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Thanks for the warning! Do you have any references for this, btw, or is it just your own sentiment?
FWIW I'm a grad student in econ, and in my experience the undergrad and graduate macro are completely different. I recall Greg Mankiw sharing a similar sentiment on his blog at some point, but can't be bothered to look it up.
Basically, we need our meta-preferences over the relative badness of doing the wrong thing under competing ethical theories to play some role in determining >, and that information simply isn't present in the >_m's.
That was like, half the point of my post. I obviously suck at explaining myself.
And yes, I agree now that starting with utility functions is the wrong way. We should actually just build something from the ground up aimed squarely at indirect normativity.
(Even though my comment is a criticism, I still liked the post - it was good enough to get me thinking at least)
Even though my post is an argument, the point really is to get us all thinking about this and see where we can go with it.
Thanks for throwing your brain into the pile.
That was like, half the point of my post. I obviously suck at explaining myself.
I think the combination of me skimming and thinking in terms of the underlying preference relation instead of intertheoretic weights caused me to miss it, but yeah, It's clear you already said that.
Thanks for throwing your brain into the pile.
No problem :) Here are some more thoughts:
It seems correct to allow the probability distribution over ethical theories to depend on the outcome - there are facts about the world which would change my probability distribution over ethical theories, e.g. facts about the brain or human psychology. Not all meta-ethical theories would allow this, but some do.
I'm nearly certain that if you use preference relation over sets framework, you'll recover a version of each ethical theory's utility function, and this even happens if you allow the true ethical theory to be correlated with the outcome of the lottery by using a conditional distribution P(m|o) instead of P(m). Implicitly, this will define your k_m's and c_m's, given a version of each m's utility function, U_m(.).
It seems straightforward to add uncertainty over meta-preferences into the mix, though now we'll need meta-meta-preferences over M2xM1xO. In general, you can always add uncertainty over meta^n-preferences, and the standard VNM axioms should get you what you want, but in the limit the space becomes infinite-dimensional and thus infinite, so the usual VNM proof doesn't apply to the infinite tower of uncertainty.
It seems incorrect to have M be a finite set in the first place since competing ethical theories will say something like "1 human life = X dog lives", and X could be any real number. This means, once again, we blow up the VNM proof. On the other hand, I'm not sure this is any different than complaining that O is finite, in which case if you're going to simplify and assume O is finite, you may as well do the same for M.
In response to
An Attempt at Preference Uncertainty Using VNM
This strikes me as the wrong approach. I think that you probably need to go down to the level of meta-preferences and apply VNM-type reasoning to this structure rather than working with the higher-level construct of utility functions. What do I mean by that? Well, let M denote the model space and O denote the outcome space. What I'm talking about is a preference relation > on the space MxO. If we simply assume such a > is given (satisfying the constraint that (m1, o1) > (m1, o2) iff o1 >_m1 o2 where >_m1 is model m1's preference relation) , then the VNM axioms applied to (>, MxO) and the distribution on M are probably sufficient to give a utility function, and it should have some interesting relationship with the utility functions of each competing ethical model. (I don't actually know this, it just seems intuitively plausible. Feel free to do the actual math and prove me wrong.)
On the other hand, we'd like to allow the set of >_m's to determine > (along with P(m)), but I'm not optimistic. It seems like this should only happen when the utility functions associated with each >_m, U_m(o), are fully unique rather than unique up to affine transformation. Basically, we need our meta-preferences over the relative badness of doing the wrong thing under competing ethical theories to play some role in determining >, and that information simply isn't present in the >_m's.
(Even though my comment is a criticism, I still liked the post - it was good enough to get me thinking at least)
Edit: clarity and fixing _'s
One interesting fact from Chapter 4 (on weather predictions) that seems worth mentioning: Weather forecasters are also very good at manually and intuitively (i.e. without some rigorous mathematical method) fixing the predictions of their models. E.g. they might know that model A always predicts rain a hundred miles or so too far west from the Rocky Mountains. So to fix this, they take the computer output and manually redraw the lines (demarking level sets of precipitation) about a hundred miles east, and this significantly improves their forecasts.
Also: the national weather service gives the most accurate weather predictions. Everyone else will exaggerate to a greater or lesser degree in order to avoid getting flak from consumers about, e.g., rain on their wedding day (because not-rain or their not-wedding day is far less of a problem).
In response to
What are you working on? July 2013
I just started a research project with my adviser developing new posterior sampling algorithms for dynamic linear models (linear gaussian discrete time state space models). Right now I'm in the process of writing up the results of some simulations testing a couple known algorithms, and am about to start some simulations testing some AFAIK unknown algorithms. There's a couple interesting divergent threads coming off this project, but I haven't really gotten into those yet.
In response to
Anticipating critical transitions
Similar weird things happen for the Cauchy distribution (whose probability density function is proportional to 1/(1+x^2)), which is symmetric around 0 but does not have mean 0 because the sum doesn't converge.
Exercise: what do you expect to happen if you try to find the mean of the Cauchy distribution by simulation?
Off the cuff: it's probably a random walk.
Edit: It's now pretty clear to me that's false, but plotting the ergodic means of several "chains" seems like a good way to figure it out.
Edit 2: In retrospect, I should have predicted that. If anyone is interested, I can post some R code so you can see what happens.
In response to
Open Thread, May 1-14, 2013
Has there been an atempt at a RATIONAL! Wizard of Oz? I spontaneously started writing one in dialog form, then realized I would need to scrap it and start over with actual planning if I wanted to keep going. I like this idea, but I'm not sure how motivated I am to go through with it; I'd rather read an existing such fic, if one exists.
In response to
Open Thread, May 1-14, 2013
Anyone here have experience hiring people on sites like Mechanical Turk, oDesk, TaskRabbit, or Fiverr? What kind of stuff did you hire them to do, and how good were they at doing it? It seems like these services could be potentially quite valuable so I'd like to get an idea of what it's possible to do with them.
Experimental economists use mechanical turk sometimes. At least, were encourage to use it in the experimental economics class I just took.
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I would say that undergrad and grad econ are very different methodologically (at least at most schools), but a lot of the content is the same.
Stephen Williamson's intermediate macro textbook tries to bring in a lot of grad-level models/concepts, albeit in a "toy" form.
What do you mean by 'content' here? The basic narrative each model tells about the economy?
I think I agree with you. The big difference between the models I learned in undergrad and the models I learned in grad school was that in undergrad, everything was static. In grad school, the models were dynamic - i.e. a sequence of equilibria over time instead of just one.