If he were elected, there would be a 'tilt' [='shift'] in the political balance of the city council. [=the city council would become more liberal or conservative]
The quarterback's injury could 'tilt' (the outcome of) the game in the other team's favor. [=could make it more likely that the other team will win]
His election 'tilted' the city council to the left/right. [=made the city council more liberal/conservative]
(..) of the cherry blossom announces the beginning of spring. The sun's energy brings colour to the landscape. The earth, as it makes its annual journey around the sun, spins on a tilted axis. And it's this tilt that creates the seasons. The advance of the seasons brings constant change. (..)2006 TvShow: Planet Earth Title: From Pole to Pole Season: 1 Episode 1
(..) - El! Eleven! El? Oh, God. He's not breathing, he's not breathing. All right, Joyce, Joyce, listen to me, listen to me, listen to me. - I need you to tilt his head back... - Okay. - ...and lift his chin. - Okay. One, two, three, four. Now when I tell you, you're gonna pinch his nostrils, - twice. (..)2016 TvShow: Stranger Things Title: Chapter Eight: The Upside Down Season: 1 Episode 8