Matt_Simpson

Karma: 2,393

Matt_Simpson 31 Jan 2014 5:14 UTC
0 points
in reply to: A1987dM’s comment on: Open thread, January 25- February 1
Since utility functions are only unique up to affine transformation, I don’t know what to make of this comment. Do you have some sort of canonical representation in mind or something?

Matt_Simpson 31 Jan 2014 5:13 UTC
0 points
in reply to: Oscar_Cunningham’s comment on: Open thread, January 25- February 1
See also Kreps, Notes on the Theory of Choice. Note that one of these two restrictions are required in order to specifically prevent infinite expected utility. So if a lottery spits out infinite expected utility, you broke something in the VNM axioms.

For anyone who’s interested, a quick and dirty explanation is that the preference relation is primitive, and we’re trying to come up with an index (a utility function) that reproduces the preference relation. In the case of certainty, we want a function U:O->R where O is the outcome space and R is the real numbers such that U(o1) > U(o2) if and only if o1 is preferred to o2. In the case of uncertainty, U is defined on the set of probability distributions over O, i.e. U:M(O) → R. With the VNM axioms, we get U(L) = E_L[u(o)] where L is some lottery (i.e. a probability distribution over O). U is strictly prohibited from taking the value of infinity in these definition. Now you probably could extend them a little bit to allow for such infinities (at the cost of VNM utility perhaps), but you would need every lottery with infinite expected value to be tied for the best lottery according to the preference relation.

Matt_Simpson 14 Oct 2013 2:07 UTC
0 points
in reply to: somervta’s comment on: Open Thread, October 7 - October 12, 2013
I do this too, though in smaller bites. fitfths? fourths? I’m not sure, actually, but it seems to work.

Matt_Simpson 1 Aug 2013 19:42 UTC
0 points
in reply to: A1987dM’s comment on: Open thread, July 29-August 4, 2013
Good point.

Matt_Simpson 31 Jul 2013 16:57 UTC
10 points
in reply to: Prismattic’s comment on: Open thread, July 29-August 4, 2013
Funny, I read your post and my initial reaction was that this evidence cuts against PUA. (Now I’m not sure whether it supports PUA or not, but I lean towards support).

PUA would predict that this phrase

...while I devote myself to worshiping the ground she walks on.

is unattractive.

Matt_Simpson 28 Jul 2013 20:10 UTC
3 points
in reply to: gwern’s comment on: Open thread, July 23-29, 2013
Well based on your track record there, it seems like a prudent move to avoid making bets with you ;)

(Though I agree with you and should be shaming them rather than defending them.)

Matt_Simpson 24 Jul 2013 22:41 UTC
0 points
in reply to: cousin_it’s comment on: An argument against indirect normativity
If the basilisk is correct* it seems any indirect approach is doomed, but I don’t see how it prevents a direct approach. But that has it’s own set of probably-insurmountable problems, I’d wager.

* I remain highly uncertain about that, but it’s not something I can claim to have a good grasp on or to have thought a lot about.

Matt_Simpson 24 Jul 2013 20:47 UTC
2 points
on: An argument against indirect normativity
I think I understand X, and it seems like a legitimate problem, but the comment I think you’re referring to here seems to contain (nearly) all of X and not just half of it. So I’m confused and think I don’t completely understand X.

Edit: I think I found the missing part of X. Ouch.

Matt_Simpson 22 Jul 2013 14:40 UTC
2 points
in reply to: falenas108’s comment on: Open thread, July 23-29, 2013
I also have this problem and would like to know how to fix it / if dual n-back might help.

Matt_Simpson 22 Jul 2013 13:57 UTC
1 point
in reply to: Prismattic’s comment on: Open Thread, June 2-15, 2013
Politics is the mind killer for a variety of reasons besides ridiculously strong priors that are never swayed by evidence. Strong priors isn’t even the entirety of the phenomena to be explained (though it is a big part), let alone a fundamental explanation.

Also, I really like Noah’s post (and was about to post it in the current open thread before I found your post). Not only did Noah attach a word to a pretty commonly occurring phenomenon, the word seems to have a great set of connotations attached to it, given some goals about improving discourse.

Matt_Simpson 20 Jul 2013 20:29 UTC
1 point
in reply to: framsey’s comment on: Valuable economics knowledge available, ironically, for free
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.

Matt_Simpson 19 Jul 2013 9:19 UTC
9 points
in reply to: Stuart_Armstrong’s comment on: Valuable economics knowledge available, ironically, for free
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.

Matt_Simpson 17 Jul 2013 6:37 UTC
0 points
in reply to: [deleted]’s comment on: An Attempt at Preference Uncertainty Using VNM

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.

Matt_Simpson 16 Jul 2013 22:54 UTC
0 points
on: 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

Matt_Simpson 16 Jul 2013 22:10 UTC
0 points
in reply to: [deleted]’s comment on: Pinpointing Utility
Thanks!

Matt_Simpson 13 Jul 2013 20:44 UTC
13 points
on: Some highlights from Nate Silver’s “The Signal and the Noise”
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).

Matt_Simpson 2 Jul 2013 21:02 UTC
4 points
on: 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.

Matt_Simpson 12 Jun 2013 20:40 UTC
0 points
in reply to: Kindly’s comment on: Anticipating critical transitions
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.

Matt_Simpson 10 May 2013 20:26 UTC
0 points
in reply to: CAE_Jones’s comment on: Open Thread, May 1-14, 2013
The book, Wicked is based on Wizard of Oz and has some related themes IIRC. (I really didn’t like the musical based on the book though. But I might just dislike musicals in general; FWIW I also didn’t like the only other musical I’ve seen in person—Rent.)

Matt_Simpson 10 May 2013 20:17 UTC
0 points
in reply to: Qiaochu_Yuan’s comment on: Open Thread, May 1-14, 2013
Experimental economists use mechanical turk sometimes. At least, were encourage to use it in the experimental economics class I just took.