Here's how it's done in Ontario where I live:
1. Assessed value ≠ market value. Assessed value is determined by some criteria such that sqft, #rooms, desirability of neighbourhood, pools, etc correlate with the final value.
2. Actual value doesn't matter at all. If everyone's assessed values go up 10% in the municipality, property tax bills change by $0. What matters is the relative assessed values. They determine how much of a city's tax bill the household pays.
3. The actual process for determining the tax bill: city comes up with a total figure to be collected. City sums all assessed values of all properties. Divide former by latter to get a multiplier (e.g. 1.355%). That multiplier times assessed value is your property tax. (It's a bit more complicated because they collect slightly different amounts from different property types).
Is it different in California?
This means that two side by side buildings can have assessed values differing by orders of magnitude. This has all the inequitable downstream consequences you would expect.
We might consider moving to a looser market, and therefore opening up one more house in a tight market, but we're retired and a large increase in property tax (plus potentially larger increases every year if it's outside California) is a serious disincentive for us.
Prop 13 is friction that resists the smoothing out of conditions across regions. It reduces market efficiency.
p.s. - It doesn't help the housing situation that we have access to incredible natural features all around us, but that's more about California's demand side.
It is different in California on all three points listed.
In California the assessed value is the purchase price (thus, market value) on year zero (when you buy it). From there on assessed value goes up 2% every year.
The base tax is 1% of the assessed value. (Actual property tax is higher because they can tack on all kinds of fees).
So if you buy a $1M home, your taxes this year are $10K (plus other local fees). Next year it will be $10.2K and so on.