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Sounds like a nightmare to try to explain to someone. Technically it should work, but practically it might be difficult.
Why? To me it'd be much more intuitive. I find brackets quite confusing
The brackets are pretty simple. It's percentages and subtractions. Think "buckets" that spill over in the next when they're full, and each "bucket" has a larger percentage that's taken as taxes. Keep the numbers small so its easier. Imagine that there are three brackets. 0-100$ pays 10% tax. 101-200$ pays 20%. 200$ and more pays 30%.
Someone who wins 150$ pays 10% on the money they made from 0 to 100$, and 20% on the 101st dollar until their last, so they'll win 150-10-10=130$ after tax. They didn't win more than 200$, so no money gets taxed at the third bracket's rate.
Say that person wins 250$ next year. Their first 100$ will result in the exact same 10$ in taxes. Their 100th to 199th dollars will be in the second 20% bracket. Their remaining 50$ falls in the last bracket, so gets taxed 30%. They will therefore this year make 250-10-20-15=205$ after tax.
Said person gets a big promotion and is now making 1000$ the third year. Their first 100$ gets the same 10$ tax, same for their second 200$ with the same 20$ tax. They have 800$ left in the last bracket, which at 30% means 240$. So they'd be winning 1000-10-20-240=730$ that year.
How would an infinitely adjusting tax percentage be intuitive? Brackets are simple. You pay x% on your income in some bracket and y% on your income in a different bracket. You only need simple multiplication and addition to figure out what you would owe.
A continuous bracket could be defined by a single equation. You'd plug in your income and you'd get out your taxation. No need to look up what bracket you are in.
If you expect the average person to be able to understand an algebraic equation better than the existing system, then I’d suggest you get out of your social bubble and meet more ‘average’ people.
I honestly think they'd understand it about as much as they'd currently understand it - that is, not understanding it very much at all. So I think it would be about the same level of understanding but it would make a lot more sense and would be easier to calculate with.
It'd also remove a lot of incentives for squeezing your income/pension contribution to align with certain thresholds (i.e. tax bracket thresholds).
Give it a shot. Let me see an equation.
For example, a sigmoid function (click link for equation). You'd need to mess with the constants to align the function with a range of incomes but the general shape will be the same - a low, almost-zero taxation rate for those who earn the least, rising to a threshold (perhaps even 100%, but a lower value like 75% would probably work as well), giving a high taxation to those who earn the most.
You think the general population is going to have an easier time understanding the sigmoid function that some simple multiplication and addition?
Brackets are lobbied for. You cant lobby a straight line.