesus Christ of Latter-day Saints is also fighting a lawsuit saying the church discriminates against nonmembers and denies them municipal services.
Experts say the trial will provide a rare glimpse into a secretive splinter sect of Mormonism.
The stars of the reality show used the Supreme Court's recent same-sex marriage ruling to support their case against Utah's polygamy ban.
"My second wife Christine... she's put up with my crap for a lot of years. She deserves legitimacy."
The study examined the medical histories of 687 men from Saudi Arabia and the United Arab Emirates