Hmm, I’m not sure what I should be taking away from that. You’ve pointed out that the morning and evening lotteries are materially different, but that’s not contentious to me: if uncertainty has costs then those costs have to show up as differences in the world compared to a world without that uncertainty.
I guess the restaurant story failed to focus on the-bit-that’s-weird-to-me, which is that if my friend and I were negotiating over the lottery parameter p, then my mental model of the expected utility boundary as p varies is not a straight line.
To be explicit, the “standard model” of my friend and I having a lottery looks like this, whereas once you account for the costs of increasing uncertainty when p is away from 0 or 1 it ends up looking like this.
Yes, I’m not contending against your fundamental point. In fact, I think that the curve from 0 to 1 can be even stranger than that with discontinuities in it, and that under some circumstances it can even have parts that go above the straight line. Focusing on a specific formula based on entropy doesn’t really match reality and detracts from the main point.
Hmm, I’m not sure what I should be taking away from that. You’ve pointed out that the morning and evening lotteries are materially different, but that’s not contentious to me: if uncertainty has costs then those costs have to show up as differences in the world compared to a world without that uncertainty.
I guess the restaurant story failed to focus on the-bit-that’s-weird-to-me, which is that if my friend and I were negotiating over the lottery parameter p, then my mental model of the expected utility boundary as p varies is not a straight line.
To be explicit, the “standard model” of my friend and I having a lottery looks like this, whereas once you account for the costs of increasing uncertainty when p is away from 0 or 1 it ends up looking like this.
Yes, I’m not contending against your fundamental point. In fact, I think that the curve from 0 to 1 can be even stranger than that with discontinuities in it, and that under some circumstances it can even have parts that go above the straight line. Focusing on a specific formula based on entropy doesn’t really match reality and detracts from the main point.
Fair point re. focusing on a specific formula, I’ll remove that from the post.