[SilverbeardUnix]

You pay tax based on unimproved land value so what your neighbor builds doesn't matter. In your scenario, for what you're talking about to happen, everyone in the neighborhood needs to be building fourplexes and opening local businesses which would change the makeup of the entire neighborhood and taxes would adjust accordingly. So no, your neighbor building a duplex doesn't spike grandmas taxes. Under the current system, grandmas neighbor building a fourplex can increase her property value and have her paying a higher property tax anyway.

[aeternum]

If the land around you is developed, land value generally goes up.

How are you proposing to calculate land value?

[SilverbeardUnix]

It would take more than just your neighbor developing their land for your land to increase in value. land value taxes calculate the value of the undeveloped land as in land in denser areas is more valuable than suburban land. Unless all of your neighbor are putting up fourplexes changing the entire makeup of the neighborhood, your land value is unlikely to increase. This can't be said of property value where if your neighbor improves their property, your property value and property taxes might increase as a result.