It needs to be done in such a way that the total-income curve is monotonically increasing, so recipients never have a disincentive to make a little more money in their job. This should be fundamental and obvious, but because doing it requires just the tiniest bit of linear algebra, our elected representatives are not capable of it. Mind-blowing.
Actually, it mostly shows that the programs are not a system, and were designed separately from each other, with inadequate consideration of their interactions. The fact that they often have overlapping target populations and that benefit reductions due to means-testing are therefore sometimes much greater than 1:1 isn't due to problems with math, its due to the fact that the questions that were asked and which math was deployed to answer weren't even the right questions.
For example, food stamps (SNAP) were made permanent in 1964 as one of the great society programs. WIC came a few years later. I suspect - but have not researched - that you will find this is true for a lot of current welfare programs.
There may be people in power making bad decisions about administering these programs, but I don't believe they were designed to ensnare.
Really wish we'd focus less on what is fair and more on what brings the greatest outcome.