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CannibalSmith comments on Individual vs. Group Epistemic Rationality - Less Wrong
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Alternatively, they each roll an appropriately sided die and get on with the task if the die comes up one.
D20, naturally:
Better than random: They are each in a rotation that assigns such tasks to one agent as they come up.
That would require coordination.
The random assignment also requires coordination. The only reason an agent in the group would accept the chance that it has to do the work is that the other agents accept the chance for themselves.
But why are we worrying so much about this? We actually can coordinate.