Yes, I now understand.He is right, although there are still a number of drawbacks with having thresholds. I'll describe one of them below.
Only if there is an endless array of thresholds, evenly arranged* and covering all of the range of incomes/ property values/ capital values (for CGT) and so on. In practice, this is never done. As with Property Band G in Council Tax calculations there is always an upper threshold which is below the highest figure by a very considerable way.
*Evenly is the wrong word. I mean arranged in such a way as the curving line on the graph you described remains smooth. This could well mean that the gaps are logarithmic, for all I know. They aren't normally so well thought out, being as they are subject to political whim.
I agree that the community charge (and by the same measure the water rates for those of us who are unmetered) can seem unfair but that's what happens when a fee is a flat amount rather than a % of income or asset value.
I don't understand however why thresholds have to be evenly spaced to be fair. In my mind the unfairness comes when a small increase in asset value or income results in a marginal tax rate of more than 100%. In the UK, stamp duty is the only tax that comes to mind that behaves in that way.
@ddt
Thanks for the clarification on the German income tax codes. It didn't sound right to me but I didn't want to tell a colleague that the didn't understand his own taxes