I like how you apply game theory to the problem, but I don’t understand why it supports the answer “nay”. The calculations at the beginning of your comment seem to indicate that the “yea” equilibrium gives a higher expected payoff than the “nay” equilibrium, no?
If all ten individuals were discussing the problem in advance the would conclude that nay was better, so, by the rule I set up, when faced with the problem you should say nay.
The problem comes from mixing individual thinking, where you ask what is the best thing for you to do, with group thinking (no relation to groupthink), where you ask what is the best thing for the group to do. The rule I suggested can be expressed as “when individual thinking leaves you with more than one possible solution, use group thinking to decide between them”. Updating on the fact that you are a decider is compulsory in individual thinking but forbidden in group thinking, and problems arise when you get confused about this distinction.
I like how you apply game theory to the problem, but I don’t understand why it supports the answer “nay”. The calculations at the beginning of your comment seem to indicate that the “yea” equilibrium gives a higher expected payoff than the “nay” equilibrium, no?
If all ten individuals were discussing the problem in advance the would conclude that nay was better, so, by the rule I set up, when faced with the problem you should say nay.
The problem comes from mixing individual thinking, where you ask what is the best thing for you to do, with group thinking (no relation to groupthink), where you ask what is the best thing for the group to do. The rule I suggested can be expressed as “when individual thinking leaves you with more than one possible solution, use group thinking to decide between them”. Updating on the fact that you are a decider is compulsory in individual thinking but forbidden in group thinking, and problems arise when you get confused about this distinction.