I'm not sure what you mean.

In Illinois (the state from the article) the assessor is calculating the market value:

Most real property in Illinois must be assessed based on its value on the open market, or its “market value.” This value is the amount at which a property would sell in a competitive and open market... [1]

[1]http://tax.illinois.gov/Publications/LocalGovernment/PTAX100...

Then it likely varies from state to state - or county to county.

See http://www.investopedia.com/articles/tax/09/calculate-proper... for different methods used. As an example, some places merely look at the cost of replacing the house if destroyed.

That's not how it worked where I grew up in Upstate New York. The assessed value was a number way below market value, but assessed values among different houses pretty much differ by the same proportions as the actual market values. I do not know why it is the case.