(1) I like Trek, and I'd like to see the owners and writers of Star Trek officially declare that Participatory Economics is what the Federation uses. Why? Because doing this opens up the Star Trek universe to better stories. If the Federation uses a parecon system, we can get stories that involve Federation citizens in their daily routine, and have a reasonable idea what this routine is like. Plus you can have a group of Ferengi trying to buy off Federation citizens to corrupt the Federation Economic system, etc. There's alot of story telling potential here, not only for Star Trek, but for all of science fiction. There is yet to be a published novel that involves parecon in any way, I hope this will change soon.
(2) I'm a pareconist, I guess, and I'd like to promote the idea. Hopefully this website will serve in that function. I think that parecon would work if implemented, and I hope we can all work towards that.
There does exist a website that argues that Star Trek uses a communist system, but the arguments presented there to prove this point can mostly be transferred to arguments that Star Trek is a parecon. Also, given that communism is quite prone to takeover by a coordinator elite, it seems pretty unlikely that the Federation uses it. Also, communism doesn't lend itself well to technological innovation, but parecon does.
Assuming Trek is a parecon explains alot of things (in no particular order)
(1) Trek is NOT capitalist. Captain Kirk specifically in Star Trek IV that they don't use money in the federation. Picard clearly says "the economics of the future are different" when asked about the cost of his ship. It's gotta be something else.
(2) Trek is NOT centrally planned (communist). As above, central planning creates a new ruling class of coordinators (managers, bureaucrats, conceptual workers, etc.). If this happened, the federation would be a terrible place to live, it's not a terrible place to live. Central planning still uses money too. It doesn't encourage technological innovation. The only viable alternative is parecon.
(3) Federation citizens are nice to each other, care about each other, and seem pretty empowered. This sort of thing is encouraged by parecon to the nth degree.
(4) Holoaddiction (being addicted to living in the holodeck) is pretty rare. You could almost believe this in a parecon, because all citizens have enjoyable, empowering work, as well as feelings of solidarity and caring for the rest of humankind. So it's not too much of a stretch to believe that people could find everyday life exciting enough.
(5) As mentioned, parecon jives well with technological innovation.
(6) People are pretty tolerant of other cultures and species, which would be encouraged by parecon.
(7) As above, parecon explains all the major clues we have about the Federation Economic system.
(8) Parecon is pretty just. It would have to be for the federation to have policies of not starting a war, not interfering in other cultures, etc.
(1) First and foremost, Star Trek creators and writers have always maintained that people magically started being nice to one another after first contact with other alien races. Sorry to all the creators and writers, but this is silly. People are products of their environment, leave them in a capitalist environment, and the elites will behave like they do today, terribly that is. You can't expect the kind of world portrayed by Star Trek to exist without an entirely new economic, political, cultural, and kinship systems and institutions. Thus the entire philosophy of Star Trek has been whacky for a long time. Accepting the magical explanation is inconsistent with parecon. Ironically, accepting parecon as the federation system will make it much more realistic (as realistic as a show can be that has sound in space) and better, I think.
(2) One thing that might be inconsistent is that Picard's family seems to own a vineyard, and Sisko's father seems to own a restaurant. In a parecon, ownership of productive assets are not allowed. However, these things could still be mostly run by families through long traditions, and still be collectively owned by all.
(3)Also, since no Star Trek writer has ever heard of parecon, no show or book has ever had a story written with parecon in the background, so no show has addressed issues of hierarchy or anything like that. I don't think it's that important, but I can see why this would lead people to not think parecon suitable for Star Trek.
(4)I'm mostly a Next Generation and Deep Space Nine guy, so I don't know the original series that well, nor Enterprise (I don't get the TV station, poor me :( ). So there might be things in there that are more strikingly inconsistent with parecon.