Twitter CEO Jack Dorsey saw an opportunity last month to please the political left and embarrass a competitor. Now he’s stuck with a jury-rigged ads policy that will damage confidence in his company and do nothing to improve political discourse.

In October Democrats and the press were pummeling Facebook CEO Mark Zuckerberg for refusing to take down a Donald Trump campaign ad against Joe Biden. If Facebook did not fact-check and censor politicians, they said, democracy would be undermined. So Mr. Dorsey tweeted on Oct. 30...