The price of a first-class US stamp is set to increase from 46 to 49 cents on January 26. Like Cosmo Kramer’s Michigan bottle redemption plan (see below), Allison Schrager and Ritchie King ran the numbers on whether it would be possible to provide from Forever Stamp arbitrage.

Could the scheme make money? Maybe–if you get the timing right and pay low interest on capital:

Assuming we sell all 10 million stamps for the bulk discount price of \$0.475 each, our profit will be \$150,000. Subtract out the \$399 for the distributor database. Let’s also assume we spent the \$3,500 for Check Stand Program plus, say, \$300 to make the 100 displays for advertising in stores. That gives us \$145,801.

If we do manage to shift the stamps in a month, the interest on our debt will be \$29,000. That brings our profits to \$116,801. Then we’ll return the equity to our shareholders, along with 50% of the profits.

That leaves us with the other 50%: \$58,400.50. If you look at that as a profit on the \$4.6 million initial outlay, it’s not very much: less than 1.3%. But remember, all that outlay was leveraged. So if you look at it as a return on our investment—\$33.25 for shipping—it’s 175,541%.

How Traveling Salesmen Complicate the Traveling Salesman Problem

The traveling salesman problem is simple in its setup but remarkably complicated to solve. You need to visit a number of cities, say 10, and want to find the shortest route that visits all of them exactly once and brings you back to where you started. From a list of routes it is easy to find the shortest one, but it is incredibly hard to verify that it is the shortest of all possible routes.

Finding a solution gets even more difficult when you go from a (mathematically) feasible solution to one that can be implemented in the real world. That is because you have to incorporate a notoriously unreliable component into your plans: human beings.

[I]n trying to apply this mathematics to the real world of deliveries and drivers, UPS managers needed to learn that transportation is as much about people and the unique constraints they impose, as it is about negotiating intersections and time zones….

For one thing, humans are irrational and prone to habit. When those habits are interrupted, interesting things happen. After the collapse of the I-35 bridge in Minnesota, for example, the number of travelers crossing the river, not surprisingly, dropped; but even after the bridge was restored, researcher David Levinson has noted, traffic levels never got near their previous levels again. Habits can be particularly troublesome for planning fixed travel routes for people, like public buses, as noted in a paper titled, “You Can Lead Travelers to the Bus Stop, But You Can’t Make Them Ride,” by Akshay Vij and Joan Walker of the University of California. “Traditional travel demand models assume that individuals are aware of the full range of alternatives at their disposal,” the paper reads, “and that a conscious choice is made based on a tradeoff between perceived costs and benefits.” But that is not necessarily so.

People are also emotional, and it turns out an unhappy truck driver can be trouble. Modern routing models incorporate whether a truck driver is happy or not—something he may not know about himself. For example, one major trucking company that declined to be named does “predictive analysis” on when drivers are at greater risk of being involved in a crash. Not only does the company have information on how the truck is being driven—speeding, hard-braking events, rapid lane changes—but on the life of the driver….

In other words, the traveling salesman problem grows considerably more complex when you actually have to think about the happiness of the salesman.

That’s from Tom Vanderbilt over at Nautilus, and the whole thing is worth a read. Oh, and there’s also an app for that.

This is Your Brain on Hunger

In his book Thinking Fast and SlowDaniel Kahneman describes the brain as made up of two systems. System 1 is fast, emotional, and almost automatic–I think of this as “intuition.” System 2 controls more logical, deliberate processes. There are many factors that can influence which system you use to make a decision (anchoring, availability, substitution, loss aversion, framing, etc.) and Kahneman’s book discusses these. But other environmental factors can influence which system takes over. This post discusses how hunger shifts the balance from System 2 to System 1.

First up is a study on Israeli judges’ parole decisions broken up by time of day by Shai DanzigeraJonathan Levavb, and Liora Avnaim-Pessoa (edited for PNAS  by Kahneman). Here’s the abstract:

Are judicial rulings based solely on laws and facts? Legal formalism holds that judges apply legal reasons to the facts of a case in a rational, mechanical, and deliberative manner. In contrast, legal realists argue that the rational application of legal reasons does not sufficiently explain the decisions of judges and that psychological, political, and social factors influence judicial rulings. We test the common caricature of realism that justice is “what the judge ate for breakfast” in sequential parole decisions made by experienced judges. We record the judges’ two daily food breaks, which result in segmenting the deliberations of the day into three distinct “decision sessions.” We find that the percentage of favorable rulings drops gradually from ≈65% to nearly zero within each decision session and returns abruptly to ≈65% after a break. Our findings suggest that judicial rulings can be swayed by extraneous variables that should have no bearing on legal decisions.

The Economist summarized the paper and produced a graphic with the main takeaway:

The second paper, by Ilona Grunwald-Kadow and coauthors, analyzes the neural behavior of fruit flies when deprived of food (via @tylercowen and @IFLscience). Their results are explained in this press release from the Max Planck Institute:

The results show that the innate flight response to carbon dioxide in fruit flies is controlled by two parallel neural circuits, depending on how satiated the animals are. “If the fly is hungry, it will no longer rely on the ‘direct line’ but will use brain centres to gauge internal and external signals and reach a balanced decision,” explains Grunwald-Kadow. “It is fascinating to see the extent to which metabolic processes and hunger affect the processing systems in the brain,” she adds.

Remember this next time you’re trying to decide between working through lunch or grabbing a bite to eat. Do your body and your neighbors a favor by taking a break.

More on Food Truck Regulation

Popular Durham-area food truck Chirba Chirba serves dumplings. Photo via livewell.

More on the plight of food truck operators in NYC, from the Times:

There are numerous (and sometimes conflicting) regulations required by the departments of Health, Sanitation, Transportation and Consumer Affairs. These rules are enforced, with varying consistency, by the New York Police Department. As a result, according to City Councilman Dan Garodnick, it’s nearly impossible (even if you fill out the right paperwork) to operate a truck without breaking some law. Trucks can’t sell food if they’re parked in a metered space . . . or if they’re within 200 feet of a school . . . or within 500 feet of a public market . . . and so on.

Enforcement is erratic. Trucks in Chelsea are rarely bothered, Nafziger said. In Midtown South, where I work and can attest to the desperate need for more lunch options, the N.Y.P.D. has a dedicated team of vendor-busting cops. “One month, we get no tickets,” Thomas DeGeest, the founder of Wafels & Dinges, a popular mobile-food businesses that sells waffles and things, told me. “The next month, we get tickets every day.” DeGeest had two trucks and five carts when he decided he couldn’t keep investing in a business that was so vulnerable to overzealous cops or city bureaucracy. Instead, DeGeest reluctantly decided to open a regular old stationary restaurant.

We’ve discussed food truck regulations and the competition between vendors before. There is certainly a place for regulation, but inconsistent and seemingly arbitrary enforcement undermines the goal of clarifying expectations between all parties.

Five Lessons on Strategic Thinking from Jane Austen

On Monday I mentioned Michael Suk-Young Chwe‘s new book, Jane Austen, Game Theorist. In this post we take a deeper look at Chwe’s argument: that Jane Austen was teaching lessons about strategic thinking through her novels in what he calls “folk game theory.” We will do that by going through chapters nine and ten in which Chwe examines five lessons on strategic thinking found in Austen’s six novels. I will focus here on examples from Pride and Prejudice as a way of narrowing the field and because it is probably the most popular of the six; page numbers refer to Chwe’s book.

1. Strategic thinking can lead to strong partnerships

One of Chwe’s goals in his book is to help dispel the notion that game theory is strictly atomistic. Austen does a good job of this because some of the strongest couples in her novels result from two characters jointly strategizing. Elizabeth Bennet and Mr. Darcy are first in conflict because they are strategizing differently (Mr. Darcy cannot imagine Elizabeth turning down his proposal of marriage; p. 146). Austen is shows the importance of choice and in particular the choice of a woman to accept to reject a proposal. As they encounter other strategic situations throughout the novel, though, Elizabeth and Mr. Darcy gradually establish a pattern of working together. By learning how the other thinks, they engage in what for Austen is the height of intimacy. This type of joint strategizing can also strengthen female friendships (for Austen females are the more strategic of the two genders; p. 151).

2. You can strategically manipulate yourself

Another matter of choice–again, a primary theme in Austen’s work–is the decision to engage in “self-management” (156). An individual can have multiple “selves,” some of which are more in line with her long-term goals than others. Temperament alone is not sufficient to maintain commitment to your long-term interests, so you must allow your more rational self to override your short-term interests. This strategy can also be used to work against your own biases if you are aware of them (157-8). Mr. Darcy argues in a letter to Elizabeth that he was aware of his bias and was able to avoid letting it influence him: “That I was desirous of believing her indifferent is certain,–but I will venture to say that my investigations and decisions are not usually influence by my hopes or fears.–I did not believe her indifferent because I wished it.”

3. Preferences can be changed

Most social science models take preferences as given, but Austen is interested in how they can be shaped. One mechanism for changing preferences is gratitude (158-9). When Elizabeth learns that Mr. Darcy helped support the marriage between her sister Lydia and Wickham she becomes much more open to the idea of a relationship with him  (telling him that “her sentiments had undergone so material a change… as to make her receive with gratitude and pleasure, his present assurances”). Love in Austen’s novels is a coordination problem, and being in love can also affect individuals’ preferences (160). A third factor that influences preferences is reference dependence: to what baseline are you comparing your current options (161-2).

4. Commitment requires strategic thinking

As discussed above, understanding how someone makes decisions–their preferences and strategies–is for Austen the basis of intimacy. By understanding another, you can view subsequent choices that might otherwise seem inconsistent as flowing from the same strategic point of view. This allows you to understand their goals and recognize their commitments (169). It also helps you to predict how they will react in changing circumstances, allowing you to assess whether and how committed they are to you.

5. Strategic thinking has its disadvantages

This final lesson is truly an innovation on Austen’s part, since contemporary game theory does not often consider downsides to rational thinking. Several complications may arise if you are known to be a strategic thinker. First, others might rely on you too heavily to make decisions for them (172). It may also lead to moral complications if others ask you to engage in strategic actions on their behalf, such as deception. Others might be less willing to help you if they know you are thinking strategically (173). If they view you as always looking for your own most preferred outcome, they may also become less trusting (175-6).

Through these lessons we can see that the manner in which an individual engages in strategic thinking can either strengthen or weaken her social interactions. Austen’s “folk game theory” helped to teach a disadvantaged social class how to outthink their counterparts and end up in more desirable circumstances. She also showed that game theory need not be individualistic, and how strategic thinking can be used to help others. If you enjoyed this post, there is much more to learn from Austen and Chwe does a great job of drawing out those lessons from all six of her novels. One of the biggest lessons in Austen’s novels–that others think differently from you–is still valuable today.

Reducing the Hidden Costs of Urban Living

USC graduate student Jeremy Fuller put it eloquently when he said, “Traffic really just defines your possibilities at any given time.” When traveling from one side of a large metro area to another in the US, a single individual has very little control over her travel time. You can try to pick a less congested time of day or select from a few alternate routes but if the city is gridlocked you are out of luck.

According to the most recent Annual Urban Mobility Report, annual hours wasted in traffic in the largest metro areas of the US increased by 33 hours per year between 1982 and 2012 (from 19 to 52). That means every year Americans in the largest cities are wasting one more hour of their life in traffic. There are 15 of these areas with over 3 million residents each, so even small differences in time wasted add up. The worst offender is the DC area at 67 wasted hours per driver per year.

The Los Angeles area is notorious for its traffic, but the situation is improving. Although the 2011 figure of 61 hours per driver-year is still high, it is down from 78 hours in 2005.  Part of the improvement comes from synchronizing the city’s 4,500 traffic signals over the 469 square-mile metro area:

The system uses magnetic sensors in the road that measure the flow of traffic, hundreds of cameras and a centralized computer system that makes constant adjustments to keep cars moving as smoothly as possible. The city’s Transportation Department says the average speed of traffic across the city is 16 percent faster under the system, with delays at major intersections down 12 percent.

Without synchronization, it takes an average of 20 minutes to drive five miles on Los Angeles streets; with synchronization, it has fallen to 17.2 minutes, the city says. And the average speed on the city’s streets is now 17.3 miles per hour, up from 15 m.p.h. without synchronized lights.

The natural question to ask is, “but then what?” There could be second-order effects: as traffic time is reduced, more commuters could switch to driving. And as the city continues to grow there will be more cars on the road. For now, though, this represents a major improvement that cuts down on one of the main hidden costs in urban life.

Read more about how other major cities are fighting traffic problems here. You may also be interested in traffic signals as a metaphor for property rights or the safety of traffic circles.

How Much is a Publication Worth?

Rembrandt, Scholar at a Table by Candle-light

How much is a publication worth? If you are a professor of economics at the University of California, this study says that each article published in your field’s top journals (American Economic ReviewEconometrica, and Review of Economics and Statistics) increases your annual salary by 1.5 percent or about \$2,053. Here’s the abstract, which details a few other factors:

We study salaries of economics faculty at the University of California to determine how publications affect salary. We find that each publication in a top 10 journal has a positive and significant effect on annual base salary of 1.5%, or \$2,053. Unlike previous research, our analysis specifies the impact of publications in specific journals. Publications in American Economic ReviewEconometrica, and Review of Economics and Statistics have an independent positive effect on salary. Compensation is also affected by faculty rank, seniority, university of employment, and teaching awards. Base salary does not significantly differ by gender, however, gross salary is about 9% lower for women. After controlling for migration and faculty rank, seniority has a negative impact on salary.

Let’s plug this in to the calculation that Mike Munger used in a post late last year.

[A] journal article publication is “worth” at least \$10k, in terms of increment to future expected value of lifetime salary.  A good journal publication, in a top field journal, is worth more than \$25k.  Sure, you don’t get paid by check, when the thing gets accepted.  But if you add up the differences in salary, over time, for your whole career, when you are very young, small differences in hiring, raises, and promotion make a big difference.  (For example, if a young scholar published a paper, and gets a \$1,000 dollar raise, assuming a 10% discount rate, that’s \$9,427 in present value over a 30 year career.  At a 5% discount rate, that would be more than \$15,000).

So, if you want money, publish journal articles.  Your time is worth at least \$100 per hour, maybe more, since you can write a journal article in 100 hours of actual work (and 100x\$100=\$10,000)

The present value of a \$2,503 salary bump over thirty years with 10 percent discounting is \$23,596. If the 100 hour figure is still accurate for the top journals listed above, that is \$235/hour. Even it takes twice as long to write a top journal article it is still more profitable than publishing in the “average” \$1,000/year/article journal. But if you have no chance of making it into the top journals you should aim your sights a bit lower and make up for it by increasing your output. Either way, these calculations show that time spent writing is valuable if it leads to publications.

Nearly two years into my graduate school experience, I now feel qualified to write this post–especially since it is an aggregation of others’ experiences and recommendations. This is by no means all the relevant wisdom, but hopefully it will be a useful resource for others who are earlier in the process than I am. The immediate impetus for this post was this recent interview with Gary King:

The highlight is at 4:33 when he says:

Another general suggestion is that most academics tend to use the same methods their whole career and they’re the methods that they learned in graduate school. Don’t be like them, right? That’s the first suggestion. Don’t be like them. Keep learning tools. The second suggestion is to realize that, realize the social science generalization that people are who they are. People tend to be the same and you’re probably going to be like them. What that means is that when you’re in graduate school or you’re an undergraduate, pick up the tools because the tools will enable you to do the things that others haven’t been able to do. So if you have the choice, take some statistics courses, take some courses in political methodology, take a computer science course or two now and then you’ll have a framework on which to build. Then you can prove me wrong after you become a professor and you can learn more tools, but those tools will be taken to the next level.

The full list of recommended reading, watching, and listening is here.

Coughing at Classical Concerts

Not being an opera fan myself I will take their word for it:

Classical concerts comes with a set of very strict rules for the public: you cannot applaud while the music plays (the only exception being after opera arias), you are supposed to dress up, and there should be complete silence from the audience during the performance. And that urge to cough should be repressed until an applause. Yet, it turns out that coughing is more frequent during the performance.

Here’s the abstract from Andreas Wagener’s paper on the topic:

Concert etiquette demands that audiences of classical concerts avoid inept noises such as coughs. Yet, coughing in concerts occurs more frequently than elsewhere, implying a widespread and intentional breach of concert etiquette. Using the toolbox of (behavioral) economics, we study the social costs and benefits of concert etiquette and the motives and implications of individually disobeying such social norms. Both etiquette and its breach arise from the fact that music and its “proper” perception form parts of individual and group identities, convey prestige and status, allow for demarcation and inclusion, produce conformity, and affirm individual and social values.

Micro-institutions indeed.

The Political Economy of Scrabble: Currency, Innovation, and Norms

Scrabble Christmas ornaments made by Jennifer Bormann, 2011

In Scrabble, there is a finite amount of resources (letter tiles) that players use to create value (points) for themselves. Similarly, in the real world matter cannot be created so much of human effort is rearranging the particles that exist into more optimal combinations. The way that we keep track of how desirable those new combinations are in the economy is with money. Fiat currency has no intrinsic value–it is just said to be worth a certain amount. Sometimes this value changes in response to other currencies. Other times, governments try to hold it fixed. The “law of Scrabble” has remained unchanged since 1938 when it was introduced–but that may be about to change.

Like any well-intentioned dictator, Scrabble inventor Alfred Butts tried to base the value of his fiat money–er, tiles–on a reasonable system:  the frequency of their appearance on the front page of the New York Times. As the English language and the paper of record have evolved over the years, though, the tiles’ stated value has remained static. This has opened the door for arbitrage opportunities, although some players try to enforce norms to discourage this type of play:

What has changed in the intervening years is the set of acceptable words, the corpus, for competitive play. As an enthusiastic amateur player I’ve annoyed several relatives with words like QI and ZA, and I think the annoyance is justified: the values for Scrabble tiles were set when such words weren’t acceptable, and they make challenging letters much easier to play.

That is a quote from Joshua Lewis, who has proposed updating Scrabble scoring using his open source software package Valett. He goes on to say:

For Scrabble, Valett provides three advantages over Butts’ original methodology. First, it bases letter frequency on the exact frequency in the corpus, rather than on an estimate. Second, it allows one to selectively weight frequency based on word length. This is desirable because in a game like Scrabble, the presence of a letter in two- or three-letter words is valuable for playability (one can more easily play alongside tiles on the board), and the presence of a letter in seven- or eight-letter words is valuable for bingos. Finally, by calculating the transition probabilities into and out of letters it quantifies the likelihood of a letter fitting well with other tiles in a rack. So, for example, the probability distribution out of Q is steeply peaked at U, and thus the entropy of Q’s outgoing distribution is quite low.

Lewis’s idea seems to fit with a recent finding by Peter Norvig of Google. Norvig was contacted last month by Mark Mayzner, who studied the same kind of information as the Valett package but did it back in the early 1960s. Mayzner asked Norvig whether his group at Google would be interested in updating those results from five decades ago using the Google Corpus Data. Here’s what Norvig has to say about the process:

The answer is: yes indeed, I (Norvig) am interested! And it will be a lot easier for me than it was for Mayzner. Working 60s-style, Mayzner had to gather his collection of text sources, then go through them and select individual words, punch them on Hollerith cards, and use a card-sorting machine.

Here’s what we can do with today’s computing power (using publicly available data and the processing power of my own personal computer; I’m not not relying on access to corporate computing power):

1. I consulted the Google books Ngrams raw data set, which gives word counts of the number of times each word is mentioned (broken down by year of publication) in the books that have been scanned by Google.

3. I then condensed these entries, combining the counts for all years, and for different capitalizations: “word”, “Word” and “WORD” were all recorded under “WORD”. I discarded any entry that used a character other than the 26 letters A-Z. I also discarded any word with fewer than 100,000 mentions. (If you want you can download the word count file; note that it is 1.5 MB.)

4. I generated tables of counts, first for words, then for letters and letter sequences, keyed off of the positions and word lengths.

Here is the breakdown of word lengths that resulted (average=4.79):

Sam Eifling then took Norvig’s results and translated them into updated Scrabble values:

While ETAOINSR are all, appropriately, 1-point letters, the rest of Norvig’s list doesn’t align with Scrabble’s point values….

This potentially opens a whole new system of weighing the value of your letters….  H, which appeared as 5.1 percent of the letters used in Norvig’s survey, is worth 4 points in Scrabble, quadruple what the game assigns to the R (6.3 percent) and the L (4.1 percent) even though they’re all used with similar frequency. And U, which is worth a single point, was 2.7 percent of the uses—about one-fifth of E, at 12.5 percent, but worth the same score. This confirms what every Scrabble player intuitively knows: unless you need it to unload a Q, your U is a bore and a dullard and should be shunned.

However, Norving included repeats like “THE”–not much fun to play in Scrabble, and certainly not with the same frequency it appears in the text corpus (1 out of 14 turns). With the help of his friend Kyle Rimkus, Eifling conducted a letter-frequency survey of words from the Scrabble dictionary and came up with these revisions to the scoring system:

Image from Slate

Eifling points out that Q and J seem quite undervalued in the present scoring system. So what is an entrepreneurial player to do? “Get rid of your J and your Q as quickly as possible, because they’re just damn hard to play and will clog your rack. The Q, in fact, is the worst offender,” he says.

Now as with any proposed policy update that challenges long-standing norms, there has been some pushback against these recent developments.  at Slate quotes the old guard of Scrabble saying that the new values “take the fun out” of the game. Fatsis seems to hope that the imbalance between stated and practical values will persist:

Quackle co-writer John O’Laughlin, a software engineer at Google, said the existing inequities also confer advantages on better players, who understand the “equity value” of each tile—that is, its “worth” in points compared with the average tile. That gives them an edge in balancing scoring versus saving letters for future turns, and in knowing which letters play well with others. “If we tried to equalize the letters, this part of the game wouldn’t be eliminated, but it would definitely be muted,” O’Laughlin said. “Simply playing the highest score available every turn would be a much more fruitful strategy than it currently is.”

In political economy this is known as rent-seeking behavior. John Chew, doctoral student in mathematics at the University of Toronto and co-president of the North American Scrabble Players Association, went so far as to call Valett a “catastrophic outrage.”

Who knew that the much beloved board game could provoke such strong feelings? With a fifth edition of the Scrabble dictionary due in 2014 it seems possible but highly unlikely that there could be a response to these new findings. A more probable outcome is that we begin to see “black market” Scrabble valuations that incorporate the new data, much like underground economies emerge in states with strict official control over the value of their money. Yet again, evidence for politics in everyday life.

For more fun with letter games, data, and coding, check out Jeff Knups’ guide to “Creating and Optimizing a Letterpress Cheating Program in Python.”