The specifics may differ, but assuming a generic and uninspired representative-social-democratic model:
Diopolis wrote:How do you incentivize new housing to be built if the end user doesn't pay?
By state fiat.
Diopolis wrote:Does the government pay for new housing construction at need(and how does the government pay for this)?
Yes, with taxes (and the other usual methods by which a government collects revenue).
Diopolis wrote:If so, what incentivizes the government to prioritize housing quality?
Because if they don't, people will be upset and therefore less inclined to re-elect the sitting government.
Diopolis wrote:What about converting housing in between occupants? Who pays for major repairs, and what incentivizes them to actually do so? Who coordinates distribution of available housing?
The State, for all of these, because if they don't do it properly, see above.
Diopolis wrote:What role do individual preferences play in housing allotment?
Letting the State know in what economic basin you are being educated/employed/etc. in, so the State knows what general region your house ought to be in. Some limited personal choice regarding orientation, height, etc might be indulged, depending on availability
In a capitalist market, sellers who have resources and desire profit come out and compete for the patronage of buyers who have money by offering them services. In a democratic state, sellers who have resources and desire re-election come out and compete for the patronage of citizens who have voting rights by offering them services. The primary difference between the two is that there isn't very much inequality in how many votes any given citizen wields, but there is a vast inequality in how much money they have.
I don't hold Ifreann's opinion that the housing market should be fully decommodified, but it is perfectly possible to run a private housing market and housing provided as a public service in parallel. After all, many civilised countries do the same with education or healthcare - these things are often both a right and a commodity. Why not housing?