That’s perfect, I was thinking along the same lines, with a range of options available for sale, but didn’t do the math and so didn’t realize the necessity of dual options. And you are right of course, there’s still quite a bit of arbitrariness left. In addition to varying the distribution of options there is, for example, freedom to choose what metric the forecasters are supposed to optimize. It doesn’t have to be EV, in fact in real life it rarely should be EV, because that ignores risk aversion. Instead we could optimize some utility function that becomes flatter for larger gains, for example we could use Kelly betting.
That’s perfect, I was thinking along the same lines, with a range of options available for sale, but didn’t do the math and so didn’t realize the necessity of dual options. And you are right of course, there’s still quite a bit of arbitrariness left. In addition to varying the distribution of options there is, for example, freedom to choose what metric the forecasters are supposed to optimize. It doesn’t have to be EV, in fact in real life it rarely should be EV, because that ignores risk aversion. Instead we could optimize some utility function that becomes flatter for larger gains, for example we could use Kelly betting.