This is how I understand Michigan property taxes:
Say we decide that the city should deliver each Ann Arbor resident a fresh pie every week, and we vote in a 1.5-mill property tax to fund that.
Suppose you bought a house this year. Take its market value, and divide it by two. That's called the "assessed value" of your house. (Why? I have no idea.)
Take 1.5 thousandths of that assessed value. That's your property tax.
So, for a $380,000 house (about the Ann Arbor median as of this writing), the assessed value would be $190,000 (half of $380,000), and the pie millage would cost you $285 a year ($190,000 times 1.5 divided by 1000).
That works for the first year in your house. But we should actually be using the "taxable value". The taxable value starts out the same as the assessed value (half the market value), but it is only allowed to increase by inflation (CPI) or 5%, whichever is less. If you modify the house (say, you make an addition), the value of the addition is also added to the taxable value (explanation from Ann Arbor Asessing office).
Ann Arbor market values have gone up faster than inflation over the years, so if you pick a property someone's been living in a while and look it up in the online property tax database, you'll see that the taxable value is likely lower than the assessed value.
When the house is sold, the taxable value will be "uncapped", and the next owner's taxable value will reset to the assessed value.
This limit on the growth of taxable values was imposed by Proposal A in 1994.
There's also a second limit which affects the total amount of tax that can be collected from a given millage. That amount is *also* limited to the lesser of inflation or 5%.
So if the total taxable value of all Ann Arbor properties is 5.5 billion, then the 1.5 mill pie tax will collect 1.5 thousandths of that, or 8.25 million. If Ann Arbor's total taxable value increases by more than inflation, then the millage rate is automatically decreased to ensure the total collected is no more than 8.25 million plus inflation. So the 1.5 mill pie tax may eventually become a 1.4 mill pie tax, etc.
This limit was put into place by the Headlee Amendment in 1978. The automatic decrease in millage rate is called a "Headlee rollback".
There's an important exception to this limit: it doesn't apply to new construction. Just as proposition A allows a new addition to your house to increase its taxable value, the Headlee Amendment allows the city to add revenue from any new construction. This makes sense--new construction is going to require new pie deliveries, after all.
All of this has some rather interesting affects on municipal finances--a subject for another post....