WASHINGTON — “Judge Alex” lost his case at the Supreme Court yesterday when the justices ruled that the star of the syndicated TV show must go to arbitration with his dispute over an attorney’s claim to 12% of his earnings.

In a ruling with special significance for the entertainment industry in California, the court upheld that arbitration agreements must be honored. In an eight to one ruling, with Judge Clarence Thomas dissenting, it held that actors and managers who signed arbitration agreements must resolve their disputes in arbitration. In two other cases, the Supreme Court gave business two big wins by shielding companies from different kinds of lawsuits and state regulations. In one ruling, the court said the makers of medical devices cannot be sued by patients who are injured or killed, so long as those devices were approved in advance by the Food and Drug Administration. The eight to one ruling throws out a lawsuit brought by a widow whose husband was badly hurt and later died after a balloon catheter burst in his chest. Justice Ruth Bader Ginsburg dissented.

In the second ruling, the court ruled unanimously to shield shippers and delivery services from state regulations that require them to check for proof of age before dropping off cigarettes or alcohol at a residence.