A judge has refused to set an earlier election for the seat formerly held by retired U.S. Rep. John Conyers.
Judge Mark Goldsmith on Wednesday says there's no evidence that the constitutional rights of people in the 13th District have been violated by having a vacancy for 11 months.
He says critics have failed to show that Gov. Rick Snyder discriminated against black residents.
Conyers, a Detroit Democrat, quit in December. Snyder set a primary election for Aug. 7, the date for primary elections statewide, followed by a special election on Nov. 6.
The winner would serve only for two months.
The judge says attorney and candidate Michael Gilmore didn't help his case by waiting until Feb. 2 to seek an injunction.