Does passing priority both times cause a spell on the stack to resolve?

When a spell or ability is on the stack, each player receives priority in turn order. A spell or ability resolves when all players pass priority in succession without anyone adding anything new to the stack (CR 608.1, 117.4). In a two-player game, this means the active player passes, then the non-active player passes — two consecutive passes with nothing new added — and the top object of the stack resolves.

It's important to understand that priority resets whenever a new spell or ability is placed on the stack. If one player responds by casting an instant or activating an ability, that new object goes on top, and both players must pass priority again before anything resolves (CR 117.3b). Simply put, the 'two passes in a row' clock starts fresh each time the stack changes.

After the top object resolves, the active player receives priority again (CR 608.2m). If the stack is not empty, the same process repeats for the next object. Only when the stack is completely empty and both players pass priority does the game move to the next step or phase (CR 500.2).

Concrete example: Your opponent casts Lightning Bolt targeting your creature. You choose not to respond and pass priority. Your opponent also passes priority. Both players have passed in succession — Lightning Bolt resolves, dealing 3 damage to your creature.