I think if you asked the typical economist for their views on housing support for low-income households, you would hear the following preference relationship. Ed Glaesar makes this point in his paper on Rethinking Federal Housing Policy
$$ \text{Cash} \gg \text{Vouchers} \gg \text{Project Based}
$$
The justification is that from EC101, cash is preferred to “in-kind” assistance because it expands the consumers choice set ($F$) — with a housing voucher, tenants only have to pay 30% of their income on rent.
$$ \underset{x \in F}{\text{maximize}} \ U(x, \alpha) $$
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