The article on expected value theory incorrectly cites the VNM theorem as a defense of maximizing expected value. The VNM theorem says that for a rational agent, there must exist some measure of value for which the rational agent maximizes its expectation, but the theorem does not say anything about the structure of that measure of value. In particular, it does not say that value must be linear with respect to anything, so it does not give a reason not to be risk averse. There are good reasons for altruists to have very low risk aversion, but the VNM theorem is not a sufficient such reason.
Edit: I see the article on risk aversion clarifies that “risk aversion” means in the psychological sense, but without that context, it looks like the expected value article is saying that many EAs think altruists should have low risk aversion in the economic sense, which is true, an important point, and not supported by the VNM theorem. Also, the economics version of risk aversion is also an important concept for EAs, so I don’t think it’s a good idea to establish that “risk aversion” only refers to the psychological notion by default, rather than clarifying it every time.
Edit 2: Since this stuff is kind of a pet peeve of mine, I’d actually be willing to attempt to rewrite those articles myself, and if you’re interested, I would let you use and modify whatever I write however you want.
Hi Alex, thanks for the comment, great to pick up issues like this.
I wrote the article, and I agree and am aware of your original point. Your edit is also correct in that we are using risk aversion in the psychological/pure sense, and so the VNM theory does imply that this form of risk aversion is irrational. However, I think you’re right that, given that people are more likely to have heard of the concept of economic risk aversion, the expected value article is likely to be misleading. I have edited to emphasise the way that we’re using risk aversion in these articles, and to clarify that VNM alone does not imply risk neutrality in an economic sense. I’ve also added a bit more discussion of economic risk aversion. Further feedback welcome!
Even though the last paragraph of the expected value maximization article now says that it’s talking about the VNM notion of expected value, the rest of the article still seems to be talking about the naive notion of expected value that is linear with respect to things of value (in the examples given, years of fulfilled life). This makes the last paragraph seem pretty out of place in the article.
Nitpicks on the risk aversion article: “However, it seems like there are fewer reasons for altruists to be risk-neutral in the economic sense” is a confusing way of starting a paragraph about how it probably makes sense for altruists to be close to economically risk-neutral as well. And I’m not sure what “unless some version of pure risk-aversion is true” is supposed to mean.
Thanks, I’ve made some further changes, which I hope will clear things up. Re your first worry, I think that’s a valid point, but it’s also important to cover both concepts. I’ve tried to make the distinction clearer. If that doesn’t address your worry, feel free to drop me a message or suggest changes via the feedback tab, and we can discuss further.
The article on expected value theory incorrectly cites the VNM theorem as a defense of maximizing expected value. The VNM theorem says that for a rational agent, there must exist some measure of value for which the rational agent maximizes its expectation, but the theorem does not say anything about the structure of that measure of value. In particular, it does not say that value must be linear with respect to anything, so it does not give a reason not to be risk averse. There are good reasons for altruists to have very low risk aversion, but the VNM theorem is not a sufficient such reason.
Edit: I see the article on risk aversion clarifies that “risk aversion” means in the psychological sense, but without that context, it looks like the expected value article is saying that many EAs think altruists should have low risk aversion in the economic sense, which is true, an important point, and not supported by the VNM theorem. Also, the economics version of risk aversion is also an important concept for EAs, so I don’t think it’s a good idea to establish that “risk aversion” only refers to the psychological notion by default, rather than clarifying it every time.
Edit 2: Since this stuff is kind of a pet peeve of mine, I’d actually be willing to attempt to rewrite those articles myself, and if you’re interested, I would let you use and modify whatever I write however you want.
Hi Alex, thanks for the comment, great to pick up issues like this.
I wrote the article, and I agree and am aware of your original point. Your edit is also correct in that we are using risk aversion in the psychological/pure sense, and so the VNM theory does imply that this form of risk aversion is irrational. However, I think you’re right that, given that people are more likely to have heard of the concept of economic risk aversion, the expected value article is likely to be misleading. I have edited to emphasise the way that we’re using risk aversion in these articles, and to clarify that VNM alone does not imply risk neutrality in an economic sense. I’ve also added a bit more discussion of economic risk aversion. Further feedback welcome!
Even though the last paragraph of the expected value maximization article now says that it’s talking about the VNM notion of expected value, the rest of the article still seems to be talking about the naive notion of expected value that is linear with respect to things of value (in the examples given, years of fulfilled life). This makes the last paragraph seem pretty out of place in the article.
Nitpicks on the risk aversion article: “However, it seems like there are fewer reasons for altruists to be risk-neutral in the economic sense” is a confusing way of starting a paragraph about how it probably makes sense for altruists to be close to economically risk-neutral as well. And I’m not sure what “unless some version of pure risk-aversion is true” is supposed to mean.
Thanks, I’ve made some further changes, which I hope will clear things up. Re your first worry, I think that’s a valid point, but it’s also important to cover both concepts. I’ve tried to make the distinction clearer. If that doesn’t address your worry, feel free to drop me a message or suggest changes via the feedback tab, and we can discuss further.