The 4-way stop

I came to a four-way stop the other day. The traffic wasn't heavy, just myself and another person. To my right at the intersection was an older guy and by old I mean around 70 or so in a 1980s style pickup. In the passenger seat was a dog that was also old and I figured this by noticing that the dog wasn't pacing the seat while panting and drooling. It was just sitting with no care in the world. Anyway, the rule is to let the car who got to the intersection first go on their merry way before you or if you arrived at the intersection at the same time to let the person on the right go first. Well I felt this man whom I'll call Bob got to the intersection first and even if it were a tie he'd have the right of way so I motioned for him to go with my hand. But no, Bob tried to trump my hand gesture with one of his. Now this just pissed me off so I motioned back for him to go with a little more disgust in my, "No, after you"-type hand movement. Just as I figured would happen Bob was just a little bit more gentlemanly than me I guess so he gave his little hand wave again. I would've sit there all day exchanging "Go aheads" with Bob -- and I would've been entertained the whole time -- but I was in a bit of a hurry so I let Bob have his glory and went first. Can we just make it a rule right here and now that the person who waves first wins the standoff?