That's not a bad idea. Tax rate is X. First house is X. Second house is XY, third house is XY*Y, etc.

Problem is property rates are usually city, county, state so you're not going to see consistency between them.

I deal with a lot of small business owners and it's amazing how many of them have second homes. These guys are well-off but not what you think of as ultra wealthy. I think housing has been such a high-return investment that both corporations and individuals have been buying up houses they don't need.

Most states in the US I believe have homestead exemptions for property tax on your primary residence. Maybe if they just jacked the prop tax way up on anyone or entity that owns more than one single family property that would make it a less enticing investment.