Any maximum that is set high enough to let a flat tax theoretically work, isn't going to be doing anything meaningful for the people who get it, these are people who have more money saved than I am ever likely to see (and thats taking the cumulative value of every piece of money I see in my lifetime). That money does nothing for them (or for anyone else for that matter), it just sits there, possibly in some form of investment, possibly not, making them even more money they have no use for.
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There are only so many luxury jets and mansions you can own. This is why you don't live magnitudes of order better no matter how much money you have. That benefit doesn't exist, once you max out the lifestyle scale, you've won the game.
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Or to look at it from the perspective of it seems wrong to have one guy pay for loads of strangers, I doubt that guy is giving a benefit to society proportional to the combined input of the load of strangers he'd be "paying" for either, so why is his income so much higher to start with ?
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Conversely a maximum thats low enough that it wouldn't just be removing theoretical money would result in so little tax income it would be useless, most of the world's wealth is owned by a very tiny percentage of the population. And thats unlikely to change while you have a "free market" (a truly free market remains free only until the vagaries in the market, or forces outside the market, produce a defacto ruler) system.
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None of this is to say I think this is a good solution or see a better solution. I've yet to see any social, political or economic measure that is going to survive contact with people. Once you accept that some people aren't going to do the right thing, you need somebody to make sure they will , but these somebodies are people too and no more likely to do the right thing than those who they supervise and given that its easier to accumulate power if you're a liar and a cheat but you look and/or sound good/believable/honest doing it than actually *being* honest, the probability is going to very quickly be that they are on average worse.