All of RandomThinker's Comments + Replies

One thing those articles don't consider is if your career is causing high negative externalities in the world. Which banking arguable does (depend on what exactly you do, and your political views).

If so, then you need to give even more than what you earned just to undo what you did in your career.

0JonahS
See my response to Nancy Lebovitz on this point.

This is a great example. It's often very hard to tell whether MWA are independent or not. They could all derive from the same factors. Or they could all be made up by the same type of motivated reasoning.

I think that's the judgment of being a good "Fox" ala Tetlock's Hedgehog vs the Fox.

It's amazing how good humans are at this sort of thing, by instinct. I'm reading the book Hierarchy in the Forrest, which is about tribal bands of humans up to 100k years ago. Without law and social structure, they basically solved all of their social equality problems by game theory. And depending on when precisely you think they evolved this social dynamic, they may have had hundreds of thousands of years to perfect it before we became hierarchical again.

http://www.amazon.com/Hierarchy-Forest-Evolution-Egalitarian-Behavior/dp/0674006917

If you look at ... (read more)

It's much harder to make well formed predictions than one would initially suspect. The fun part about PB is trying to make them, that you don't get on GJP.

I also scored slightly on the hedgehog scale. I think people who like to "think about thinking" are already slightly hedgehog. True foxes don't believe in such grand theories.

Good article. As a fellow GJPer, my only nitpick is that the Brier rule is a squared rule, so there is a bigger loss between 95% and 100% than just 0.05. It's not as bad as a logarithm based rule though. Also, the way they do it, the maximum loss is 2 not 1.

Look forward to the next part!

You're right snarles. Thanks for spotting my error. I forgot the signs in the formula for adjugate.

What about the problem of the zero determinant in the denominator? Is that fatal? What's the real world interpretation?

I find the article very interesting, but have trouble following the math. Maybe someone here better at math can help. I do have some understanding of linear algebra, and I've tried to check it with a spreadsheet:

  1. At the very beginning, their closed form solution for V, the stationary vector, seems to allow V's that have negative numbers for the state probabilities. That can't be describing a real game. E.g. if you set p = (0.9, 0.7, 0.2, 0.1) and q = (0.5, 0.5, 0.5, 0.5), you get V = (0.08, -0.08, 0.1, -0.1). [p here is set to the Force-Opponent-Scor
... (read more)
1snarles
v cannot have negative entries. It appears that are you are forgetting the signs in the formula for the adjugate. v is guaranteed to exist and be a valid probability vector as long as M is an irreducible Markov matrix (that is, any state can eventually be reached from any other state). An equivalent and intuitively easier way to calculate v is by repeatedly squaring M: when you do this, all rows of M^k converge to v. This is a consequence of the fact that v is an equilibrium state, i.e., the probability distribution you end up with if you let the Markov chain run forever (from any starting state).