It seems to me that the real issue is rational weighing of reference classes when using multiple models. I want to assign them weights so that they form a good ensemble to build my forecasting distribution from, and these weights should ideally reflect my prior of them being relevant and good, model complexity, and perhaps that their biases are countered by other reference classes. In the computationally best of all possible world I go down the branching rabbit hole and also make probabilistic estimates of the weights. I could also wing it.
The problem is that the set of potential reference classes appears to be badly defined. The Tesla case potentially involves all possible subsets of stocks (2^N) over all possible time intervals (2^NT), but as the dictator case shows there is also potentially an unbounded set of other facts that might be included in selecting the reference classes. That means that we should be suspicious about having well-formed priors over the reference class set.
When I have some sensible reference classes pop up in my mind and I select from them I am doing naturalistic decision making where past experience gates availability. So while I should weigh their results together, I should be aware that they are biased in this way. I should broaden my model uncertainty for the weighing accordingly. But how much I broaden it depends on how large I allow the considerable set of potential reference classes to be, a separate meta-prior.
I don’t think that weights are the right answer—not that they aren’t better than nothing, but as the Tesla case shows, the actual answer is having a useful model with which to apply reference classes. For example, once you have a model of stock prices as random walks, the useful priors are over the volatility rather than price, or rather, the difference between implied options volatility and post-hoc realized volatility for the stock, and other similar stocks. (And if your model is stochastic volatility with jumps, you want priors over the inputs to that.) At that point, you can usefully use the reference classes, and which one to use isn’t nearly as critical.
In general, I strongly expect that in “difficult” domains, causal understanding combined with outside view and reference classes will outperform simply using “better” reference classes naively.
It seems to me that the real issue is rational weighing of reference classes when using multiple models. I want to assign them weights so that they form a good ensemble to build my forecasting distribution from, and these weights should ideally reflect my prior of them being relevant and good, model complexity, and perhaps that their biases are countered by other reference classes. In the computationally best of all possible world I go down the branching rabbit hole and also make probabilistic estimates of the weights. I could also wing it.
The problem is that the set of potential reference classes appears to be badly defined. The Tesla case potentially involves all possible subsets of stocks (2^N) over all possible time intervals (2^NT), but as the dictator case shows there is also potentially an unbounded set of other facts that might be included in selecting the reference classes. That means that we should be suspicious about having well-formed priors over the reference class set.
When I have some sensible reference classes pop up in my mind and I select from them I am doing naturalistic decision making where past experience gates availability. So while I should weigh their results together, I should be aware that they are biased in this way. I should broaden my model uncertainty for the weighing accordingly. But how much I broaden it depends on how large I allow the considerable set of potential reference classes to be, a separate meta-prior.
I don’t think that weights are the right answer—not that they aren’t better than nothing, but as the Tesla case shows, the actual answer is having a useful model with which to apply reference classes. For example, once you have a model of stock prices as random walks, the useful priors are over the volatility rather than price, or rather, the difference between implied options volatility and post-hoc realized volatility for the stock, and other similar stocks. (And if your model is stochastic volatility with jumps, you want priors over the inputs to that.) At that point, you can usefully use the reference classes, and which one to use isn’t nearly as critical.
In general, I strongly expect that in “difficult” domains, causal understanding combined with outside view and reference classes will outperform simply using “better” reference classes naively.