Great work! Your problem statement seems to be on the right track. But it’s not very clear why a specific polynomial would be a good answer, because the simulation model described in section 3 looks a little arbitrary… or maybe I have missed some obvious argument.
Thanks! The polynomial rules are approximations to my attempted calculation of the optimal rule. They are proper scoring rules on their own. They look close to optimal, and there is something to be said for simplicity. Deeper theory would be nice though...
What about the simulations stands out as particularly arbitrary? Presumably how agents form predictions about the opinions of others. Without stronger assumptions on agents’ rationality, it’s hard not to be little ad-hoc.
Great work! Your problem statement seems to be on the right track. But it’s not very clear why a specific polynomial would be a good answer, because the simulation model described in section 3 looks a little arbitrary… or maybe I have missed some obvious argument.
Thanks! The polynomial rules are approximations to my attempted calculation of the optimal rule. They are proper scoring rules on their own. They look close to optimal, and there is something to be said for simplicity. Deeper theory would be nice though...
What about the simulations stands out as particularly arbitrary? Presumably how agents form predictions about the opinions of others. Without stronger assumptions on agents’ rationality, it’s hard not to be little ad-hoc.