As the true knowledge of science is kept for the conspiracies then only those that have tried and failed in the conspiracies are able to work on or build technologies as those that have succeeded are busy finding new things and making new technology. To those that have only learned the publicly available knowledge this technology is like magic or religion and as they have never been curious about the conspiracies enough to try to understand the technology it remains that way. The technology provides for their every need and want and while the common people do much of the work that makes the system work they have no clue as to what it is they do or why. For them the founders of businesses, the scientists, and the whatever else the top conspirators are called are as gods that if obeyed provide for every desire and if spurned bring ruin.
Those that failed to reach that elevated status are then as priests; that is the managers and the technicians. As they, the failed, themselves do not understand fully everything that they do they allow for much ritual and elaborate rules to evolve around the technology such that if one is not a member of the conspiracies then not following the ritual can get one banned or forced into gladiator service.
Those in the conspiracies can wear whatever they wish and do whatever they wish with the technology available to them, they are denied access to anything that they have not yet discovered.
Economic: The economic conspiracy has unlocked the secret of predicting the markets with a high degree of accuracy such that only by trading with inside information can one make money by trading on the market. Likewise due to the social rules only those in the conspiracy (or only through the conspiracy) are businesses formed. This leads to moderately inefficient markets such that nearly any common person (or manager for that matter) could tell one of some business they would like to see formed but as they do not see themselves as able to form a business and it is not socially acceptable to do so they wait for some one in the conspiracy to step in and create the desired business. The AI and conspiracy attempt to stay on top of this and are aware of this inefficiency but have not been able to fix it (leaving the top level of that conspiracy empty).
The conspiracies are extremely wealthy as each has access to vast amounts of inside information and each creates unique highly beneficial products and services.
Government The vast wealth and market control of the economic conspiracies has made normal government obsolete. Elections are held in which the winner is known before hand and is powerless to do anything. Luckily due to the vast improvements of the conspiracies no one expects them to do anything so it works out okay.
The legal code slowly morphs into a neofuedalistic system where those that are in the conspiracy are immune against all accusations involving an uninitiated and presumed innocent even among the failed.
However, instead of trial judge or jury a probabilistic model is created with priors that weighs only the empirical evidence to determine who is guilty of what. Once guilt is determined the model simulates the crime to determine lost utility and an equivalent transfer of utility is assigned as punishment. As public gladiator fights provide high positive utility to the spectators and high negative utility to the criminals the most common form of punishment is gladiator fighting for a predetermined number of fights with pain modifiers to ensure a fair punishment. Cryonics and body regrowth ensure one endures the correct number of fights and allows the fights to be to the death.
Cognitive Augmentation to a high intelligence level is done automatically before birth. Basic minimal implants are given while still children but most are reserved until it is known what if any conspiracy will be sought after.
Once it becomes clear that no knowledge is sought after the option is available to turn ones body over to an AI and have the brain disconnected from the rest of the body so that the AI may use the body as an inexpensive cog in farming or manufacturing. The brain is then given infinite pleasure through simulated experiences.
If that is not desired then one must work for ones living and entertainment as a common person. Additional augmentation is given according to the task assigned to you. Family, religious, and sexual activities are only monitored enough to ensure replacement due to accident or suicide. If unlimited children are desired then one is required to join extra planetary colonization efforts.
The conspiracies limit augmentation according to what could provide evidence of information or theories that are being withheld until they are discovered by the initiates.
That is my attempt.
It's "conspiracy".
Utopia and Dystopia have something in common: they both confirm the moral sensibilities you started with. Whether the world is a libertarian utopia of the non-initiation of violence and everyone free to start their own business, or a hellish dystopia of government regulation and intrusion—you might like to find yourself in the first, and hate to find yourself in the second; but either way you nod and say, "Guess I was right all along."
So as an exercise in creativity, try writing them down side by side: Utopia, Dystopia, and Weirdtopia. The zig, the zag and the zog.
I'll start off with a worked example for public understanding of science:
Disclaimer 1: Not every sensibility we have is necessarily wrong. Originality is a goal of literature, not science; sometimes it's better to be right than to be new. But there are also such things as cached thoughts. At least in my own case, it turned out that trying to invent a world that went outside my pre-existing sensibilities, did me a world of good.
Disclaimer 2: This method is not universal: Not all interesting ideas fit this mold, and not all ideas that fit this mold are good ones. Still, it seems like an interesting technique.
If you're trying to write science fiction (where originality is a legitimate goal), then you can write down anything nonobvious for Weirdtopia, and you're done.
If you're trying to do Fun Theory, you have to come up with a Weirdtopia that's at least arguably-better than Utopia. This is harder but also directs you to more interesting regions of the answer space.
If you can make all your answers coherent with each other, you'll have quite a story setting on your hands. (Hope you know how to handle characterization, dialogue, description, conflict, and all that other stuff.)
Here's some partially completed challenges, where I wrote down a Utopia and a Dystopia (according to the moral sensibilities I started with before I did this exercise), but inventing a (better) Weirdtopia is left to the reader.
Economic...
Sexual...
Governmental...
Technological...
Cognitive...