Monday, May 28, 2007

"Stanford Impostor"

I've gotten a zillion emails about it by now, but it was recently found that a young woman had been living for a year in Stanford dorms claiming to be a freshman, when in fact she was not a student of any sort at all. This seems to have engendered much discussion in the Stanford community, e.g. here. (The LA Times has a decent piece).

I mostly think the story is just sad, but a few thoughts:
  • The security scare angle is a bit ridiculous, as is the blame game being played.
  • I suspect the Stanford community is naive and high-strung about these things. My friends who went to state schools say things like this happen all the time. Besides, staffs in co-ops are sometimes happy to let vagrants hang out. The motivations for and mechanics of her deception are clearly the important part of this story (e.g. how did she live with herself?)
  • Her first two quarters were in Kimball, then then her last quarter was in Okada. I'm surprised the Kimball staff weren't enough in-touch with their residents to know a pair of them were having someone else stay in their room for months, and that this person was often sleeping in the lounge. It's pretty standard for Stanford ResEd RA's to have at least that much knowledge. (See, the bubble usually works!)
  • The comments on the Daily article (this one or this earlier one) are disturbing in how quickly things spin into classism and accusations of classism, e.g. Berkeley vs. Stanford, etc.

Update 5/29: This editorial is funny and great.

Thursday, May 24, 2007

Rock Paper Scissors psychology

Rock, Paper, Scissors is making the blog rounds with an excellent strategy guide from the World RPS Society and a fun mental floss article too. (Though the First International RoShamBo programming contest should be noted.) Having played far too much RPS last year, I can say these tips look pretty decent for the most part. I will say I am a huge fan of the elegant move Running With Scissors -- scissors three times in a row. "You think I'm crazy enough to play that AGAIN?" Un-frickin-stoppable.

Everyone thinks, "but wait, RPS is a lame game. Playing randomly is the best strategy!" This is not true. Playing randomly is the best defensive strategy, since your opponent can never do better than 50% against it. However, it is not the best offensive strategy if you can infer what your opponent will play. For example, if you are confident that your opponent is too scared to play scissors for a third time in a row, exploit that and play paper (the only move vulnerable to scissors, which you believe will not be played). You don't have to exactly predict your opponent's next move, but rather, you merely need to believe a non-uniform distribution over their next move. That is, if you can use any information or heuristics to make decent guesses, you can exploit that.

The game only works because of information imbalances in each player's beliefs about the other's psychological state. The problem of other minds, baby! And even more satisfyingly, the ONLY world state on which players want to make inferences is psychological state. RPS is shorn of silly artifices like a board with pieces or cards on the table. It is simply your mind versus your opponent's.

Incessant trash talking makes the game even more fun.

And don't forget 25-RPS or 4-RPS!

Wednesday, May 09, 2007

Simpson's paradox is so totally solved

My friend Lukas just wrote a great formulation Simpson's Paradox as a puzzle:

Against left-handed pitchers, Player A has a higher batting average than Player B. Player A does better against right-handed pitchers also.

Is it possible that B has a better average than A?

Here's a beautiful ASCII art visualization that says Yes.

Each star represents a number of at-bats where the player hit; pluses represent misses. If you put them in a horizontal line you can see the batting averages (proportions) pretty clearly. The bar lenghts carry across rows -- so a longer bar means more at-bats.

Against left-handed pitchers:
A hits |**++| A misses --> 50% avg.
B hits |*+++| B misses --> 25% avg.

Against right-handed pitchers:
A hits |**| A misses --> 100% avg.
B hits |**************+| B misses --> 93% avg. (for many more at-bats!)

But, batting against *ALL* pitchers:
A hits |****++| A misses --> 66% avg.
B hits |***************++++| B misses --> 79% avg.

They both do well against right-handed pitchers, but B sees way more of them than A. All those right-handed pitchers B sees helps his score, but A doesn't get much of a payoff from his high average there. This effect overwhelms the within-group differences of A outperforming B.

I was tempted to write, "any random pitcher tends to be a right-handed, therefore those matter more." But that's not quite the right explanation -- rather, we're interested that among B's at-bats, it's usually against a right-handed pitcher, where A usually bats against a leftie.

A better visualization might step up to two dimensions, showing cross-cutting boxes for each group. I am personally of the opinion that cramming more dimensions of data into a visualization can often help understanding, but I don't have time to do it right now so I shouldn't natter on about it.

This was inspired by the pie chart version here [1], which was about group selection in evolutationary theory. Say altruism is socially efficient: a group with altruists does better than a group without altruists. But altruism is individually a bad bet: altruists do worse than free riders in their group. If you do well you have more children, so altruists always lose out to their fellow freeriders.

Surprisingly, the level of altruists across multiple groups can increase. If there's a group with a very high proportion of altruists, the altruists there benefit greatly from each other so have lots of offspring -- even though the few freeloaders in that group are doing better. But that altruistic group beats out the low-altruism groups, so altruists increase in the entire cross-group population. (This gain can only be temporary if groups are fixed: eventually the free-riders in the big group overwhelm the altruists.) So the effect can be characterized that the altruistic group beats out the selfish groups; this is dubbed "group selection". Group selection is working for altruism, but individual selection works against altruism; in the case of unbalanced groups, group selection is stronger.

Crazy people have written stuff about possible implications of this.

[1] Sober, Elliott, and David Sloan Wilson. 1998. Unto Others: The Evolution and Psychology of Unselfish Behavior.