Not saying I support the original idea, but there's objective, widely agreed-upon definitions for poverty, so it should be possible to transfer these to define low income.

> objective, widely agreed-upon definitions for poverty

No, there aren’t; this is a political line that doesn’t make any sense at all. This is why “livable wage” is a phrase: just getting above the poverty line does not imply you can live on your income. The poverty line is pegged too low to be meaningful, at least here in US.

Like everything that exists in the real world, it doesn't have to be perfect.

...right, but if you don't care about how accurate it is, the value of distinguishing people is questionable.

The widely agreed upon definition of poverty varies hugely from country to country.