Another case that violates the preconditions is if the information source is not considered to be perfectly reliable.
Imagine the following scenario:
Charlie repeatedly flips a coin, and tells person A and B the results.
Alice and Bon are choosing between the following hypotheses:
The coin is fair.
The coin always comes up heads.
The coin is fair, but person C only reports when the coin comes up heads.
Alice has a prior of 40% / 40% / 20%. Bob has a prior of 40% / 20% / 40%.
Now, imagine that Charlie repeatedly reports ‘heads’. What happens?
Answer: Alice asymptotes towards 0% / 66.7% / 33.3%; Bob asymptotes towards 0% / 33.3% / 66.7%. Their opinions remain distinct.
There was a good simulation of a more complicated scenario with many agents exhibiting much the same effect somewhere on this site, but I can’t find it. Admittedly, I did not look particularly hard.
Another case that violates the preconditions is if the information source is not considered to be perfectly reliable.
Imagine the following scenario:
Charlie repeatedly flips a coin, and tells person A and B the results.
Alice and Bon are choosing between the following hypotheses:
The coin is fair.
The coin always comes up heads.
The coin is fair, but person C only reports when the coin comes up heads.
Alice has a prior of 40% / 40% / 20%. Bob has a prior of 40% / 20% / 40%.
Now, imagine that Charlie repeatedly reports ‘heads’. What happens?
Answer: Alice asymptotes towards 0% / 66.7% / 33.3%; Bob asymptotes towards 0% / 33.3% / 66.7%. Their opinions remain distinct.
There was a good simulation of a more complicated scenario with many agents exhibiting much the same effect somewhere on this site, but I can’t find it. Admittedly, I did not look particularly hard.