How come the government can value a home more than was paid for the house?
The real answer why the government is "allowed" to do something is because they are the government and they make the rules. There are lots of laws that I think make no sense. I ran into a similar situation to yours. I bought a house during a time when the market in my area was way down. The previous owner had paid $140,000 but I got it for only $80,000. The government appraised it for, I forget the exact number, but over $100,000. I appealed, and the argument I made to the appeal board was that the law says it is supposed to be appraised for "fair market value". The definition of "fair market value" is the amount that a willing buyer would pay to a willing seller, absent special conditions like a sweetheart sale to a relative. The house had been advertised for a higher price and the seller had to drop the price several times before getting an offer, and finally accepting mine. This is pretty much the definition of "fair market value". The appeals board replied that it was not FMV because the market was bad at this particular time and so I got a good deal. I said that that's the definition of market value: it goes up and down as market conditions change. If the market happened to be up when someone bought a house and they had to pay a high price, would the government assess the house at a lower value because that was an unusually high price? I doubt it. They ended up reducing the assessed value, but not to what I actually paid. All that said, arguably a foreclosure sale might be considered special conditions. Prices at a foreclosure sale tend to be lower than "ordinary" sales. In a foreclosure, the bank is usually trying to get rid of the property quickly because they don't want to be in the property-management business, they want to be in the money lending and management business. Of course you could say that sort of thing about conditions surrounding many sales. Maybe the price is low because the seller needed cash now to start a business. Maybe the price is high because the buyer was too lazy to shop around. Maybe the price is low because the buyer is a very skilled negotiator. Etc etc.  My watch just broke and while I was shopping for a new one I found two listings for the exact same watch, I mean exact same manufacturer and model number, identical picture, on the same web site, one giving the price as $24 and the other as $99. What is the market value of that watch? I presume anyone who saw both listings would pick the $24 one, but I presume some number of people pay the higher price because they never see the lower price. In real life there isn't really one, exact, fair market value. That's an abstraction.