Lets say P(h) is the price that a home fetches after being listed, O(h) is the price that an owner expects to get from selling the home, and Z(h) is the price t

Lets say P(h) is the price that a home fetches after being listed, O(h) is the price that an owner expects to get from selling the home, and Z(h) is the price that Zillow expects to get if they sell the home. An owner will sell to Zillow when O(h) < Z(h). They will not sell when O(h) > Z(h). Zillow's outcome would then be (P(h) - Z(h)) * (Z(h) >= O(h)). The extremely important thing to note is that this is an asymmetric information game. Therefore O(h) < Z(h) is going to be self-selected such that O(h) < Z(h) because P(h) is closer to O(h) then Z(h) is to P(h). If Z(h) was actually able to be a reliable and better estimate of O(h) then it would mean that P(h) wasn't determined by information available to O(h) that was not also available to P(h). The market would already offer this value to O(h). So O(h) value is going to be reflective of Z(h). Its only if the non-public information changes the value that O(h) != Z(h).