I would suggest to think of this not in terms of contribution to the whole, but percentage of ($income - $housing - $food - $stdxpenses). With $stdxpenses covering standard living expenses including energy, water, basic insurance, basic commute.
I would be somewhat surprised (rather flabbergasted) if rich folks paid anywhere close to the percentage that poor people do.
In other words: if you want to compare by measuring contribution, measure tax rate to what's left for that individual's personal use.