Our society has voted to get the policy which is most likely to achieve a value of .5 [...]
I think you make a fairly good argument (in iv) about trying to maximise the probability of achieving outcome x where x could vary to being a small number, but I expect futarchy proponents would argue that you can fix this by returning E[outcome] rather than P(outcome > x). So society would vote to get the policy that maximises the expected outcome rather than the probability of an outcome. (Or you could look at P(outcome > x) for a range of x).
I have written a blog post exploring why the prices in a prediction market may not reflect the true probability of an event when the things we want to hedge against are correlated
But I think none of your explanation here actually relies on this correlation. (And I think this is extremely important). I think risk-neutrality arguments are actually not the right framing. For example, a coin flip is a risky bet, but that doesn’t mean the price will be less than 1⁄2 because there’s a symmetry in whether or not you are bidding on heads or tails. It’s just more likely you don’t bet at all because if you are risk-neutral, you value H at 0.45 and T at 0.45.
The key difference is that if the coin flip is correlated to the real economy, such that the dollar-weighted average person would rather live in a world where heads come up than tails, they will pay more for tails than heads.
I have written a bit about this (and related topics) in the past:
https://www.lesswrong.com/posts/5jA3Tvxh2jFcFBzqR/risk-premiums-vs-prediction-markets
I think you make a fairly good argument (in iv) about trying to maximise the probability of achieving outcome x where x could vary to being a small number, but I expect futarchy proponents would argue that you can fix this by returning E[outcome] rather than P(outcome > x). So society would vote to get the policy that maximises the expected outcome rather than the probability of an outcome. (Or you could look at P(outcome > x) for a range of x).
You wrote on reddit:
But I think none of your explanation here actually relies on this correlation. (And I think this is extremely important). I think risk-neutrality arguments are actually not the right framing. For example, a coin flip is a risky bet, but that doesn’t mean the price will be less than 1⁄2 because there’s a symmetry in whether or not you are bidding on heads or tails. It’s just more likely you don’t bet at all because if you are risk-neutral, you value H at 0.45 and T at 0.45.
The key difference is that if the coin flip is correlated to the real economy, such that the dollar-weighted average person would rather live in a world where heads come up than tails, they will pay more for tails than heads.