No, they don’t. Shareholders vote at a corporation’s annual meeting, but for the most part those votes are non-binding. Until the Dodd-Frank bill passed, with its “say on pay” clause, executive compensation wasn’t even required to be subject to a vote. Now it is, and shareholders get to vote, but it doesn’t count.
That’s what recently happened at Citi. The shareholders rejected the proposed executive compensation plan, but the Board of Directors can (and will) do whatever it wants. The shareholders might have felt good, but they weren’t changing anything.