how is 60% of median income affordable?—NUMTOT comment

If you think that "60% AMI" housing charges 60% of the area median income, I agree that doesn't sound affordable! The problem is, "affordable housing" (and "60% of area median income") as an improper noun, a technical term with a defined meaning that differs from how we normally use the words.

When housing is described as "affordable", that means it costs 30% of some specific income. If it's a "60% AMI" unit, that means it's affordable to someone making 60% of the area median income. For example, a 60% AMI unit in an area with a median income of $100k would be 60% * 30% * $100k/y or $18k/y, which is $1500/month. A 30% AMI unit would be half that, at $750/month. If you don't know about the factor of 30% thing you end up thinking all this housing is ~3x more expensive!

That said, this is a mildly silly way to do it: percentages of a median rarely make sense, and the right way to do this is probably with percentiles. Instead of targeting affordable housing at, say, the 60% of median income, we should target a 30th-percentile income. This is much more robust to changes in the shape of the income distribution, especially in cases where areas get into some sort of bimodal situation where a bit more than half the residents are making a lot and a smaller but significant number are making much less.