“In the absence of an oracle, I would end up writing up praise for, and updating towards, your more wrong model, which is obviously not what we want.”
Perhaps I’m missing something, but I think that’s exactly what we want. It leads to eventual consistency / improved estimates of odds, which is all we can look for without oracles or in the presence of noise.
First, strength of priors will limit the size of the bettor’s updates. Let’s say we both used beta distributions, and had weak beliefs. Your prior was Beta(4,6), and mine was Beta(6,4). These get updated to B(5,6) and B(7,4). That sounds fine—you weren’t very sure initially, and you still won’t over-correct much. If the priors are stronger, say, B(12,18) and B(18,12), the updates are smaller as well, as they should be given our clearer world models and less willingness to abandon them due to weak evidence.
Second, we can look at the outside observer’s ability to update. If the expectation is 40% vs. 60%, unless there are very strong priors, I would assume neither side is interested in making huge bets, or giving large odds—that is, if this bet would happen at all, given transaction costs, etc. This should implicitly limit the size of the update other people make from such bets.
“In the absence of an oracle, I would end up writing up praise for, and updating towards, your more wrong model, which is obviously not what we want.”
Perhaps I’m missing something, but I think that’s exactly what we want. It leads to eventual consistency / improved estimates of odds, which is all we can look for without oracles or in the presence of noise.
First, strength of priors will limit the size of the bettor’s updates. Let’s say we both used beta distributions, and had weak beliefs. Your prior was Beta(4,6), and mine was Beta(6,4). These get updated to B(5,6) and B(7,4). That sounds fine—you weren’t very sure initially, and you still won’t over-correct much. If the priors are stronger, say, B(12,18) and B(18,12), the updates are smaller as well, as they should be given our clearer world models and less willingness to abandon them due to weak evidence.
Second, we can look at the outside observer’s ability to update. If the expectation is 40% vs. 60%, unless there are very strong priors, I would assume neither side is interested in making huge bets, or giving large odds—that is, if this bet would happen at all, given transaction costs, etc. This should implicitly limit the size of the update other people make from such bets.