This one crosses my mind every morning, on my way to work down Alta Vista. Is there any logic behind having a four-way stop on a street that has a bike lane? Particularly a busy street like Alta Vista?
Generally, I'll obey the rules at a four-way stop when I come across it on a small residential street or country road (I'll pull up, and if I arrive at the same time as a car, the vehicle on the right goes first. Or, to be honest, all the cars go and then I go, because it's just safer and I don't want to hold anyone up, and stopped bikes seem to confuse some drivers.) But you wouldn't put a four-way stop on a multi-lane street. Would you? Just picture it. You arrive at the intersection beside another car, and there's a third car on the cross street. What would you do?
And that's exactly what happens to a bike. Except that you also add the fact that a bike takes much longer to accelerate away from the stop (hence our tendency to treat stop signs like 'yields' - slowing up and looking for oncoming traffic, and stopping fully only if there are other vehicles involved. Now you know.) And if you pull away from the stop at the same time as a car, you're hidden from half the traffic at the intersection... until the car speeds up, at which point you're now an unexpected bike in the middle of an intersection.
Plus, as far as I know there is no rule governing which vehicle has the right of way at a stop sign if it's on a four-lane street.
What I usually do is go at the same time as the car next to me (making sure, of course, that they're not turning right - don't get me started on the guy that turned right, yesterday, at this very intersection, without signalling. I noticed the car's rightward drift and guessed that he was going to turn, so hit the brakes. But might not have, if he hadn't been clearly edging toward the corner.) I figure it acts as shelter if nothing else. But one day when I did that - slowed up, admittedly without fully stopping, and then cruised through the intersection beside a car that was crossing at the same time as me - a driver who had been behind me pulled up alongside as I was continuing down the road, to roll his window down and tell me I should have stopped: "a car nearly hit you back there," he said, although I doubt it. Think I would have noticed nearly being hit by a car.
I don't know if there's a solution. But if you think of bikes as traffic, and bike lanes as traffic lanes, there is definitely something awkward and strange about putting a four-way stop in an intersection that amounts to a four-lane road crossing a two-lane. At this particular one, I'd say leave the stop signs up on the generally quiet cross street, and remove the stop signs from Alta Vista. Replace them with yield signs, maybe. Or a traffic circle; seeing as how that stop sign seems, in all honesty, just to be there as a traffic calming measure anyway.