Ideally, a reputation income economy would be a contribution based income economy. But since humans are quite fallible, this ideal won’t be reached in practice. The system should adopt to make that approximation better and better, however.
The basic problem is how to measure “contribution”. Such measures are very much subjective. And trying to measure some objective metrics can easily lead to perverse incentives. This is why subjective reputation is still one of the best metrics we can use. It’s not perfect, but it’s not much worse than the best reasoning done by humans.
Hehe, yes, many “altruists” would certainly hope for that 
Creating such a formula is quite hard and fraught with problems, see above.
I often hear from alternative reputation systems that are based on formulas or algorithms. They don’t convince me, because it’s easier to cheat algorithms that to cheat people. Also, the problem of perverse incentives is minimized with reputation. Sure, people can have “perverse values”, but that’s a different problem that needs to be addressed separately