We've discovered that cyclists don't follow laws and that cars don't follow laws either.
Well, what's the solution then?
I found this clip from NPR's Talk of the Nation. The topic is Shared Spaces-- or making changes to streets so users self regulate the changes you're looking for. They discuss removing traffic signs, stop signs, lights, curbs, and instead of separating spaces letting ordinary human interactions--and human communication--govern. It is also noted that you can use texture, materials, landscaping, and street furniture to give ques on expected behavior.
Listen to the clip and leave a comment if you think this will or will not work on market street.