This raises a couple of interesting questions.
1. How do you stop someone from finding the actual property location by querying that map a bunch of times and averaging the positions returned?
2. Are there any negative consequences for the people whose property a displaced marker ends up on? For example, if someone is using the map lookup to find the home of a rival gang officer in order to do a drive by attack, and I happen to live down the street, I really don't want that marker showing up on my house.
Rather than a displaced marker, maybe divide the map into rectangular or hexagonal regions, and just highlight the region containing the property.