I keep hearing about taxes being more progressive than they used to be because the rich pay a larger share of total taxes.
For this example, assume taxes on the Poor are 10% and taxes on the Rich are 30%.
Scenario A: GDP is 1000. Rich (a small number of people) receive 600, Poor (a large number of people) receive 400.
Taxes: Rich pay 180, poor pay 40, total is 220, Rich share is 180/220 = 82%
Now do nothing more than redistribute income from Poor to Rich:
Scenario B: GDP is 1000. Rich (a small number of people) receive 800, Poor (a large number of people) receive 200.
Taxes: Rich pay 240, Poor pay 20, total is 260, Rich share is 240/260 = 92%
Some people have found a way to argue that because the share of taxes paid by the wealthy is higher under B, 92% instead of 82%, and because the Rich pay more, 240 instead of 180, the burden on the Rich has risen. I'll take that burden if they don't want it.
It's also possible to cut taxes. Starting from scenario A once again, let taxes fall to 25% for the Rich and 5% for the Poor, and redistribute income in the same way as in B:
Scenario C: GDP is 1000. Rich (a small number of people) receive 800, Poor (a large number of people) receive 200.
Taxes: Rich pay 200, Poor pay 10, total is 210, Rich share is 200/210 = 95%
Now the Rich pay an even larger share of total taxes even their tax rate has fallen, they pay 95% instead of 92% under scenario B. Their "burden" has increased since taxes increased from 180 under scenario A to 200 under scenario C while the taxes of the Poor fell from 40 to 10, and the percentage of total taxes paid by the Rich increased from 82% to 95%. Once again, if the Rich feel burdened by this deal, I'll take the extra income and pay the lower tax rate. No problem.