To reiterate on the original reply, a land value tax is on the value of the land your apartment sits on, but crucially, not on the value of the apartment. If there's a derelict tyre place next door that's on the same area of land and selling for significantly less, your entire building combined pay the same LVT as its owner.

Why would you assume that a LVT would be lower than current property taxes? If your land is built up the same as the average density of the surrounding area, then you probably were already paying comparable taxes to all your neighbors and your taxes should be unchanged under LVT.

I didn't actually say that. I said that if you have an apartment you'd pay less than a derelict tyre place on the same amount of land. If you live in high density residential apartments you'll pay less than lower density neighbours.

If the entire area is equally high density, then congratulations, it sounds like you live in a very desirable location in the middle of a lot of public and private infrastructure: if that's the case, you should be taxed, to encourage even higher density development and even more productive use of the land you're on.

Aha! we'll here's the joy of different types of averages / https://en.wikipedia.org/wiki/Jensen%27s_inequality

How do we take the average density? Is it the average height weighted by land area, or floor area?

"average height of building on a piece of land" vs "average height of building a piece of floor is in"

Well, unless all buildings are the same height, the second average will always be higher, because taller buildings have more floor!

Most people would go with the former for the average. And it does make sense in general to average over the fixed thing. But that mean building will pay a greater portion of the total tax revenue than before.