Via Matt Yglesias:
The self-correcting ticket price.
It’s clear that lots of sports franchises suffer from suboptimal ticket-pricing schemes. Between games that feature many empty seats, games that sell out entirely, and the ability of scalpers to obtain profits on the secondary market, money is obviously being left on the table. The University of Minnesota is trying an interesting idea with its new Golden Ticket pricing concept that for $75 lets you attend all nine Big Ten men’s basketball matchups.
But with a catch.
The catch is that if you go to a game and Minnesota loses, then your pass expires.
The idea is that demand is low for games against weak opponents so Golden Ticket holders will fill the empty seats. They will find it too risky to attend the games against strong opponents freeing up supply to accomodate the increased demand for those games.
Coonskin curl: Mark Witte.
Here is an email I got from the Romney campaign:
You’ve stepped up
Sandeep,This week, supporters from all over the country heeded our call to raise $7 million in 7 days to bring our message into new states. Because of you we have reached our goal in just 5 days and are now on air, sharing our plan to create 12 million new jobs.
Thank you for believing it’s time for real change, and that America can do better than the last four years.
Now, with 3 days left we are asking you to dig a little deeper to support our effort to raise $2 million by tonight.
Here is one from the Obama campaign:
Hey
Sandeep –
This is in your hands now.
Chip in $141, and let’s go win.
Turns out the Hey worked better in randomized trials and so they went with it.
From Schelling’s seminal Essay on Bargaining:
A potent means of commitment, and some-times the only means, is the pledge of one’s reputation. If national representatives can arrange to be charged with appeasement for every small concession, they place concession visibly beyond their own reach. If a union with other plants to deal with can arrange to make any retreat dramatically visible, it places its bargaining reputation in jeopardy and thereby becomes visibly incapable of serious compromise. (The same convenient jeopardy is the basis for the universally exploited defense, “If I did it for you I’d have to do it for everyone else.”) But to commit in this fashion publicity is required. Both the initial offer and the final outcome would have to be known; and if secrecy surrounds either point, or if the outcome is inherently not observable, the device is unavailable.
Grover’s Pledge has been signed by 219 members of the House and 39 Senators.
Kunz was a sociologist at Brigham Young University. Earlier that year he’d decided to do an experiment to see what would happen if he sent Christmas cards to total strangers.
And so he went out and collected directories for some nearby towns and picked out around 600 names. “I started out at a random number and then skipped so many and got to the next one,” he says.
To these 600 strangers, Kunz sent his Christmas greetings: handwritten notes or a card with a photo of him and his family. And then Kunz waited to see what would happen.
But about five days later, responses started filtering back — slowly at first and then more, until eventually they were coming 12, 15 at a time. Eventually Kunz got more than 200 replies. “I was really surprised by how many responses there were,” he says. “And I was surprised by the number of letters that were written, some of them three, four pages long.”
The premise of this article is that people feel compelled to reciprocate your generosity. And once you know that, you can take advantage of it.
Exhibit A: those little pre-printed address labels that come to us in the mail this time of year along with letters asking for donations.
Those labels seem innocent enough, but they often trigger a small but very real dilemma. “I can’t send it back to them because it’s got my name on it,” Cialdini says. “But as soon as I’ve decided to keep that packet of labels, I’m in the jaws of the rule.”
The packet of labels costs roughly 9 cents, Cialdini says, but it dramatically increases the number of people who give to the charities that send them. “The hit rate goes from 18 to 35 percent,” he says. In other words, the number of people who donate almost doubles.
The article also touches on doctors, waiters, and Hare Krishnas.
From NYT, a proposed tax on beer has French imbibers, producers and intermediaries upset. E.g., from a bar owner:
“The increase is brutal; 160 percent is a lot,” said Mr. Thillou, 36, who prides himself on promoting French microbreweries. On a barrel near the entrance, a pile of fliers that say “+160% taxes on beer: Who is going to pay the price?” shows what he thinks of the government’s latest plan for raising revenue.
But the goverment may be rasing revenue the right way, by taxing goods with inelastic demand:
Philippe Lessevre, 26, who had come for a beer, said higher prices would not change his drinking. “It will affect my wallet,” Mr. Lessevre allowed, “but not my consumption.”
But Mr. Charvier was still skeptical about the government’s professed concerns for public health. “It’s the same as for cigarettes: If a percentage of the price goes into their pocket, they still need people to continue buying,” he said. “It’s hypocritical.”
But, of course, there are always lobbyists:
Many opponents of the bill suggested that wine was exempted because the industry has greater political clout, given that it is one of the country’s top three exporters and employs 250,000 people. Wine is currently taxed around the same rate as beer, per hectoliter, but unlike the rates for beer, its rates do not increase with the degrees of alcohol.
Watching the Olympic Games this Summer I noticed that the volleyball competition has changed the scoring system from the old “sideout” system to what used to be called “quick score.” (This change may have happened a long time ago, I don’t watch much volleyball.) The traditional sideout scoring method increments the score only when the serving team wins a point. When the serving team loses the point the serve is awarded to the other team (a “sideout”) but the score is unchanged. This can lead to long drawn out games with repeated sideouts and little scoring. As a stopgap, in the old days, volleyball matches would switch to the quick score system after a certain amount of time has elapsed. In quick scoring a sideout earns a point for the team that gains the serve.
I always liked the sideout system, thinking of it as a characteristic volleyball rule that is compromised for expediency by the switch to quick score. Instinctively it seemed that the fact you could only score when you are serving played a big role in volleyball strategy. But when I was watching this summer it occurred to me that the two scoring systems are less different than it appeared at first.
The basic observation is that at any stage of the game sideout scores are just quick scores minus the number of sideouts. And sideouts necessarily alternate between teams so the number you are subtracting differs by at most one across the two teams. So I started to think if there was a way to characterize the mapping between scoring systems that would clarify precisely the strategic impact of the switch. And I think I figured it out.
Quick scoring is defined as follows. The team who wins a point has its score incremented by one, regardless of who was serving that point. (The serve switches when the receiving team wins a point just as in the sideout system.) The winner of the game is the first team to have a score of at least 15 (or 25 in other cases) and at least a 2 point lead. (I.e. the game continues past 15 if neither team has a two point lead.)
Quick scoring is equivalent to the following system: 28 points will be played. After 28 points (let’s call it regulation) if the score is tied (14-14) then they continue to play until some team has a 2 point advantage.
This is in turn equivalent to side-out scoring with the following amended rules. Lets refer to the team that receives serve in the first point of the game as the receiving team.
- A total of 28 ponts is played in regulation.
- At the end of play if either team is ahead by 2 points then that team wins except if
- the receiving team either scored the last point or earned a side-out in the last point and the receiving team is ahead by 1 point. In this case the receiving team wins.
If none of these conditions are met then the game continues past regulation. We define the team that has the serve in the first point past regulation as team 1 and the other team as team 2. The score is reset to 0-0. Play continues (with side-out scoring) until the first moment at which one of the following occurs.
- Team 1 has a 2 point lead, in which case team 1 is the winner.
- Team 2 has a 1 point lead, in which case team 2 is the winner.
The proof of this equivalence is below the jump. Here’s what it means. Quick scoring is not an innoccuous change in the rules to speed up play but its pretty close. Because a near identical outcome would obtain if instead of switching to quick score, we keep sideout scoring but cap the number of regulation points at 28. Its nearly, but not exactly identical because of the two scoring “epicycles” that have to be appended, namely #3 in regulation and #2 in overtime. Note that both of these wrinkles tend to benefit the receiving team. I don’t know the stats (anybody?) but it appears to me that the receiving team already has a large advantage in volleyball at the level of an individual point. You could say that an effect of sideout scoring is that it levels the playing field by giving a small overall advantage to the serving team. The switch to quick scoring eliminates that.
I wonder if there is a noticeable difference in the frequency with which the (initially) receiving team wins a volleyball game after the switch to quick scoring.
Thanksgiving is over and everyone is back in D.C. talking about the fiscal cliff – the automatic tax increases and spending cuts to defense and entitlement programs that go into effect if no agreement is reached before January 1. These measures might put the fragile economic recovery at risk so a more nuanced deficit reduction plan would be good to have in place. Will such a plan come out of negotiations in the remaining month?
The Coase Theorem says “yes” in at least two contexts.
In the simplest version, there are deals that both sides prefer to the outside option and we should agree to one of them. For example, neither side wants tax increases for people on incomes below $250k as the consequences are bad in primaries and general elections. So they could agree to replace the fiscal cliff contract with one that simply deletes the tax increases on those earning less that $250k.
This simple version assumes that the fiscal cliff measures are enforced if there is no agreement but this is surely not the case. The measures would be the starting point for renegotiation and hence the endpoint of the renegotiation is the benchmark with which to compare proposed current deals. As in Jeff’s earlier post, the negotiations would take the form of a “war of attrition” and we could end up in an equilibrium that destroys surplus. But as long as we play an equilibrium of the war of attrition, again the Coase Theorem goes through with the expected payoffs in the concession game as the outside option.
In a similar vein, many commentators suggest that Obama would be in a stronger bargaining position once we go over the fiscall cliff. Hence, he should go over it rather than come to a deal ex ante. But this argument does not completely make sense: Republicans also know that Obama would be in a stonger position if we go over the cliff. They also know that going over the cliff has dangerous consequences for them electorally. Hence, there are agreements both sides can come to now that take into account the President’s stronger bargaining position after Jan 1 – as long as they have common expectations.
So, there are two reasons why we might go over the fiscal cliff.
First, many strategies can be rationalized in the concession game after we go over the fiscal cliff. There is no reason why Democrats and Republicans should have common knowledge of strategies. If they hold out for inconsistent deals, we will go over the fiscal cliff. Thus is the “non-equilibrium” interpretation.
Alternatively, the two sides each have private information. How confident does the President feel after winning re-election? How much pressure is he under from the liberal wing of the Democratic party? On the other hand, how much pressure is Boehner under from the Tea Party wing? What is the Chamber of Commerce saying to him about willingness to accept a higher probability of recession to avoid higher tax rates? What is each side’s willingness to bear the electoral consequences of going ovet the cliff? Each side has private information. This is the Myerson-Satterthwaite version of the problem. If there is no mutually acceptable bargain for the most confident type of Obama and the most confident type of Boehner, we will go over the fiscal cliff with positive probability.
The last two theories seem quite realistic so there is positive probability of going over the fiscal cliff.
- To indirectly find out what a person of the opposite sex thinks of her/himself ask what she thinks are the big differences between men and women.
- Letters of recommendation usually exaggerate the quality of the candidate but writers can only bring themselves to go so far. To get extra mileage try phrases like “he’s great, if not outstanding” and hope that its understood as “he’s great, maybe even outstanding” when what you really mean is “he’s not outstanding, just great.”
- In chess, kids are taught never to move a piece twice in the opening. This is a clear sunk cost fallacy.
- I remember hearing that numerals are base 10 because we have 10 fingers. But then why is music (probably more primitive than numerals) counted mostly in fours?
- “Loss aversion” is a dumb terminology. At least risk aversion means something: you can be either risk averse or risk loving. Who likes losses?
All working for tech companies and all profiled in this article in The Economist.
ON THE face of it, economics has had a dreadful decade: it offered no prediction of the subprime or euro crises, and only bitter arguments over how to solve them. But alongside these failures, a small group of the world’s top microeconomists are quietly revolutionising the discipline. Working for big technology firms such as Google, Microsoft and eBay, they are changing the way business decisions are made and markets work.
A monopolist considers whether to disclose some information about its product. The information will affect how the consumer values the product but its impossible to predict in advance how the consumer will react. With probability q the consumer will view it as good news and he would be willing to pay a high price V for the product. But with probability 1-q it will be viewed as bad news and the consumer would only be willing to pay a low price v where 0 < v < V.
The consumer’s reaction to the information is subjective and cannot be observed by the monopolist. That is, after disclosing the information, the monopolist can’t tell whether the consumer’s willingness to pay has risen to V or fallen to v.
In the absence of disclosure, the consumer is uncertain whether his the value is V or v and so his willingness to pay is equal to the expected value of the product, i.e. qV + (1-q)v. This is therefore the price the monopolist can earn.
Supposing that the monopolist can costlessly disclose the information, what would its profits be then? It won’t continue to charge the same price. Because with probability (1-q) the consumer’s willingness to pay has dropped to v and he would refuse to buy at a price of qV +(1-q)v. At that price he will buy only with probability q and since that would be true at any price up to V, the monopolist would do better setting a price of V and earning expected profit qV.
Alternatively he could set a price of v. For sure the consumer would agree to that price (whether his willingness to pay is V or v) and so profits will be v. And since this is the highest price that would be agreed to for sure, v and V are the only prices the monopoly would consider. The choice will depend on which is larger qV or v.
But note that both qV and v are smaller than qV +(1-q)v. Disclosing information lowers monopoly profits and so the information will be kept hidden.
This little model can play a role in the debate about mandatory calorie labeling.
David McAdams sends this along:
I’ve created a fun and simple game-theory problem that I thought you might enjoy … This is the sort of problem you could give undergrads to find out who are the really bright ones. It might also be fun to mention (or play) in class.Problem: Find the (unique) symmetic equilibrium of “The World’s Simplest Poker Game”, played as follows:**0** two players**1** each player pays ante of $100**2** each player receives ONE card, which we can think of as independent random numbers on [0,1]**3** each player SIMULTANEOUSLY decides whether to “raise” $100 or “stay”**4A** if one player raises and the other stays, the raiser wins the pot, for net gain +$100**4B** if both raise, the players show their cards and whoever has the highest card wins for net gain +$200
**4C** if both stay, the players show their cards and whoever has the highest card wins for net gain +$100If you decide to solve this problem, please let me know how long it takes you … I’m curious how immediately obvious the answer is to you :) I have solved it myself and, I can tell you, the answer is simple and elegant.Cheers,David
N.B. My answer based on 5 minutes of thinking was wrong. I will post David’s solution over the weekend.
Update: As promised, here is David’s solution. Looks like Keith was the first to post the correct answer in the comments and thanks to Nicolas for pointing out that this example appeared in von Neumann and Morgenstern.
According to Jean-Jacques Dethier, a development economist at the World Bank:
Goldeneye
Plot: Alec Trevelyan (Sean Bean) wants to use an electromagnetic pulse from a nuclear weapon to bring London to its knees and destroy the Bank of England, but not before electronically stealing millions of pounds from the Bank’s systems.
Plausibility: First of all, wouldn’t destroying London and the Bank of England render the pounds you’ve stolen largely worthless? “Not exactly worthless, but close,” says Dethier. Would you be able to convert it? “It’s actually very hard to convert huge amounts of something, which is a problem the Chinese now know well with all their American dollar holdings,” he says. So Trevelyan would have to spend all those pounds in the one country that’d take them: Britain. Whose economy he’s just destroyed.
Cuckoos lay their eggs in other birds’ nests and when the cuckoo chick is born it kicks all of the eggs out of the nest and monopolizes the care and attention of the cuckolded parent. Fairy wrens have evidently evolved a countermeasure:
Diane Colombelli-Negrel from Flinders University in Australia has shown that mothers sing a special tune to their eggs before they’ve hatched. This “incubation call” contains a special note that acts like a familial password. The embryonic chicks learn it, and when they hatch, they incorporate it into their begging calls. Horsfield’s bronze-cuckoos lay their eggs too late in the breeding cycle for their chicks to pick up the same notes. They can’t learn the password in time, and their identities can be rumbled.
Which is incredibly cool. An ingenious solution and a testament to the resourcefulness of the evolutionary invisible hand. Especially when you notice that the cuckoo chick “is a huge, grey monster that looks completely unlike a warbler chick.” Apparently evolution favors the complex system of teaching and repeating a singing password rather than the boring solution of just staring at the invader and noticing that he looks nothing like a cute little fairy wren.
The remaining videos for my Intermediate Microeconomics course have been uploaded for your viewing pleasure. Here’s a sample, and the rest are all at the link.
Tired of talking about nerdy poll aggregators? Time to turn to the Tech team of the Obama campaign. An interesting story by Alexis Madrigal at the Atlantic:
The team had elite and, for tech, senior talent — by which I mean that most of them were in their 30s — from Twitter, Google, Facebook, Craigslist, Quora, and some of Chicago’s own software companies such as Orbitz and Threadless, where Reed had been CTO. But even these people, maybe *especially* these people, knew enough about technology not to trust it. “I think the Republicans fucked up in the hubris department,” Reed told me. “I know we had the best technology team I’ve ever worked with, but we didn’t know if it would work. I was incredibly confident it would work. I was betting a lot on it. We had time. We had resources. We had done what we thought would work, and it still could have broken. Something could have happened.”
Announced yesterday. The main points seem to be: enrollment for credit, a coalition of schools merging curriculum in some way, and some kind of real-time virtual classroom.
“Students from all over the country, or even from abroad, will be able to attend these online classes in real time — classes of about 15 to 20 students taught by professors at some of the nation’s leading universities,” said Daniel Linzer, Northwestern University provost.
Besides Northwestern, consortium members include Brandeis University, Duke University, Emory University, The University of North Carolina at Chapel Hill, University of Notre Dame, University of Rochester, Vanderbilt University, Wake Forest University and Washington University in St. Louis.
“These courses will expand curricular options for students and will enable consortium schools to work collaboratively to develop the most innovative and successful ways to utilize new learning technologies,” Northwestern Provost Linzer said.
Initial Semester Online courses will feature primarily the same faculty and curricula as their brick-and-mortar counterparts, with additional courses designed for the online format to be included in the future. Through a state-of-the-art virtual classroom, students will participate in discussions and exercises, attend lectures and collaborate with peers while guided by renowned professors — engaging in as close to the on-campus class experience that is currently possible online.
Beginning in the fall of 2013, Semester Online will be available to academically qualified students attending consortium schools as well as other top schools across the country. Information about Semester Online courses and the application process will be available in early 2013. The consortium anticipates adding a small number of institutions prior to next year’s launch.
The website for Semester Online is back there.
A new paper by Lionel Page and David Savage. The abstract:
This study explores people’s risk attitudes after having suffered large real-world losses following a natural disaster. Using the margins of the 2011 Australian floods (Brisbane) as a natural experimental setting, we find that homeowners who were victims of the floods and face large losses in property values are 50% more likely to opt for a risky gamble – a scratch card giving a small chance of a large gain ($500,000) – than for a sure amount of comparable value ($10). This finding is consistent with prospect theory predictions of the adoption of a risk-seeking attitude after a loss.
As usual Ethan Iverson gets his subject to talk about music at an accessible but still sophisticated level and also to open up about some really interesting stuff.
FH: There were many more of them. And then there were some Chick Corea clones — the big three. But the Herbie clone thing lasted longer. I was listening on the radio on WBGO the other day, and it was some singer, and the piano player sounded so much like Herbie. It was like, he lifted all of Herbie’s greatest licks, and I thought, “Oh, that’s sad, just sad.”
Chick: I happened by Now He Sings Now He Sobs; I had never heard of it, and that was another “Jesus, what was that?” record. Like, “whoa.” I mean, I heard Light as a Featherand I heard that, and that was like, “That was the same guy?” And I got one calledInner Space, a two CD set, which is a really nice set and on there is a piece for flute, bassoon and piano, like a classical piece, which is really kind of nice. And you know, I certainly followed him a lot for a while, but certainly only to the point that he started going into the Elektric band and the Akoustic band, and “Captain Marvel” and “Leprechaun” whatever… and I haven’t bought a Chick record in 30 years.
He’s in there somewhere. But I hear Chick’s influence more in, like you said, Richie Beirach, or Joanne Brackeen, than myself.
EI: It’s funny. Chick’s lines are thornier than McCoy’s, but paradoxically squarer than McCoy’s, do you know what I mean?
FH: Chick is basically early McCoy, a bit of Bud Powell and a lot of Latin music, if you have to reduce it.
EI: He has this truly incredible facility at the instrument.
FH: Oh, he does.
EI: Unbelievable facility. But even when he plays out, I hear the grids going along in a way that I don’t hear when I hear McCoy.
FH: He’s never had a touch or a sound that invited me in. Some people’s sounds I just connect with, and I find him more admirable than enjoyable, whereas Herbie I can really enjoy, and early McCoy I can really enjoy, and a lot of Keith, if I put aside who he is, I can really enjoy it. But other than those first early records that I bought, I don’t find Chick particularly enjoyable.
EI: There’s something off-putting there, I agree. But he’s one of those guys who is the quintessential jam musician, who can show up and play with anybody.
FH: And sound great.
EI: And sound great. Despite the Akoustic band and everything else, he has something where he could show up anywhere in the world at a jam session, and not only would he play incredible, everyone else would play better too.
Here’s the explainer.
As budget negotiations get underway with the threat of sequestration looming, it’s worth recalling a basic lesson from game theory.
Consider two parties in the same vehicle speeding towards a cliff. The one who concedes, i.e. chickens out and steers the car out of danger, is the loser. Winning is better than losing but either is better than driving off the cliff. Finally, time is valuable: if you are going to concede, you prefer to do it earlier rather than later. Still you are prepared to wait if you expect your rival will concede first.
In equilibrium of this game, unless someone concedes right away there is necessarily a positive probability that they will go over the cliff.
The proof is simple. Consider player 1 and suppose his strategy is not to concede immediately. Then we will show 1′s strategy is such that if 2 never concedes there is a positive probability that 1 will also never concede and they will drive off the cliff together. To prove it, suppose the contrary: that 1′s strategy will eventually concede with probability 1 (if 2 doesn’t concede first). If that is 1′s strategy then 2′s best reply is to wait for 1 to concede. In equilibrium 2 will play such a strategy and the outcome will therefore be that 1 is the loser with probability 1. But if 1 is going to be the loser for sure anyway he should have conceded immediately. That’s a contradiction. We have shown that if 1 does not concede immediately then his strategy will allow the car to drive off the cliff with positive probability. The exact same argument applies to 2. Thus in equilibrium, if the game begins without an immediate concession there is a positive probability they will plunge from the cliff.
When the Spanish government hiked sales tax on theater tickets this past summer, Quim Marcé thought his theater was doomed. With one in four local residents unemployed, Marcé knew that even a modest hike in ticket prices might leave the 300-seat Bescanó municipal theater empty.
“We said, ‘This is the end of our theater, and many others.’ But then the next morning, I thought, we’ve got to do something, so that we don’t pay this 21 percent, and we pay something more fair,” says Marcé in Spanish.
He looked out his window at farmland that surrounds this village, two hours north of Barcelona, and suddenly had an idea: Instead of selling tickets to his shows, he’d sell carrots.
“We sell one carrot, which costs 13 euros [$16] -– very expensive for a carrot. But then we give away admission to our shows for free,” he explains in Spanish. “So we end up paying 4 percent tax on the carrot, rather than 21 percent, which is the government’s new tax rate for theater tickets.”
Classified as a staple, carrots are taxed at a much lower rate and were spared new tax hikes that went into effect here on September 1.
I associate the Republican Party with competition. The Party promotes free market ideals – even in education where it promotes charter schools and vouchers so that traditional public schools will have to improve if they want to successfully compete for students.
So why doesn’t the Republican Party embrace these ideals of fully? Republicans won reelection to the House in large part thanks to uncompetitive redistricting.
This makes the GOP weaker in the long run because it protects out of touch politicians from competition and from reality. Gerrymandering means that Republican Representatives can be oblivious to long-term demographic changes that are reshaping the electorate while Democratic Representatives in safe “districts” must disproportionately confront them. The lack of competition makes the Republican Party weaker and less responsive to demographic change. Only watching Fox News probably isn’t helping either.
The ramifications of this uncompetitive behavior likely influenced the outcome of the Presidential race and made it harder for Romney to win. Mitt Romney embraced positions associated with the far right of the Republican Party in order to win the primary nomination. Many of his opponents who forced this shift in Romney’s positions were elected to the House from uncompetitive districts. Bachmann’s district is estimated to be 8% more “Republican” than the nation.
If the Republican Party wants its next generation of leaders to be able to win state and national elections, it should embrace competition and renounce gerrymandering. It should create House Congressional Districts that reflect demographic trends. It should want to elect Representatives who could have a real shot at winning a state or a national election, not just those who can win in a District where the competition (and reality) have been eliminated.
If you are a parent you probably know of a few kids who have life-threatening allergies. And if you are forty-something like me you probably didn’t know anybody with life-threatening food allergies when you were a kid. It seems like the prevalence of food allergies have increased ten-fold in the last thirty years. Which seems impossible.
Here’s one potential explanation. Suppose that a small percentage of people have a life-threatening allergy to, say, peanuts. And suppose that doctors begin more carefully screening kids for potential food allergies. For example, a kid who gets a rash after eating something is given a skin test or blood test. A positive test correlates with food allergy but does not conclusively demonstrate it. In addition the test cannot distinguish a mild allergy from one that is life threatening.
But life-threatening food allergies are life threatening. The risk is so great that any child with a non-negligible probability of having it should be restricted from eating peanuts. Such a child will return to school with a note from the doctor that there should be no peanuts in class because of the risk of a life-threatening allergic reaction. This is what’s knows as “being allergic to peanuts.”
This is all unassailable behavior on everybody’s part. And note that what it means is that while there continues to be just a small percentage of people who are deathly allergic to peanuts, there is a much larger percentage of people who, perfectly rightly, avoid peanuts because of the significant chance it could give them a life-threatening allergic reaction.
Remember how baffled Kasparov was about Deep Blue’s play in their famous match? It gets interesting.
Earlier this year, IBM celebrated the 15-year anniversary of its supercomputer Deep Blue beating chess champion Garry Kasparov. According to a new book, however, it may have been an accidental glitch rather than computing firepower that gave Deep Blue the win.
At the Washington Post, Brad Plumer highlights a passage from Nate Silver’s The Signal and the Noise. Silver interviewed Murray Campbell, a computer scientist that worked on Deep Blue, who explained that during the 1997 tournament the supercomputer suffered from a bug in the first game. Unable to pick a strategic move because of the glitch, it resorted to its fall-back mechanism: choosing a play at random. “A bug occurred in the game and it may have made Kasparov misunderstand the capabilities of Deep Blue,” Campbell tells Silver in the book. “He didn’t come up with the theory that the move it played was a bug.”
As Silver explains it, Kasparov may have taken his own inability to understand the logic of Deep Blue’s buggy move as a sign of the computer’s superiority. Sure enough, Kasparov began having difficulty in the second game of the tournament — and Deep Blue ended up winning in the end.
Visor volley: Mallesh Pai.
Suppose that what makes a person happy is when their fortunes exceed expectations by a discrete amount (and that falling short of expectations is what makes you unhappy.) Then simply because of convergence of expectations:
- People will have few really happy phases in their lives.
- Indeed even if you lived forever you would have only finitely many spells of happiness.
- Most of the happy moments will come when you are young.
- Happiness will be short-lived.
- The biggest cross-sectional variance in happiness will be among the young.
- When expectations adjust to the rate at which your fortunes improve, chasing further happiness requires improving your fortunes at an accelerating rate.
- If life expectancy is increasing and we simply extrapolate expectations into later stages of life we are likely to be increasingly depressed when we are old.
- There could easily be an inverse relationship between intelligence and happiness.
The last of Strogatz’ series blog entries on mathematics and it may be the best one:
For the Hilbert Hotel doesn’t merely have hundreds of rooms — it has an infinite number of them. Whenever a new guest arrives, the manager shifts the occupant of room 1 to room 2, room 2 to room 3, and so on. That frees up room 1 for the newcomer, and accommodates everyone else as well (though inconveniencing them by the move).
Now suppose infinitely many new guests arrive, sweaty and short-tempered. No problem. The unflappable manager moves the occupant of room 1 to room 2, room 2 to room 4, room 3 to room 6, and so on. This doubling trick opens up all the odd-numbered rooms — infinitely many of them — for the new guests.
Later that night, an endless convoy of buses rumbles up to reception. There are infinitely many buses, and worse still, each one is loaded with an infinity of crabby people demanding that the hotel live up to its motto, “There’s always room at the Hilbert Hotel.”
The manager has faced this challenge before and takes it in stride.
Read on for more highly accessible writing on Cantor’s infinities.
