I mean... theoretically, we could lock ourselves in a room and keep discussing and have a final vote to see who is CEO and that would solve our problem.

The issue is that I'm afraid how the person who didn't become CEO would feel, especially if they were equally as deserving. From a founder's standpoint, it's hard to say that one person is better than the other when both people have been there from the beginning and contributed equally as much to the venture.