Your boolean disagreement is relevant because it's actionable. Suppose that:
In this case, Bob is much closer to Claire than to Alice in terms of their beliefs. But Bob agrees with Alice about the correct action, which is often the thing where disagreement actually matters.
(Politics-related examples are left as exercises for the reader).
I think this is definitely an effect, but I do not think that Bughouse would have been my first example for 'a game where you need to cooperate with random other people online and can be sabotaged by their inexplicable ineptitude.'
See e.g. this Reddit meme.
This does not sound to me like good advice in general? It could work with a small, driven team on a single focused project who wants to be sure everyone has hands on everything. But in general, specialization is an extremely powerful tool that we use to accomplish things we cannot accomplish alone. I would not benefit from insisting on understanding the whole fertilizer production supply chain before I could eat breakfast.
You seem to be conflating 'amount of money paid to the worker as salary' with 'amount of capital used to equip the worker'.
...I would say that the Soft PNR has clearly already occurred?
They will show you the money if you use the new app Neon Mobile to show the AI companies your phone calls, which shot up to the No. 2 app in Apple’s app store. Only your side is recorded unless both of you are users, and they pay 30 cents per minute, which is $18 per hour. The terms let them sell or use the data for essentially anything.
I feel like this paragraph should at least mention the whole 'they have already accidentally leaked all your data' thing.
I have not played Secret Hitler specifically, but in similar games (Mafia and Resistance) it is not in fact the case that members of the majority team should immediately share all information, and some of the best plays I've seen have involved members of the majority bluffing the minority.
(With that said, everyone following both of the first two bullets on your list above seems like clearly not a Nash equilibrium).
...but now the winner is a four-and-a-half-way tie. Just take the credit, it'll be neater. :P
Another downside of this strategy is that a political faction not currently perceived by voters as 'in power' has an incentive to use any power they do have to actively worsen the lives of voters, who will blame their opposition.