Thursday, February 26, 2009

Ricardian Equivalence

Yes it's super cheap to blatantly copy blog posts from Greg Mankiw but this was WAY too good to pass up, even just so I have a direct record of it. You must go guffaw at this website, now.

Wednesday, February 25, 2009

Safari!

With my old version of Safari plagued by sudden death syndrome for the last week or so, the Safari 4 release was right on time. And it is SUCH an improvement, and FAST (no really). I haven't been able to stomach using Firefox in OSX since it stalls incessantly and doesn't allow you to type anything new while it's solemnly pondering your last click, so thank god Safari now also has such boneheadedly obvious features as the smart address bar which have been standard in Firefox for ages. And apparently it copied the "top pages" feature from Chrome/Opera, although it only figures out your favorites for you instead of letting you set them. (Perfectly in line with Mac's consistent philosophy of patronization. It would bug me but I won't be using that feature much anyway.)

So, altogether highly recommended, except for the fact that some knucklehead decided to make it impossible to open ALL links in new tabs by default, rather than new windows (although you can open all links in other applications in tabs...). Why......

Download here!

Addendum: To force all links to open in tabs (yay!), run the following command: "defaults write com.apple.Safari TargetedClicksCreateTabs -bool true". And not really related, but I'm tired of googling this over and over so I should write it down, if internet stops working in Parallels desktop, run "sudo killall -hup pvsnatd" and re-enable the connection.

Friday, February 20, 2009

Brilliant

Thursday, February 19, 2009

!!!!!!!

Pardon the ├╝berexcitedness, but I got a job with Ted Miguel! On a really really awesome project with Pam Jakiela (at WashU now) involving (err, I think, a little fuzzy on the details at this point) education and effort-rewarding behavior with experimental evidence from Kenya. I'd be hard-pressed to invent a summer RA job that I'd want more than this one...

I think I should go calm down by panicking over the two midterms coming up that I just realized are on the same day. Ooh boy.

Saturday, February 14, 2009

Valentine's Day Math

(The Stable Marriage Problem, in other words.)

I was recently reminded of this fun problem from Combinatorics, which was my favorite math class in college. The goal is to match N men with N women in such a way that no man and woman would both prefer to be married to each than to their assigned spouse (ie, it is a stable matching). There's a simple algorithm for this, invented by Gale and Shapley:

Each round, every single man proposes to his favorite woman who has not previously rejected him. The women collect and consider all these offers, and accept their favorites. If a woman has already accepted another proposal, this engagement is broken off, and that man becomes single again. This continues until everyone is paired up (which necessarily happens, since eventually every man can propose to every woman.)

Notice three properties of the resulting matching:
  1. It is stable. If there existed a man and woman in the final matching who wanted to have an affair, then that man would have proposed to that woman before his actual spouse, and that woman would have accepted.
  2. The men are paired with their favorite women that they could possibly be paired with in a stable matching. If this were not true, then there is some man M1 who is the first man to be rejected by his favorite feasible wife, W1. Say she rejected M1 in favor of another man, M2. Since men propose in order of preference, and M1 is the first man to be rejected by his favorite feasible wife, M2 must prefer W1 to any of his feasible wives. But in that case, in the stable matching (existent by hypothesis) in which M1 marries W1, W1 prefers M2 and M2 prefers W1 to W2. This contradicts the definition of stable.
  3. The women are paired with their least favorite man that they could possibly be paired with in a stable matching. This is true since if M1 is married to W1 in the algorithm, and in some other stable matching, M1 is married to W2 and W1 is married to M2, then by fact 2, we know M1 prefers W1 to W2, and therefore W1 must prefer M2 to M1 or otherwise that other matching wouldn't be stable.
The moral of the story is obvious.

But, now let's abandon traditional gender roles and sexual orientation and consider the PC version of the puzzle, say the Stable Life Partnering Problem. Now we have N people, all of whom might like to marry any of the other people, and each person chooses at the beginning whether s/he wants to be an asker or an askee. The trick is, asker's can now also be asked. I'm not sure what an easy fix for this would be. The problem is, in any round, an asker of course prefers to get a "yes" from their askee than to say yes to any other offer made to him. But then you can have a cycle of askers proposing to each other, and everyone is waiting for the person downstream to respond before accepting or rejecting other offers. There needs to be different rules for timing to make the problem tractable. Any ideas? (If asker's can't ask other askers, of course this boringly devolves into the other problem.)

(By the way, Happy V-day to all others whose revealed preferences rank writing about math over going out for the holiday =)

Thursday, February 12, 2009

Three awesome websites

I just discovered BeFunky and Jinni. And re-discovered Pandora (I don't think it always had genre stations, did it?)

Jinni is a pandora-like movie search engine. Search for moods, settings, anything really, and it finds them. And you can fine-tune other criteria like well-knownness and realism. Definitely awesome.

Pandora has been around many years but I just noticed the genre stations, and have been thoroughly enjoying "Delta Blues" "Folk/Country Rock" and "Contemporary Country", genres I always enjoy when I hear them randomly but didn't know enough about to download good stuff until now...

And BeFunky turns pictures into "artwork", thus eliminating my desire to learn photoshop. Here's me "scribbled" and my kitten as a cartoon.

Sunday, February 8, 2009

US travel

Marginal revolution posted something right up my alley today: a top five list of places to visit in the US to give the foreigner to most complete experience of America in all its diversity. Having lived in 5+ very different corners of the country and traveled extensively through the rest, comparing subcultures and regions and best travel destinations within the continental US is one of my favorite subjects.

1. New York City. I agree wholeheartedly with Cowen on this one. But I would add to this, take a drive up the Hudson River Valley from there and explore some of the little New England towns on the way. That's the feel of most of the northeast, which you definitely don't get from the city itself.

2. The Grand Canyon, Route 66 in Arizona, and southern Utah. GC and Utah makes number 5 on Cowen's list. Beautiful mountains and woods can be had anywhere, but the Grand Canyon is singularly majestic (but you HAVE to hike down in it), and the many wonderful desert parks across the southwest are unique to this region of the world. A circle around southern Utah and northern Arizona also brings you in contact with Native American, and Mexican/Spanish colonial/missionary culture, and infamous Route 66 kitsch.

3. New Orleans and the Mississippi River Valley/Delta - I haven't been to Memphis, but New Orleans is my third favorite city, so I slightly modified Cowen's #3. I'm less an authority on this region, having only spent three days in the deep south between the Florida panhandle and New Orleans and a few more days in Georgia and the Carolinas, but it's an obvious must-hit on a top 5 list of Americana. Be sure to find the blues and jazz clubs, cajun eateries, and boiled peanuts.

4. Los Angeles and San Francisco - Yes, I'm sort of cheating to include both together, but you really should explore LA, the 101, and SF for a good West Coast exposure. The cities are too vastly different to omit one. Cowen makes a good point that LA is difficult for foreigners to grasp, but that doesn't change the fact that grasping it is crucial to an overall image of the country.

5. South Dakota - This was the best single destination I could come up with that gets you into the northern plains / midwestern whitest-of-the-white-states culture. Get a hearty meal at a local diner, crash a lutheran church potluck, visit Mt. Rushmore, and eat rhubarb pie. Bonus points for visiting at harvest time and going through a corn field maze or to a tractor pull.

Saturday, February 7, 2009

kids in a bubble

YES, the answer is a resounding yes:
Yet, I wonder sometimes if avoiding the vinyl lunch box — I don’t care if it has “Hello Kitty” on the front — is just another blade in a helicopter parent’s propeller, another version of the overzealous monitoring that has produced kids who leave for college without ever having crossed the street by themselves. In this era when children symbolize emotional fulfillment rather than free household labor, we cling to the belief that if we just do everything right — starting with what a woman eats before she’s even pregnant — we can protect them from pain or failure or sadness.
(Also, "the smugly green hamlet of Berkeley, CA" is the best description I've read in awhile. Even the public schools are required to serve organic lunches. Chain businesses are considered the impending doom to civilization. No one microwaves plastic anymore. Still, I guess I'd much rather live around that kind of nut job than the Hollywood nut job in Socal or the Bible-thumpin' Edumucation-hatin' nut job in Oklahoma, but really, are there no normal moderate rough-and-tumble-raised-kids communities anymore? Maybe I should move to New Hampshire.)

Friday, February 6, 2009

football meets economics

Slate had an interesting article recently about proposed changes to an overtime rule in the NFL, specifically, how it is decided which team gets the first possession. This paper on the subject makes the point more formally, for those who, like me, prefer their stories with a side of math. The analysis leaves out some considerations, however, that I think should change the conclusion.

Currently, a coin flip determines who gets the first possession, and a kick-off by the other team determines the initial field position. As overtime is decided by sudden death, the team with first possession has an advantage: they win in overtime in the last ten years more than 60% of the time. (Interesting, the historical average is lower. But better offensive drives have pushed up the advantage.) This coin-flip determination is thus nonideal, although there is no ex ante advantage for either team, because the probability of winning is randomly decided.

Two solutions to this unfairness are proposed. One is the simple fair-division mechanism familiar to any rival siblings: one chooses a split, and the other chooses which side to take. That is, one team would choose an initial field position, and the other team would choose whether to play or defend from that position. The "fair" position would depend on the teams involved of course, and it would take a couple seasons for teams to work out the best strategy, but the average fair position is estimated to be 15-20 yards. Also, note that any improvement in offense will never push the fair position as far back as the 0 yard line, since the probability of giving up a safety enforces this lower bound. (The paper makes this assumption explicitly, but for some reason does not point out this reason for its realism.)

The imperfection in this mechanism arises from imperfect information: The choosing team knows its strengths better than the dividing team, so the dividing team is at a disadvantage. A different mechanism, based on auctions, does better in this respect. In this rule, each team "bids" on field position, and the one willing to take possession closer to their own goal gets the ball at some compromise between the bids of the two teams. This is a perfectly symmetric rule, and thus favored by the economists and by the guys who wrote to the NFL to try to get the rule changed.

My first objection to this conclusion is that a little bit of unfairness in the divide-and-choose scheme is ok. It's true that if a coin toss determines which team divides and which chooses, this introduces an arbitrary element into the game. But, instead of introducing additional arbitraryness, the asymmetry could be used to counteract an arbitrary advantage that already occurred: the coin flip at the beginning of the game to assign first possession. The winner of that coin flip had a small advantage, and thus if the game ends up tied, they played slightly worse. They should thus be forced to divide the field and allow the other team to choose possession in overtime. Both advantages are small, so cancelling them out in this way should be a nearly perfect resolution.

My second objection is to the pragmatic details of the implementation of an auction rule. There are several ways it could be done, as listed by the guy, Quanbeck, who tried to get the rules changed. First is a live dutch auction, then an ascending live auction, and last a sealed bid auction. The last way is just boring. The first two ways would of course cause the coaches to plan ahead what yard they would seize or concede possession at, but in a live auction format, they would also try to read each other's body language for subtle clues and adjust their strategy on the fly. This puts too much visible responsibility on the coach, when it's better for the game if the players are the ones responsible for their fate and the coaches stay on the sidelines. Additionally, can you picture a non-trivial pause in a super-tense hard-fought violent game for a geeky field-position auction exercise? Quanbeck can, but he's an electrical engineer =) A divide-and-choose rule would take no longer than the coin toss, and make a lot more sense to the masses.

Thursday, February 5, 2009

econ/math blogs?

Any economists have advice for me? Here is the quandary:

As particularly evident during the current (vicious condescending personal-attack-riden intelligence-insulting) blogworld stimulus debates, there's sort of a Brad DeLong / Paul Krugman et al blogger camp, and a Tyler Cowen / Greg Mankiw et al blogger camp, and a third camp of more carefree bloggers of interesting random economics observations, like Freakonomics and Al Roth. But I really don't enjoy reading Brad DeLong or Paul Krugman (for aesthetic, not ideological, reasons). So who is a good replacement from that blog category? I don't want to call it the "liberal blogger" category, since it's really not a left-right issue, but that's sort of how it's currently manifesting. And well, no one ever has to hesitate to put Krugman in a "liberal blogger" box.

And any mathematicians know any good math blogs that have a significant fraction of their content accessible to someone who has effectively forgotten their math degree, or at least the accompanying lexicon?

While we're on the subject of blogs, these are my current econ blog favorites, in case you haven't seen them:
The Economist's Free Exchange would make the list if they included author names. It's not that I want to abandon objective discussion by making things personal; I think keeping faces on things actually helps with objectivity (and maybe more relevantly, memory.)