"Conspiracy theory" is nothing more/less than attributing the cause of something to manipulation by some (usually secret) group, i.e. a conspiracy. Some are correct, some are wrong.
Believing the Earth is flat isn't a conspiracy theory; believing that a secret organisation is suppressing this knowledge in favour of a false globe model is a conspiracy theory.
Believing that certain social structures/institutions disadvantage the poor isn't a conspiracy theory; believing that these are consciously perpetuated by the richest, through media control, political influence, etc. is a conspiracy theory.
There's also "conspiratorial thinking", which is distinct from any individual theory. This is a form of incorrect/irrational reasoning, whose chains of argument tend to produce conspiracy theories. A common example is getting logical implications the wrong way round, i.e. treating Theory -> Observation ("if atmospheric CO2 spontaneously condensed into dirty clothes, it would explain why my laundry basket keeps filling up") as if it were Observation -> Theory ("since my laundry basket does keep filling up, that means CO2 does condense into dirty clothes!").
Conspiratorial thinking is dangerous, since it allows any observations to be used as "proof" of basically any statement; including mutually-inconsistent ideas. Incorporating more and more of these into a single worldview requires adding epicycles and exceptions; more extraordinary, convoluted coincidences; requiring a state of affairs that is incredibly unlikely to occur by chance. The fixed-point of such reasoning is that it's not chance, but is instead engineered by someone. This is a stable solution, since any evidence to the contrary is just "proof" that it's a wider conspiracy; or involves more powerful people; or advanced secret technology; or aliens; or divine intervention; etc.
PS: Whilst implications don't logically imply their inverse; they do provide statistical evidence of their inverse. In other words, a full laundry basket isn't proof of CO2 condensation, but it is evidence. The conspiratorial mistake is to avoid normalising this evidence by the theory's prior probability. Specifically, my belief in CO2 condensation after seeing a full laundry basket should be the probability that CO2 condensation would cause it (~100%), divided by the probability of seeing a full laundry basket regardless of cause (~90%), multiplied by my previous belief that CO2 condenses into dirty clothes (~0%). Whilst the division by 90% will slightly boost my belief, that final multiplication will dominate; ensuring it stays near zero.
PPS: The conspiracy theory that the rich maintain societal systems that disadvantage the poor doesn't require conspiratorial reasoning; e.g. we can look at how much is donated to progressives/conservatives and their respective policies, etc. In contrast, maintaining a belief that the Earth is flat, despite all of the clear evidence to the contrary, requires some form of irrationality, such as conspiratorial thinking.
I agree about conspiratorial thinking, I think you wrote a good exposition on that subject, and I think the way you incorporated Bayesianism is interesting.
I disagree with the part where you say "merely," a conspiracy theory plays a particular role within political discourse.
Conspiracy theories are intimately connected with power relations and ideology. They are also syncretic (or at least, the ones that fail to be perish) - they can incorporate any idea and even contradictory ideas and accommodate them, and the contradictions only serve to reinforce the theory rather than weaken it. That's very different than other kinds of "theory".
True, the dynamics I stated are pretty broad (scarily so!): they don't describe why any particular set of ideas will take hold or not. The ones which appear will certainly depend on politics, as various goals/agendas are pushed (some good, some bad; subjectively speaking). There's also an aspect of cultural darwinism, that certain theories/agendas/politics are good at "reproducing" and others go "extinct".
I suppose the best we can hope for is to try and remain grounded in empiricism; call out incorrect arguments when we notice them (even for causes we agree with; we should prefer alternative, better arguments); and always allow for the possibility that we're wrong ;)
Believing the Earth is flat isn't a conspiracy theory; believing that a secret organisation is suppressing this knowledge in favour of a false globe model is a conspiracy theory.
Believing that certain social structures/institutions disadvantage the poor isn't a conspiracy theory; believing that these are consciously perpetuated by the richest, through media control, political influence, etc. is a conspiracy theory.
There's also "conspiratorial thinking", which is distinct from any individual theory. This is a form of incorrect/irrational reasoning, whose chains of argument tend to produce conspiracy theories. A common example is getting logical implications the wrong way round, i.e. treating Theory -> Observation ("if atmospheric CO2 spontaneously condensed into dirty clothes, it would explain why my laundry basket keeps filling up") as if it were Observation -> Theory ("since my laundry basket does keep filling up, that means CO2 does condense into dirty clothes!").
Conspiratorial thinking is dangerous, since it allows any observations to be used as "proof" of basically any statement; including mutually-inconsistent ideas. Incorporating more and more of these into a single worldview requires adding epicycles and exceptions; more extraordinary, convoluted coincidences; requiring a state of affairs that is incredibly unlikely to occur by chance. The fixed-point of such reasoning is that it's not chance, but is instead engineered by someone. This is a stable solution, since any evidence to the contrary is just "proof" that it's a wider conspiracy; or involves more powerful people; or advanced secret technology; or aliens; or divine intervention; etc.
PS: Whilst implications don't logically imply their inverse; they do provide statistical evidence of their inverse. In other words, a full laundry basket isn't proof of CO2 condensation, but it is evidence. The conspiratorial mistake is to avoid normalising this evidence by the theory's prior probability. Specifically, my belief in CO2 condensation after seeing a full laundry basket should be the probability that CO2 condensation would cause it (~100%), divided by the probability of seeing a full laundry basket regardless of cause (~90%), multiplied by my previous belief that CO2 condenses into dirty clothes (~0%). Whilst the division by 90% will slightly boost my belief, that final multiplication will dominate; ensuring it stays near zero.
PPS: The conspiracy theory that the rich maintain societal systems that disadvantage the poor doesn't require conspiratorial reasoning; e.g. we can look at how much is donated to progressives/conservatives and their respective policies, etc. In contrast, maintaining a belief that the Earth is flat, despite all of the clear evidence to the contrary, requires some form of irrationality, such as conspiratorial thinking.