It turns out there are a large family of expectations we can use to build utility functions, including the arithmetic expectation E, the geometric expectation G, and the harmonic expectation H, and they’re all equivalent models of VNM rationality! And we need something beyond that family like Scott’s G[E[U]] to formalize geometric rationality.
Thank you for linking to these different families of means! The quasi-arithmetic mean turned out to be exactly what I needed for this result.
I can answer this now!
Expected Utility, Geometric Utility, and Other Equivalent Representations
It turns out there are a large family of expectations we can use to build utility functions, including the arithmetic expectation E, the geometric expectation G, and the harmonic expectation H, and they’re all equivalent models of VNM rationality! And we need something beyond that family like Scott’s G[E[U]] to formalize geometric rationality.
Thank you for linking to these different families of means! The quasi-arithmetic mean turned out to be exactly what I needed for this result.
Very interesting! I’m excited to read your post.