To create a real, global economic democracy, you'd have to put economic decision-making power in the hands of local people themselves, everywhere.  This would mean, first of all, granting them control over the issuance and use of their currency, and secondly, putting them collectively in charge of the means of production.  Once they have that, what kind of bribe or pressure would dislodge them from tasks of ecosystem co-existence?

How do you ensure it stays that way? That is, is the system stable against a local community reverting to a capitalist political economy and infecting the rest?

Societies in the capitalist past were concerned with "progress," the ultimate triumph of science and technology in increasing the productivity of human labor to bring technological utopia into being.  The scientific paradigm that was to bring "progress" into being was based on mechanics, as the various sciences were created to fine-tune the economic and physical machines of world society, to make them ever-more-efficient producers of the dreamed-of technological utopia.

It is rather sad that out of the Enlightenment idea of "progress" have come both capitalism and communism, whose practical realisations in the 20th have both proven totally ecologically unsustainable.

The ultimate result of this trend will be the ecological dystopia described, in part, by Mark Lynas in Six Degrees, in which climatic disruption is completely out of control, eventually leading to the breakdown of civilization and the release of the methane hydrates from beneath the ocean floors.  The "Communist" societies were no different in this regard.

When the capital development of a country becomes a by-product of the activities of a casino, the job is likely to be ill-done. — John M. Keynes