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Here is a good metaphor for a problem Mother Nature has to solve.  A small child is playing on the equipment at the playground.  The child knows what she is physically capable of but doesn’t know what is safe.  If Nature knew about swings and see-saws and monkey bars she would just encode their riskiness into the genes of the child and let the child do the optimization.

But these things came along much too recently for Nature to know about them. Fortunately Nature knows that whatever is in the child’s world was pretty likely also in the parents’ world and by now the parents have learned what is safe. So Nature can employ the parent as her agent.

But in this family-firm, the child is a specialist too.  For one thing she has up-to-the-minute information about her physical abilities which change too quickly for the parents to keep track of.  But just as importantly the child is the cheapest source of information about what’s in front of her.  Nature could press the parent into service again to investigate the set of possible activities available to the child, but this would be costly to the parent (for whom this carrier of only half of his genes is just one of many priorities) and so would require extra incentives and anyway that information is more directly accessible to the child.

So Nature’s organizational structure utilizes a tidy division of labor.  The child’s job is to identify the feasible set and the parent’s job is to veto all the alternatives that are too dangerous.  One last constraint explains the reckless kid.   The child cannot communicate the feasible set to the parent.  This leads to the third-best solution. The child just picks something nearby, say the rope bridge, and starts climbing on it. The parent is stationed nearby ready to intervene whenever the child’s first choice is too dangerous.

And thus the seeds of much later conflict are sown.

Via kottke, an argument against children’s menus in restaurants:

Nicola Marzovilla runs a business, so when a client at his Gramercy Park restaurant, I Trulli, asks for a children’s menu, he does not say what he really thinks. What he says is, “I’m sure we can find something on the menu your child will like.” What he thinks is, “Children’s menus are the death of civilization.”

I would guess that many parents would appreciate the removal of the child’s menus even if they aren’t worried about its implications for the fate of civilization.  At home the kids know what’s in the pantry and if one of the parents is not prepared to make the children starve, they quickly learn to gag and choke on the fava beans to get to the mac-n-cheese (organic!)

If the restaurant has no children’s menu then this strategy is cut from the feasible set.  The parents are effectively committed to make the child starve if she tries it.  With that commitment in place, the child’s best response is to find something on the menu she will like and eat it.

I coach my 7-year-old daughter’s soccer team.  It’s been a tough Spring season so far: they lost the first three games by 1 goal margins.  But this week they won something like 15-1.

I noticed something interesting.  In all of the close games the girls were emotionally drained. By the end of the game they didn’t have much energy left.   Many of them asked to be rotated out.

But this week nobody asked to be rotated out.  In fact this week they had the minimum number of players so each of them played the whole game and still nobody complained of being tired.  Obviously they were having fun running up the score but they didn’t get tired.

Incentives are about getting players to want conditions to  improve.  So incentives necessarily make them less happy about where they are now.  Feeling good about winning means feeling bad about not winning.  That’s the motivation.

But encouragement is about being happy about where you are now.  And it has real effects:  it energizes you.  You don’t get tired so fast when you are having fun.

There is a clear conflict between incentives and encouragement.  At the same time incentives motivate you to win, they discourage you because you are losing.  A coach who fails to recognize this is making a big mistake.

And I am not giving a touchy-feely speech about “it’s not whether you win or lose…”  I am saying that a cold-hearted coach who only cares about winning should, at the margin, put less weight on incentives to win.

If my daughter’s team loved losing, is it possible they would lose less often?  Probably not.  But that’s because the love of losing would give them an incentive to lose.  They would be discouraged when they win but that would only help them to start losing.  (Unless the opposing coach used equally insane incentives.)

Nevertheless, to love winning by 10 goals is a waste of incentive and is therefore a pure cost in terms of its effect on encouragement when the game is close.  Think of it this way:   you have a fixed budget of encouragement to spread across all states of the game.  If you make your team happy about winning by 10 goals,  that directly subtracts from their happiness about winning by only 1 goal.

My guess is that, against a typically incentivized opponent, the optimal incentive scheme is pretty flat over a broad range. That range might even include losing by one goal.  Because when the team is losing by one goal, the positive attitude of being in the first-best equivalence class will keep them energized through the rest of the game and that’s a huge advantage.

Like me, ants like  dark houses/nests with small entrances.  Facing a choice between a dark nest with a large entrance (option A) and a light nest with a small entrance (option B), an ant colony faces a trade-off.  Some go this way to A and some go that way to B.  Suppose we add a third decoy nest option D. Option D is as dark as A but has an even larger entrance.  It is thus dominated by A but not by B.   How will the ant colony’s behavior change when they face the three options together versus just A and B?

Rational choice theory says that the fractions choosing A and B should not change.  Option D is dominated and should never chosen and hence is an irrelevant alternative.  Its presence or absence should not affect the choice between A and B.

One psychological theory suggests that the proportion choosing A should go up.  Option D helps to crystallize the advantages of option A (the smaller entrance).  This may increase the perception of the advantages of A over B as well leading to a change in the proportion of ants choosing A over B.

So what actually happens?

A controlled experiment by Edwards and Pratt answers this question.  Edwards and Pratt built nests with the properties above and made ant colonies make repeated binary and  ternary choices.  They randomized the order of choices, where the nests were located etc.  And because they were experimenting with ants, they could cruelly force the choice of nest upon the ants by destroying the old nest the ants lived in by removing it’s roof.

They find no significant change in the proportions choosing A vs B when the decoy D is present.  Ant colonies are rational and do not violate the axiom of independence of irrelevant alternatives (IIA).

In other work, Pratt shows that ant colonies obey transitivity (i.e. if a colony prefers A to B and B to C, it prefers A to C).

Why are ant colonies more rational than individual humans?  The authors offer a cool hypothesis: choice between colonies is typically made by sending independent scouts sent to the different options.  No scout visits different locations.  The scouts reports are simply compared and the best option is chosen.   A human being contemplates all the choices by herself and has a harder time comparing the attributes independently leading to a violation of IIA.

An ant colony is like a well performing and coordinated decentralized firm with employees passing information up the hierarchy and efficient decisions coming down from the center  Can we import lessons into designing firms?  Alas, I believe not.  A human scout evaluating a decision/option will not be as impartial an ant scout.  He will exagerrate its qualities, hoping his option “wins”.  He hopes to get the credit for finding the implemented option, get promoted, receive stock options and retire young to the Bay Area.  In other words, career concerns ruin a simple transfer of ant colony principles to firms.  If we eliminate career concerns within the firm, we will induce moral hazard as there is no incentive to exert costly effort to find the best decisions for the firm.  Ants in the same colony do not face the same issue as they are genetically related and have “common values”.

Still,  a thought-provoking paper and it has many references to other papers that it builds on. I am going to read more of them.

(Hat tip to Christophe Chamley for the reference)

Via Barker, a pointer to a theory from evolutionary psychology that tears are a true signal that the person crying is vulnerable and in need.

Emotional tears are more likely, however, to function as handicaps. By blurring vision, they handicap aggressive or defensive actions, and may function as reliable signals of appeasement, need or attachment.

Usually you should be skeptical that signaling is evolutionarily stable.  For example if tears convince another that you are defenseless then there is an evolutionary incentive to manipulate the signal.  Convince someone you are defenseless and then take advantage of them.

A typical exception is when the signal is primarily directed toward a family member.  Family members have common interests because they share genes.  Less incentive to manipulate the signal means that the signal has a better chance of being stable.  And babies of course have few other ways of communicating needs.

Of course children eventually do start manipulating the signal.  They learn before their parents do that they are becoming self-sufficient but they still have an incentive to free-ride on the parents’ care.  Fake tears appear.  But this is a temporary phase until the parents figure it out.  Not surprisingly, once the child reaches adulthood, crying mostly stops:  Nature takes away a still-costly but  now-useless signal.

Is it a superstition that babies born in a Year of the Dragon will have good luck?  The Taiwanese government wanted to dispell the superstition.

The demographic spike in 1976 was sufficiently large that governments decided to issue warnings in 1987 against having babies in Dragon years because of the problems they caused for the educational system, particularly with respect to finding teachers and classroom space. Editorials were issued that claimed no special luck or intelligence for Dragon babies and a government program in Taiwan was designed to alert parents to the special problems faced by children born in an unusually large cohort (Goodkind, 1991, p. 677 cites multiple newspaper accounts of this).

But the effort failed and another spike was seen in 1988.  Why?  Because the dragon superstition is true. In this paper by Johnson and Nye, among Asian immigrants to the US, those born in Dragon years are compared to those born in non-Dragon years.  Dragon babies are more successful as measured in terms of educational attainment.  And the difference is larger than the corresponding difference for other US residents.

And of course it turns out that this is due to the self-fulfilling nature of the superstition.  Asian Dragon babies have parents who are more successful and they are more likely to have altered their fertility timing in order to have a baby in a Dragon year.  Is this because the smarter parents were more likely to be dumb enough to believe the superstition?

Or is it because of statistical discrimination?  Since the Dragon superstition is true, being a Dragon is a signal of talent and luck.  Unless these traits are observable without error, even unlucky and untalented Dragons will be treated preferentially relative to unlucky and untalented non-Dragons.  Smart parents know this and wait until Dragon years.

Thanks to Toomas Hinnosaar for the pointer.

The phamily kind.  Let’s say you are hiding something from your husband.  For example, let’s say that you are trying to teach your husband a lesson about putting things “in their right place” and you hide his newly-arrived tomato seeds.  Its time to germinate them indoors to be ready for a mid-May transplanting and he comes to you and says

H:  I found the seeds.

Y:  You did?

H:  Yep.  Were they there all the time? I am sure I looked there.

Y:  I thought you would have.  That’s where you always put stuff.  You never put stuff in the right place.

H:  I always put stuff there?  Like what?

Y:  Like remember you put X and Y and Z there and I couldn’t find them?

H:  Ahh yes, X, Y and Z, I remember them well.  Thanks for telling me where my tomato seeds are.

You are having dinner with your child in a restaurant.  He has ordered chicken tenders with fries and you force him to have a small salad before the main course arrives.  In a “When Harry met Sally” moment, you ask for the fries to be brought “on the side”, i.e. on another plate.

He has a small amount of the chicken and you give him a few fries as a reward.  He then claims that he is full.  Is he really?

There are two states of the world, full F and hungry H.  The state is known to the agent/child but the principal/parent does not know the state.  The agent has private information.  How does the principal work out the true state?  Offer the agent another french fry. If it is accepted, the true state is H – he is truly hungry and only pretending to be full.  If he refuses, it is F and the chips he had earlier filled him up. Of course you have to know your kids to determine which food product separates or screens the two states.

The first few times you try this trick, you can go a  bit further.  Once he has accepted the fry, you point out he must really be in state H and make him have some more chicken.  In the long run, he will work out that accepting the fry leads to more chicken.  He will refuse the fry and you’ll never work out if the true state is F or H. Your solution depends on bounded rationality and if learning helps to eliminate it, you are powerless in the long run.  Also, if you choose the wrong food group you won’t be able to screen the two states in the first place.  In our case, ice cream is always acceptable in all states while more french fries are acceptable if and only if the true state is H.

With best play tick-tack-toe is a draw.  It comes as a surprise to people however that best play is hard to maintain when you are playing 50 games in succession, especially if you’ve had a few. Most people are willing to bet that they can go 50 games without losing one, many are even willing to give odds.  You can make some money this way.  (You are betting just that you can win at least one game, its safe to throw a few and that can knock a careful opponent out of his rhythm.  And the sheer boredom that sets in around game #37 works to your advantage.)

One warning however.  Only wager with with law-abiding adults.  I tried this on my 3 year old and he cheats:

Roland Eisenhuth told me that when he was very young, the first time he had an examination in school his mother told him that she knew a secret for good luck.  She leaned in and spit over his shoulder.  This would give him an advantage on the exam, she told him.

Indeed it gave him a lot of confidence and confidence helped him do well on the exam.  For every school examination after that until he left for University, his mother would spit over his shoulder and he would do well.

Here are the ingredients for a performance-related superstition.   Something unusual is done before a performance, say a baseball player has chicken for dinner, and by chance he has a good game.  Probably just a fluke.  Just in case, he tries it again.  Maybe it doesn’t repeat the second time, but maybe he does have another dose of luck and it “pays off” again.  And there’s always a chance it repeats enough times in a row that its too unlikely to be a statistical fluke.

Now once you believe that chicken makes you a good hitter, you approach each game with confidence.  And confidence makes you a good hitter.  From now on, luck is no longer required:  your confidence means that chicken dinner correlates with a good game. And you won’t have reason to experiment any further so there will be no learning about the no-chicken counterfactual.

If you are a coach (or a parent) you want to instill superstitions in your student.  My wife has been stressing about our third-grade daughter’s first big standardized test coming up in a couple weeks.  Not me.  I am just going to spit over her shoulder.

Joshua Gans on the grade school ritual (a very entertaining read as usual):

This Friday (12th February) is Valentine’s Day. Now before you say, “oh no it isn’t!” I have to beg to differ. That is the day our two youngest children are, near as I can tell, compelled to bring a Valentine’s card to every other person in the class. The school sent home a convenient list of the some 45 names in total that require cards and the instruction that they be prepared for Friday. And by prepared, you can’t just go to the store, buy a pack and put names on it. Nor can you, as I had wanted to do, draw a card on the computer and hit print (quantity = 45). Each requires individual attention. Suffice it to say, this is an exercise requiring many hours and, frankly, if we didn’t have a snow day today (that is, a day whereupon fear of snow = no school for you), it is unclear whether the household could produce the required amount of love.

And of course the parents wind up doing most of the work.  I would suggest however that schools will push parents to their limits in terms of busy work whether or not that includes making Valentines.  That is,  if the Valentine exchange were banned it would only be replaced by some other after-school craft or chore.

What’s surprising is that Valentines has survived this long in US schools.  It’s too focal and so too easy for parents to coordinate their outrage against.  Whereas yet another assignment to look up native american tribes on the internet just blends in with all the rest.

Our youngest son went to a preschool in Evanston and goes halfday to a nursery school here. The kids muck about with Lego, go to a playground in both settings and the only difference is that the nursery school has an all day option which some kids in the morning class (or their parents!) take up.   Therein lies the rub.

Anyone who values the all day option uses the nursery school as daycare as both spouses work and do not have a nanny.   The parents’ are sometimes forced to drop off a child with a cold or the beginnings of flu.  On the other hand, if your child goes to preschool you must have some afternoon solution, a solution you can employ if your child is sick.  So, halfday nursery school leads to more infections than preschool, as we are finding out.

That’s the question taken up at Wired’s GeekDad blog.  My third-grader gets weekly “homework” which is supposed to teach her cursive writing.  I am sure that a lot of time is being wasted.  But I am not sure that it’s cursive that should go.  Handwritten text is losing its practical purpose, so if we are going to retire something, perhaps the fancy stuff should surive.

Summer is over.  But that’s old news. My buddy Dave maintained a tradition of polling us for the album of the summer around the time that the season was drawing to a close.  Of course in SoCal, summer never really ends, but at some point you have to start climbing the fence to get into the neighborhood pool and that’s as good a demarcation line as any.

The album of the summer is not necessarily one that came out that summer.  Its not even necessary that you listened to it that summer.  But it should be the album that will always remind you of that summer whenever you hear it.  This summer I had my midlife crisis and the background music was Seven Swans by Sufjan Stevens.

I spent the first 25 years of my life a few miles from the Pacific Ocean and never really learned to surf.  I am a fine body surfer and boogie boarder but around the time that most of my buddies got into surfing I was spinning my wheels playing chess (I suck.)  I turned 40 last fall and now I live on the shores of Lake Michigan.  There’s no surf here.

Fortunately I spend a month in California in the summer and this summer it was time to learn.  My buddy Dave gave me a surfboard.  It’s about twice as tall as me and weighs more than my 8 year old.  Its also about 5 inches thick which made it impossible for me to get my arm around it to carry it like a regular cool surfer dude.  I looked like a dork carrying it on my head.

But I can’t imagine a better board to learn on.  Its more like a canoe than a surf board.  It was hilarious to me looking at all of these really cool surfer guys sitting on their tiny little boards that sunk from the weight until they were submerged nearly to their shoulders.  Meanwhile I could dip my toes in the water as I lounged around on my Steve Behre (pronounced berry) cruise liner waiting for waves.  Dave said “It’s massive, its dangerous, and its embarrassing but just in terms of having fun surfing… the next one’s going to be a lot better.”  Thanks Dave.


I got myself a wet suit.  The water stays around 70F in San Diego in August so I probably could have got by without one but (again relying on Dave’s advice) since I was going to be surfing in the morning and since, thanks to Steve Behre, my most temperature-sensitive parts would be afloat and exposed to the morning air, I broke down got myself a spring suit.  When I tried it on, the dude at the surf shop (Rusty’s in Del Mar) says “Its a little loose in the arms, but you’ll grow into it.”  He either thought I was 13 years old or he could just tell that I was going to grow tremendous muscles from paddling.

So I was set. Every morning at 5AM I would start my day with these objects:


You will notice the Advil which is pretty much indispensible when you are a 40 year old man trying to paddle a barge through crashing waves by yourself in the dark.  OK not exactly dark, but I was in the water every morning before sunrise.  I would surf until about 7:30 and then head back to the apartment, usually before the kids were awake.  Parenting advice:  arriving at breakfast with your wetsuit on and harrowing surf tales makes you the coolest Dad in the world. Not to mention the tremendous muscles.

I stood up the very first day.  Fleetingly.  By the end of the first week I could consistently catch waves and stand.  They were small waves thankfully.  I was bragging to my buddy Storn and then I got this email back.

If you are just standing in front of the whitewater after the wave has broken then it doesn’t technically count.  (Not that it isn’t fun.)

How did he know??  In my defense, the Steve Queen-Behre was almost impossible to turn.  I guess that’s the tradeoff.  Storn came down from the Bay Area and he brought his board, which while still technically a longboard was about half the width and weight of mine.


We swapped boards and I could actually get my arm around his (that’s me on the left.)  Didn’t catch any waves though.  Turns out that if you want a surfboard with some degree of maneuverability, you also have to paddle with some finesse.   I put that on the todo list for next summer and went back to my trusty Steve Buoy.  (When you can’t catch a wave you can’t ride the last one all the way in.  “The paddle of shame” is what Storn called it.)

That day was the only time I surfed in daylight so I had Jennie bring the camcorder.  Here’s some shredding on video.

Not video of me, mind you, Jennie was too busy making drip castles with the kids.  Anyway, I don’t need help from no jet-ski.  By the end of the month I could turn and ride the shoulder.

Sufjan Stevens was in my CD rotation that whole month.  It’s a powerful album and one that was made to be played before sunrise.  In your rented Toyota Sienna with a boat strapped to the top:


What’s your album of the summer?

Iceland is seeing a small baby boom.

The Icelandic press buzzed with the good news. One article quoted a midwife in the town of Húsavik who noted a bump in births in June and July — an auspicious nine months after the worst of Iceland’s meltdown. Wrote blogger Alda Sigmundsdóttir: “I think many, many of us must have sought solace in love and sex and all that good stuff.”

Italians too, and condom sales were brisk at the low point of the recession in the US.  But historical pattern has been procyclical procreation*

“total fertility” — roughly, the average number of children per woman during her childbearing years — was 2.53 in 1929 and had slid to 2.15 by 1936. Then came the baby boom of postwar prosperity: The birth rate crossed 3 in 1947 and remained above that threshold until the mid-1960s. The next trough, 1.74, came in 1976 — a year earlier, unemployment had hit a postwar peak of 8.5%.

The article is in the Wall Street Journal.


*The pun involving “hump” is an exercise left to the reader.

Start when he is 13 months old:

(sorry for the low quality.  two years ago = ancient technology.)  Yes at that age a child can be taught to float.  In fact almost no teaching is required.  You place the child on his back, he floats.  He cries too, it turns out.  A lot.  That’s why its not me there teaching him to float.  Instead it is a highly trained swimming teacher and one of the most inspirational people I have ever known.  That year was our kids’ first year of swimming lessons with him and we have been spending the summer in La Jolla, CA every year since primarily because of him and these swimming lessons.  10 minute lessons, daily for four weeks.

Here is what he learned last year when he was 2. (rss readers probably need to click through to the blog to see the video.)

A 2 year, 2month old child can learn to kick with his face in the water, roll over onto his back when he needs to breathe, and then continue on.  And at this early age he learns something which is subtle but which is central to swimming at every level:  looking at the floor to point the top of your head in the direction you are swimming and getting a breath by rotating on that axis.  The hardest thing to teach the child is not to look where he is going.  Looking where you are going means tilting your head up and that pushes your body down and makes you sink. For a two-year-old that is a deal-breaker, but even among adults head orientation is what distinguishes good swimmers from the best swimmers.

Here is how you teach a two-year-old to look at the floor.

Many repetitions of placing the child in the water, putting your hand deep under water and tell him to swim and grab the hand.  He has to look down to find your hand.  The typical swimming teacher hold out his hands near the surface of the water which instead trains the child to look up, a disaster.  This tiny difference has an enourmous impact on how smoothly the child can learn to swim.

It also teaches the child to go slow.  Another subtlety with swimming is that moving your arms and legs faster usually makes you go slower.  Slowing down all of the movements teaches him how to move more efficiently through the water.

This summer, at age 3 years 2 months he reached the stage where he could swim by himself without an adult in the pool with him, keeping himself going with the swim-float-swim sequence.  Then he began to learn to swim with his arms.

Next summer:  how to tech a four-year-old to snorkel.

Its easy to make up just-so stories to explain differences across siblings as being caused by birth-order.  This article casts doubt on the significance of birth order.

But we can ask the question of whether birth order should matter and in what ways.  Should natural selection imply systematic differences between older and younger siblings?  Here is one argument that it should.  Siblings “share genes” and as a consequence siblings have an evolutionary incentive to help each other.  Birth order creates an asymmetry in the ways that different siblings can help each other.  In particular, oldest siblings learn things first.  They are the first to experiment with different survival strategies.  The results of these experiments benefit all of the younger siblings.  (Am I a good hunter?  If so, my siblings are likely to be good hunters too.) Younger siblings have less to offer their older siblings on this dimension.

As a result we should expect older siblings to be more experimental than their younger siblings and more experimental than only children.

Here is evidence that older siblings have more years of education than younger siblings and more years of education than only children.

Start by removing the pedals.  Learning to ride a bike involves a chicken-and-egg problem:  you need to learn to pedal in order to learn balance, but before you learn to balance you can’t practice pedaling.  You can break these out by taking off the pedals so that he can straddle the bike easier and learn to balance by “scooting.” (These videos are in hd, to see the hd quality, click on the HD icon.  For some reason I can’t get wordpress to embed the hd version directly.)

Once he has balance, learning to pedal is easy.  Here is his first try (and second try) on the very next day.

Here is a previous installment.  Next week, how to teach a 3 year old to swim.

At Legoland, admission is discounted for two-year-olds. But a child must be at least three for most of the fun attractions.

At the ticket window the parents are asked how old the child is. But at the ride entrance the attendants ask the children directly.

The parents lie. The children tell the truth.

Smartphones are valuable because they make it possible to substitute tasks over time and across locations.  As a result we are freer to be where we want to be when we want to be even if we have work to do.  So when you see, say a parent thumbing away on his iPhone at an otherwise family function, before you judge him remember that without his iPhone he might not be there at all.

Never ask a woman if she is pregnant right?  The explanation given to me is that if it turns out she is not pregnant you are in big trouble.  But, what if I keep quiet and she really is pregnant.  Then she’s thinking “he doesn’t think I am pregnant.  That means he thinks I am actually fat in real life.  Bastard.”  So I am not sure I agree with the conventional wisdom here.

Maybe you are just being cautioned against equivocation.  If you ask then you don’t know and whatever the answer is, your uncertainty reveals that you considered it a possibility that she’s fat.  Under this theory the right strategy is to use your best judgement and just come out and pronounce it with no hesitation.

Kids are taught that when crossing the street, they should check for oncoming cars by looking left, then right, then left again.  Why left again?  Isn’t that redundant?  You already looked left.

You could imagine that the advice makes sense because during the time he was looking right, cars appeared coming from the left that he did not see when he first looked left.  But then wasn’t the first left-look a waste?  Maybe not because at the first step if he saw cars coming from the left then he knows that he doesn’t have to look right yet.  But then shouldn’t he insert a look-right at the beginning in hopes that he can pre-empt an unnecessary look-left?

I thought for a while and in the end I could not come up with a coherent explanation for the L-R-L again sequence.  When you can’t find an example, you prove the counter-theorem.  Here it is.

Take any stochastic process for arrival of cars.  Consider the L-R-L again strategy.  Consider the first instance when the strategy reveals that it is safe to cross.  Let t be the moment of that instance that the L-R-L again strategy looks to the left for the second time.

Now, consider the alternative strategy R-L.  This strategy begins by looking right, then when there is no car coming from the right it looks left and if there is no car coming from the left he crosses.  If he is using R-L there are two possibilites.

  1. The traffic from the right is not clear until time t.  In this case, by definition of t, he will next look left and see no traffic and cross.
  2. The traffic from the right clears before t.  Here, he looks left and either sees clear traffic and crosses or sees traffic.  In the latter case he is now in exactly the same situation as if he was following L-R-L from the beginning.  He waits until the traffic from the left clears and then re-initializes R-L.

In all cases, he crosses safely no later than he would with L-R-L again, and in one case strictly sooner.  That is, the strategy R-L dominates the strategy L-R-L.  Three further observations.

  1. This does not mean that R-L is the optimal strategy.  I would guess that the optimal strategy depends on the specific stochastic process for traffic.  But this does say definitively that L-R-L is not optimal and is bad advice.
  2. He might get run over by a car if after looking left for the last time he crosses without noticing that a car has just appeared coming from the right.  But this would also happen in all the same states when using L-R-L.  Crossing the street is dangerous business.
  3. I believe that the rationale for the L-R-L advice is based on the presumption that the child will not be able to resist looking left at the beginning.  Starting by looking right is very counterintuitive.  Under this theory, the longhand for the advice is “Go ahead and look left at the beginning, but when you see that the traffic is clear, make sure you look right as well before crossing.  And if you see traffic and have to wait for it to clear, don’t forget to look left again before starting out because a car may have appeared in the time you were looking right.”

The No Trade Theorem says that two traders with common prior beliefs will not find a mutally beneficial speculative trade provided they began with a Pareto efficient allocation.  There is in fact a converse.  If the traders do not share a common prior, then they can always find such a trade.

My kids demonstrated this experimentally today in the car coming home from Evanston’s Dixie Kitchen and Bait Shop (Recommended by Barack Obama!)  Two kids have identical rubber alligator swag from the restaurant.  3 year old believes that 6 year old has his alligator and demands a swap.  6 year old insists that all gators are with their rightful owners.  There is common knowledge that they disagree about this and therefore by Aumann’s famous theorem they do not share a common prior.

Dad takes temporary posession of both rubber reptiles.  In plain view of the 6 year old, Dad pretends to switch but doesn’t.  Sleight of hand deceives 3 year old.  Alligators returned to original owners.  Viola, Pareto improvement.

I forgot to get my commission.

He writes the blog Game Theorist and he is the author of the book Parentonomics.  Here he is on the BBC sharing his wisdom on potty training and peas.  (About 2/3 of the way in.)

There is a summary of the research in the New York Times:

In those families, if the first child was a girl, it was more likely that a second child would be a boy, according to recent studies of census data. If the first two children were girls, it was even more likely that a third child would be male.

Demographers say the statistical deviation among Asian-American families is significant, and they believe it reflects not only a preference for male children, but a growing tendency for these families to embrace sex-selection techniques, like in vitro fertilization and sperm sorting, or abortion.

Here is the source article.  There is one small problem with the conclusion:

To reduce the probability that there was an eldest child not in the household, we also restricted our sample to families where the oldest child was 12 years or younger.

Here is the problem.  Let’s suppose that Asian-American parents have a preference for boys but do not engage in any manipulation, except that they keep trying until they get one boy.  Consider two families.  Both families have kids spaced 3 years apart.  The first family has a girl and then a boy and stops.  The second family has 4 girls before the first boy is born.  The first family is included in the sample, the second is not.  More generally, families whose first two children are girls are less likely to be included in the sample than the boy-girl families.  This statistical selection makes it look as if the parents are actively engaged in selection.

The 12 year cap may exclude very few families and so this selection effect may be too small to generate the statistics they are reporting, but it’s hard to know for sure.  The sample sizes are not large.   Here is a graph showing large and overlapping confidence intervals.

It is worth acknowledging that even my alternative story relies on Asian-American parents having a stronger preference for boys than the American population as a whole.  However, it doesn’t require the assumption that they engage in pre-natal sex selection.

Update: The ever-vigilant Marit Hinnosaar (are you noticing a pattern here?) has pointed out to me that I mis-interpreted their sample selection criterion.  As she puts it:

The situation you discribed would create a problem if their sampling method was: include in the sample each household iff the age difference of the children is no more than 12 years. But that is not what they did. With the sampling method they used, they included households, where the oldest child in the household was born not earlier than in 1988 (they used 2000 census data and excluded households that had a child older than 12). This does not lead to the biased sample that you described, since for the researchers these two households that you described are equivalent in terms of whether to include in the sample.

You write several novels and transfer copyright to a publisher in exchange for royalty payment.  When you die your heirs have a legally granted option to negate the transfer of copyright.  This option limits how much your publisher will pay you for the copyright.  So you attempt to block your heirs by entering a second contract which pre-emptively regrants the copyright.

Eventually you die and your heirs ask the courts to declare your pre-emptive contract invalid.

You are (or were) John Steinbeck and your case is before the Supreme Court. If I am reading this right the appelate court decision went against the heirs.  And remarkably the Songwriter’s Guild of America filed an amicus brief in favor of the heirs. (ascot angle: scotusblog.)

Parents today in the US worry too much about letting their kids play outside without supervision.  Are they paranoid?

The crime rate today is equal to what it was back in 1970. In the ’70s and ’80s, crime was climbing. It peaked around 1993, and since then it’s been going down.

If you were a child in the ’70s or the ’80s and were allowed to go visit your friend down the block, or ride your bike to the library, or play in the park without your parents accompanying you, your children are no less safe than you were.

But it feels so completely different, and we’re told that it’s completely different, and frankly, when I tell people that it’s the same, nobody believes me. We’re living in really safe times, and it’s hard to believe.

This ignores two crucial details.  First, if fewer kids are being left unsupervised then there are fewer crimes to commit so if the number of crimes committed is the same as in the 1970’s then in fact we are living in a more dangerous world.  Second, even holding constant the crime rate there is a coordination problem that parents must contend with.  If all of your neighbors kids are inside playing their Wii and you let your kid go to the playground then he is the only target so you would be right to pass and go out and get your own Wii.  In the 1970’s there were enough of us targets out there already that the marginal kid was safe.

The article is here.  Cap clap:

Family conversation at restaurant:

Wife: …her husband is a political scientist at U of C.

Son (7 years old): What is a political scientist?

Wife: Your father can answer that question better.

Me: Well, scientists who are physicists study physics. Chemists study chemistry and political scientists study politics.

Son: Oh, so they’re not really scientists.

Wife and I fall about laughing.

Me to son: Why do you say that?   What do they do?

Son: They study votes and stuff like pollsters.  That’s not science.

Out of the mouths of children…..

(True story, I swear.  Have yet to have a long conversation about economists.)

Robert Akerlof, the son of Nobel Laureate economist George Akerlof, was on the economics PhD job market this year from Harvard.  It raises the question of which academic disciplines are the most recurrent within families.  I see two arguments about the heridity of economics.

On the positive side, economics is a language and framework for thinking about things that come up in everyday life.  It will be more natural and common for an economist parent to explain economic concepts to their kids than it would be for parents in other disciplines, even other social sciences.  On top of that, being an economist probably shapes one’s style of parenting more than being, say, a chemist does and so there is an additional, covert, channel of transmission.

On the negative side, I sometimes think that what inspires someone to go for a PhD in some discipline is when they discover that it allows them to organize and understand things in a new way.  If a child is raised to think like an economist at an early age, they will never have this kind of revelatory moment and so may never feel drawn to economics as an academic discipline.

Finally, the question of heredity conditions on the child going to academia at all.  It could be that having parents who are economists make you less likely to get any sort of advanced degree.

It would be interesting to see the data.

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