Granular progressive taxation is the best answer to your question.
Trying to define buckets with arbitrary thresholds is futile.
It greatly benefits the top outliers, since the top bucket will have a huge disparity between its strictly defined lower bounds, and an infinite upper bound.
There's no need to "define rich". A formula without defined bounds (this is the most important part) should determine how much tax you pay, and it shouldn't discriminate between different forms of income. More importantly, all net worth gains should be taxed equally.
Pretty sure they're getting at what the wealth is stored in, not monetary bounds. Those are the details that often get ignored when the "tax the rich" soundbite is used.
Well, these are really difficult implementation details to agree upon. There's no chance anyone will agree to something like this without seeing those details.
Unironically I have watched this repeat out amongst friends and colleagues all my life. People with $5 million homes that are below average (but consider themselves to be about average globally at least) because there are houses worth 10 mil in the same street.
How do you define rich?