Some options:

a) Also using competition, prices and money, but with factories, companies and lands organized by worker's cooperatives, with the profit shared according with some logic not based in mere property.

b) Using only prices and money while keeping updated data about production and consumption, and updating prices based in these data. Perhaps easier with modern technology than in the past. The information about these things can propagate in wires and communication means like the other kind of information that the society needs.

I think that a) already happens when a company shares its profits with the workforce. Mere competition will force the competitors of such a company to do that as well to attract talent.

Item b) sounds like capitalism and blockchain to me :)

About item c), heuristics and politics don't go well together, according to my intuition.

But these are just my opinions. This is a fascinating topic.

There were some nasty edits from the parent

Precisely. "Prices and money" is the "free market" part. The "socialism" part means "collective/social ownership of companies and means of production".