Simplistic answers (such as equal dollar burdens) seem to work very well for simplistic minds. But such answers aren't really answers because they fall apart when you try to implement them.
For an example of why a tax with a flat dollar amount, the same for each person, won't work consider a country with 10 citizens that costs $20 per year to operate. Total personal income is $2,000 so the total tax burden is just 1% of total personal income. Not bad at all. $2 per person per year.
But that income isn't distributed across the citizens uniformly. Two citizens are very poor, two are very rich, and the other six are somewhere in the middle, something like
Two @ $1
Two @ $2
Two @ $20
Two @ $100
Two @ $877
It's not only not fair to tax everyone $2, it's not possible. That's why the rich pretty much have to have a higher tax burden than the very poor.
A comment talks about John Kerry as a billionaire. His wife is the one that's rich, not him.
The same commenter argues for a flat tax, where everyone pays the same percentage. That also falls apart if you have large dispersion in income for the same reason having everyone pay the same amount falls apart -- to those at the very low end the tax might mean skipping a few meals.
This post had been a response to a thread in rec.gambling.poker where there was a lot of debate about "fair" taxation. I often turn a discussion group post into a blog post. My point was that we're never going to agree on what fair means.