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]
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.
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...