Shouldn’t the king just make markets for “crop success if planted assuming three weeks” and “crop success if planted assuming ten years” and pick whichever is higher? Actually, shouldn’t the king define some metric for kingdom well-being (death rate, for instance) and make betting markets for this metric under his possible roughly-primitive actions?
This fable just seems to suggest that you can draw wrong inferences from betting markets by naively aggregating. But this was never in doubt, and does not disprove that you can draw valuable inferences, even in the particular example problem.
These would be good ideas. I would remark that many people definitely do not understand what is happening when naively aggregating, or averaging together disparate distributions. Consider the simple example of the several Metaculus predictions for date of AGI, or any other future event. Consider the way that people tend to speak of the aggregated median dates. I would hazard most people using Metaculus, or referencing the bio-anchors paper, think the way the King does, and believe that the computed median dates are a good reflection of when things will probably happen.
It seems like the moral of this parable should be “don’t make foolish, incoherent hedges” — however, the final explanations given by Eternidad don’t touch on this at all. I would be more satisfied by this parable if the concluding explanations focused on the problems of naive data aggregation.
The “three reasons” given are useful ideas, but the king’s decision in this story is foolish even if this scenario was all three: a closed game, an iterated game, and only a betting situation. (Just imagine betting on a hundred coin flips that the coin will land on its edge every time.)
Shouldn’t the king just make markets for “crop success if planted assuming three weeks” and “crop success if planted assuming ten years” and pick whichever is higher? Actually, shouldn’t the king define some metric for kingdom well-being (death rate, for instance) and make betting markets for this metric under his possible roughly-primitive actions?
This fable just seems to suggest that you can draw wrong inferences from betting markets by naively aggregating. But this was never in doubt, and does not disprove that you can draw valuable inferences, even in the particular example problem.
These would be good ideas. I would remark that many people definitely do not understand what is happening when naively aggregating, or averaging together disparate distributions. Consider the simple example of the several Metaculus predictions for date of AGI, or any other future event. Consider the way that people tend to speak of the aggregated median dates. I would hazard most people using Metaculus, or referencing the bio-anchors paper, think the way the King does, and believe that the computed median dates are a good reflection of when things will probably happen.
Agreed.
It seems like the moral of this parable should be “don’t make foolish, incoherent hedges” — however, the final explanations given by Eternidad don’t touch on this at all. I would be more satisfied by this parable if the concluding explanations focused on the problems of naive data aggregation.
The “three reasons” given are useful ideas, but the king’s decision in this story is foolish even if this scenario was all three: a closed game, an iterated game, and only a betting situation. (Just imagine betting on a hundred coin flips that the coin will land on its edge every time.)