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Yesterday just before the start of a seminar I went to the thermostat to try to warm up the room. The speaker saw me fiddling with it and nodded with approval. I said nothing, turned up the heat and returned to my seat.
The thing is, she couldn’t see whether I was raising the temperature or lowering it. She just assumed that I would be moving the temperature in the same direction as her preference. And of course with good reason. We both want a comfortable room. We each get private signals about whether the room is currently too cold or too warm. Our private signals are correlated. If her private signal suggests the room is too warm then she knows that more likely than not my private signal says the same thing, and since I am acting on my private signal and nothing more I am most likely adjusting the thermostat exactly how she wants it.
I know all of this and therefore I strictly prefer to say nothing about what I am doing. By saying nothing I allow her to continue to believe that I am doing what she wants me to do even though I don’t know for sure what it is she wants. Her signal of course could be different than mine. If instead I tell her I am raising the temperature then in the best case I am just confirming what she already believed and nothing is gained. But there is the risk that I inform her that actually I am doing the opposite of what she wants and then we have a conflict.
Her seminar was awesome.
There was 20 seconds left, Vanderbilt had just scored a layup to go ahead by 1 and Northwestern’s Bryant Mcintosh was racing to midcourt to set-up a final chance to regain the lead and win the game. Vanderbilt’s Matthew Fisher-Davis intentionally fouled him, sending McIntosh to the line and the commentators and all of social media into a state of bewilderment. Yes, we understand intentionally fouling when you are down 1 with 20 seconds to go, but when you are ahead by 1?
But it was a brilliant move and it failed only because the worst-case scenario (for Vanderbilt) realized: McIntosh made two clutch free throws and Vanderbilt did not score on the ensuing possession.
(Before we get into the analysis, a simple way to understand the logic of the play is to notice that intentionally fouling late in the game very often is the right strategic move when you are down by a few points and there is no reason that should change precipitously when the point differential goes from slightly negative to slightly positive.The tactic is based on a tradeoff between giving away (random) points and getting (for sure) possession. The factors in that tradeoff are continuous as a function of the current scoring margin.)
Let be the probability that a team scores (at least two points) on a possession. Let be the probability that Bryant McIntosh makes a free throw. Roughly, the probability that Vanderbilt wins if they do not foul is because Northwestern is going to play for the final shot and win if they make a field goal.
What is the probability that Vanderbilt wins when Fisher-Davis fouls? There are multiple, mutually-exclusive ways they could win. First, McIntosh might miss both free-throws. This happens with probability . The other simple case is McIntosh makes both free-throws, a probability event, in which case Vanderbilt wins by scoring on the following possession, which they do with probability . Thus, the total probability Vanderbilt wins in this second case is .
The third possibility is McIntosh makes one free-throw. This has probability . (I am pretty sure McIntosh was shooting two, i.e. Northwestern was in the double bonus, but if it was a one-and-one this would make Fisher-Davis’ case even stronger.) Now there are two sub-cases. First, Vanderbilt could score on the ensuing and win. Second, even if they don’t score, it will be tied and the game will be sent into overtime. Let’s say Vanderbilt wins with probability in overtime, a conservative number since Vanderbilt had all the momentum at that stage of the game.
Then the total probability of a Vanderbilt win in this third case is . Adding up all of these probabilities, Vanderbilt wins using the Fisher-Davis foul with probability
Fisher-Davis made the right move provided the above expression exceeds . Let’s start by noticing some basic properties. First, if then fouling is always the right move, no matter what is. (If Northwestern is going to score for sure, you want to foul and get possession so that you can score for sure and win.) If then again fouling is the right strategy, regardless of . (If he’s going to miss his free-throws then send him to the line.)
Next, notice that the probability Vanderbilt wins when Fisher-Davis fouls is monotonically increasing in . Since the probability Vanderbilt wins without fouling is decreasing in , the larger it is the better the Fisher-Davis gambit looks.
Finally, even if , so that McIntosh is surely going to sink two free-throws, Fisher-Davis made the right move as long as .
Ok so what are the actual values of and . McIntosh is an 85% free-throw shooter so . Its harder to estimate but here are some guidelines. First, both teams were scoring (at least two points) on just about every possession down the stretch of that game. An estimate based on the last 3 minutes of data would put at at least , in any case certainly larger than .
More generally, I googled a bit and found something basketball stat guys call offensive efficiency. It’s an estimate of the number of points scored per possession. Northwestern and Vanderbilt have very similar numbers here, about 1.03. A crude way to translate that into the number we are interested, namely probability of at least 2 points in a possession, is to simply divide that number in half, again giving . (This would be exactly right if you could only ever score 2 points. But of course there are three-point possessions and one-point possessions.) A third way is to notice that Northwestern was shooting a 49% field goal percentage for the game. This doesn’t equal field goals per possession of course because some possessions lead to turnovers hence no field goal attempt, and on the other side some possessions lead to multiple field goal attempts due to offensive rebounds.
So as far as I know there isn’t one convincing measure of but its pretty reasonable to put it above at that phase of the game. This would be enough to justify Fisher-Davis even if McIntosh was certain to make both free throws. (I used Wolfram Alpha to figure out what would be required given the precise value and it is about .45).
Finally, even if is below say around it means that the foul lowered Vanderbilt’s win probability but not by very much at all. Probably less than every single time in the game that someone missed a shot. Certainly less than a few seconds later when LaChance missed the winning shot on the final possession. Its interesting how in close games the specific things we focus our attention on when in fact pretty much every single play in the game turned out to be pivotal.
How do you assess whether a probabilistic forecast was successful? Put aside the question of sequential forecasts updated over time. That’s a puzzle in itself but on Monday night each forecaster will have its final probability estimate and there remains the question of deciding, on Wednesday morning, which one was “right.”
Give no credibility to pronouncements by, say 538, that they correctly forecasted X out of 50 states. According to 538’s own model these are not independent events. Indeed the distinctive feature of 538’s election model is that the statewide errors are highly correlated. That’s why they are putting Trump’s chances at 35% as of today when a forecast based on independence would put that probability closer to 1% based on the large number of states where Clinton has a significant (marginal) probability of winning.
So for 538 especially (but really for all the forecasters that assume even moderate correlation) Tuesday’s election is one data point. If I tell you the chance of a coin coming up
Armageddon Tails is 35%, you toss it once and it comes up Tails you certainly have not proven me right.
The best we can do is set up a horserace among the many forecasters. The question is how do you decide which forecaster was “more right” based on Tuesday’s outcome? Of course if Trump wins then 538 was more right than every other forecaster but we do have more to go on than just the binary outcome.
Each forecaster’s model defines a probability distribution over electoral maps. Indeed they produce their estimates by simulating their models to generate that distribution and then just count the fraction of maps that come out with an Electoral win for Trump. The outcome on Tuesday will be a map. And we can ask based on that map who was more right.
What yardstick should be used? I propose maximum likelihood. Each forecaster on Monday night should publish their final forecasted distribution of maps. Then on Wednesday morning we ask which forecaster assigned the highest probability to the realized map.
That’s not the only way to do it of course, but (if you are listening 538, etc) whatever criterion they are going to use to decide whether their model was a success they should announce it in advance.
- Suppose one forecaster says the probability Trump wins is q and the other says the probability is p>q. If Trump in fact wins, who was “right?”
- Suppose one forecaster says the probability is q and the other says the probability is 100%. If Trump in fact wins, who was right?
- Suppose one forecaster said q in July and then revised to p in October. The other said q’ < q in July but then also revised to p in October. Who was right?
- Suppose one forecaster continually revised their probabilistic forecast then ultimately settled on p<1. The other forecaster steadfastly insisted the probability was 1 from beginning to end. Trump wins. Who was right?
- Suppose one forecaster’s probability estimates follow a martingale (as the laws of probability say that a true probability must do) and settles on a forecast of q. The other forecaster‘s “probability estimates” have a predictable trend and eventually settles on a forecast of q’>q. Trump wins. Who was right?
- Suppose there are infinitely many forecasters so that for every possible sequence of events there is at least one forecaster who predicted it with certainty. Is that forecaster right?
What I wrote yesterday:
When Fox broadcasts the Super Bowl they advertise for their shows, like American Idol. But those years in which, say, ABC has the Super Bowl you will never see an ad for American Idol during the Super Bowl broadcast.
This is that sort of puzzle whose degree of puzzliness is non-monotonic in how good your economic intuition is.
If you don’t think of it in economic terms at all it doesn’t seem at all like a puzzle. Try it: ask your grandpa if he thinks that its odd that you never see networks advertising their shows on other networks. Of course they don’t do that.
When you apply a little economics to it that’s when it starts to look like a puzzle. There is a price for advertising. The value of the ad is either higher or lower than the price. If its higher you advertise. If its another network that price is the cost of advertising. If its your own network that price is still a cost: the opportunity cost is the price you would earn if instead you sold the ad to a third-party. If it was worth it to advertise American Idol when your own network has the Super Bowl then it should be worth it when some other network has it too.
But a little more economics removes the puzzle. Networks have market power. The way to use that market power for profit is to artificially restrict quantity and set price above marginal cost. (The marginal cost of running another 30 second ad is the cost in terms of viewership that would come from shortening, say, the halftime show by 30 seconds.)
When a network chooses whether to run an ad for its own show on its own Super Bowl broadcast it compares the value of the ad to that marginal cost. When a network chooses whether to run an ad on another network’s Super Bowl broadcast it compares the value to the price.
Indeed even if the total time for ads is given and not under control of the network (i.e. total quantity is fixed) the profit maximizing price for ads will typically only sell a fraction of that ad time. Then the marginal (opportunity) cost of the additional ads to pad that time is zero and even very low value ads like for American Idol will be shown when Fox has the Super Bowl and not when any other network does.
In fact that last observation and the fact that you never ever see any network advertise its shows on another network tells us that the value of advertising television shows is very low. Perhaps that in fact tells us that the networks themselves understand (but their paying advertisers don’t) that the value of advertising in general is very low.
When Fox broadcasts the Super Bowl they advertise for their shows, like American Idol. But those years in which, say, ABC has the Super Bowl you will never see an ad for American Idol during the Super Bowl broadcast.
More generally, networks advertise their own shows on their own network but never pay to advertise their shows on other networks. I never understood this. But I think I finally figured it out, there’s some very simple economics behind this.
Right now at Primary.guide, you can read the current betting market odds for a “contested convention” and a “brokered convention.” The definitions are as follows. A contested convention means that no candidate has 1237 delegates by the end of the last primary. A brokered convention means that no candidate wins on the first ballot at the convention.
Right now the odds of a brokered convention are 50%. Note also that the odds of a Trump nomination are 50% as well. And Trump is the only candidate with any chance of winning a majority on the first ballot (even if he doesn’t get 1237 bound delegates he will be close and no other candidate could combine their bound delegates with unbound delegates to get to a majority.)
Thus, if there is no brokered convention Trump is the nominee. The probability of no brokered convention is 50%. Thus the entire 50% probability of a Trump nomination is accounted for by the event that he wins on the first ballot.
In other words there is zero probability, according to betting markets, that Trump wins a brokered convention.
The odds of a contested convention are 80%. That means that betting markets think there is a 30% chance Trump fails to get 1237 bound delegates but still wins on the first round. I.e. according to betting markets we have the following three mutually exclusive events:
- Trump gets to 1237 by June 7. 20% odds
- Trump fails to get 1237 bound delegates but wins on the first ballot. 30%
- Nobody wins on the first ballot and Trump is not the nominee. 50%
Cato Unbound is running a discussion with this topic. Alex Tabarrok and Tyler Cowen kicked things off by suggesting that technological advances are ending asymmetric information as an important feature of markets. My response, “Let’s Hope Not” was just published. Josh Gans and Shirley Svorny are also contributing.
Here is an article on the latest Michelin stars for Chicago Restaurants. The very nice thing about this article is that it tells you which restaurants just missed getting a star. As of yesterday you would have preferred the now-starred restaurants over the now-snubbed restaurants. But probably as of today that preference is reversed.
Any punishment designed for deterrence is based on the following calculation. The potential criminal weighs the benefit of the crime against the cost, where the cost is equal to the probability of being caught multiplied by the punishment if caught.
Taking surveillance technology as given, the punishment is set in order to calibrate the right-hand-side of that comparison. Optimally, the expected punishment equals the marginal social cost of the crime so that crimes whose marginal social cost outweighs the marginal benefit are deterred.
When technology allows improved surveillance, the law does not adjust automatically to keep the right-hand side constant. Indeed there is a ratchet effect in criminal law: penalties never go down.
So we naturally hate increased surveillance, even those of us who would welcome it in a first-best world where punishments adjust along with technology.
Suppose there’s a precedent that people don’t like. A case comes up and they are debating whether the precedent applies. Often the most effective way to argue against it is to cite previous cases where the precedent was applied and argue that the present case is different.
In order to maximally differentiate the current case they will exaggerate how appropriate the precedent was to the specific details of the previous case, even though they disagree with the precedent in principle because that case was already decided and nothing can be done about that now.
The long run effect of this is to solidify those cases as being good examples where the precedent applies and thereby solidify the precedent itself.
These are my thoughts and not those of Northwestern University, Northwestern Athletics, the Northwestern football team, nor of the Northwestern football players.
- As usual, the emergence of a unionization movement is the symptom of a problem rather than the cause. Also as usual, a union is likely to only make the problem worse.
- From a strategic point of view the NCAA has made a huge blunder in not making a few pre-emptive moves that would have removed all of the political momentum this movement might eventually have. Few in the general public are ever going to get behind the idea of paying college athletes. Many however will support the idea of giving college athletes long-term health insurance and guaranteeing scholarships to players who can no longer play due to injury. Eventually the NCAA will concede on at least those two dimensions. Waiting to be forced into it by a union or the threat of a union will only lead to a situation which is far worse for the NCAA in the long run.
- The personalities of Kain Colter and Northwestern football add to the interest in the case because as Rodger Sherman points out Northwestern treats its athletes better than just about any other university and Kain Colter is on record saying he loves Northwestern and his coaches. But these developments are bigger than the individuals involved. They stem from economic forces that were going to come to a head sooner or later anyway.
- Before taking sides, take the following line of thought for a spin. If today the NCAA lifted restrictions on player compensation, tomorrow all major athletic programs and their players would mutually, voluntarily enter into agreements where players were paid in some form or another in return for their commitment to the team. We know this because those programs are trying hard to do exactly that every single year. We call those efforts recruiting violations.
- Once that is understood it is clear that to support the NCAA’s position is to support restricting trade that its member schools and student athletes reveal year after year that they want very much. When you hear that universities oppose removing those restrictions you understand that whey they really oppose is removing those restrictions for their opponents. In other words, the NCAA is imposing a collusive arrangement because the NCAA has a claim to a significant portion of the rents from collusion.
- Therefore, in order to take a principled position against these developments you must point to some externality that makes this the exceptional case where collusion is justified.
- For sure, “Everyone will lose interest in college athletics once the players become true professionals” is a valid argument along these lines. Indeed it is easy to write down a model where paying players destroys the sport and yet the only equilibrium is all teams pay their players and the sport is destroyed.
- However, the statement in quotes above is almost surely false. Professional sports are pretty popular. And anyway this kind of argument is usually just a way to avoid thinking seriously about tradeoffs and incremental changes. For example, how many would lose interest in college athletics if tomorrow football players were given a 1% stake in total revenue from the sale of tickets to see them play?
- My summary of all this would be that there are clearly desirable compromises that could be found but the more entrenched the parties get the smaller will be the benefits of those compromises when they eventually, inevitably, happen.
I just saw Malcolm Gladwell on The Daily Show. Apparently his book David and Goliath is about how it can actually be an advantage to have some kind of disadvantage. He mentioned that a lot of really successful people are dyslexic for example.
But its either an absurdity or just a redefinition of terms to say that disadvantages can be advantageous. The evidence appears to be a case of sample selection bias. Here’s a simple model. Everyone chooses between two activities/technologies. There is a safe technology, think of it as wage labor, that pays a certain return to everybody except those the disadvantaged. The disadvantaged would earn a significantly lower return from the safe technology because of their disadvantage
Then there is another technology which is highly risky. Think of it as entrepreneurship. There is free entry but only a randomly selected tiny fraction of entrants succeed and earn returns exceeding the safe technology. Everyone else fails and earns nothing. Free entry means that the expected return (or utility thereof) must be lower than the safe technology else all the advantaged would abandon the latter.
The disadvantaged take risks because of their disadvantage and a small fraction of them succeed. All of the highly successful people have “advantageous” disadvantages.
I liked this account very much:
there are two ways of changing the rate of mismatches. The best way is to alter your sensitivity to the thing you are trying to detect. This would mean setting your phone to a stronger vibration, or maybe placing your phone next to a more sensitive part of your body. (Don’t do both or people will look at you funny.) The second option is to shift your bias so that you are more or less likely to conclude “it’s ringing”, regardless of whether it really is.
Of course, there’s a trade-off to be made. If you don’t mind making more false alarms, you can avoid making so many misses. In other words, you can make sure that you always notice when your phone is ringing, but only at the cost of experiencing more phantom vibrations.
These two features of a perceiving system – sensitivity and bias – are always present and independent of each other. The more sensitive a system is the better, because it is more able to discriminate between true states of the world. But bias doesn’t have an obvious optimum. The appropriate level of bias depends on the relative costs and benefits of different matches and mismatches.
What does that mean in terms of your phone? We can assume that people like to notice when their phone is ringing, and that most people hate missing a call. This means their perceptual systems have adjusted their bias to a level that makes misses unlikely. The unavoidable cost is a raised likelihood of false alarms – of phantom phone vibrations. Sure enough, the same study that reported phantom phone vibrations among nearly 80% of the population also found that these types of mismatches were particularly common among people who scored highest on a novelty-seeking personality test. These people place the highest cost on missing an exciting call.
From Mind Hacks.
It doesn’t make sense that exercise is good for you. Its just unnecessary wear and tear on your body. Take the analogy of a car. Would it make sense to take it out for a drive up and down the block just to “exercise” it? Your car will survive for only so many miles and you are wasting them with exercise.
But exercise is supposed to pay off in the long run. Sure you are wasting resources and subjecting your body to potential injury by exercising but if you survive the exercise you will be stronger as a result. Still this is hard to understand. Because its your own body that is making itself stronger. Your body is re-allocating resources away from some other use in order to build muscles. If that’s such a good thing to do why doesn’t your body just do it anyway? Why do you first have to weaken yourself and risk injury before your body begrudgingly does this thing that it should have done in the first place?
It must be an agency issue. Your body can either invest resources in making you stronger or use them for something else. The problem for your body is knowing which to do, i.e. when the environment is such that the investment will pay off. The physiological processes evolved over too long and old a time frame for them to be well-tuned to the minute changes in the environment that determine when the investment is a good one. Your body needs a credible signal.
Physical exercise is that signal. Before people started doing it for fun, more physical activity meant that your body was in a demanding environment and therefore one in which the rewards from a stronger body are greater. So the body optimally responds to increased exercise by making itself stronger.
Under this theory, people who jog or cycle or play sports just to “stay fit” are actually making themselves less healthy overall. True they get stronger bodies but this comes at the expense of something else and also entails risk. The diversion of resources and increased risk are worth it only when the exercise signals real value from physical fitness.
My friend and Berkeley grad school classmate Gary Charness posted this on Facebook:
It has finally happened. This could be a world record. I now have 63 published and accepted papers at the age of 63. I doubt that there is anyone who *first* matched their (positive) age at a higher age. Not bad given that my first accepted paper was in 1999. I am very pleased !!
Note that Gary is setting a very strict test here. Draw a graph with age on the horizontal axis and publications on the vertical. Take any economist and plot publications by age. It’s already a major accomplishment for this plot to cross the 45 degree line at some point. Its yet another for it to still be above the 45 degree line at age 63. But its absolutely astounding that Gary’s plot first crossed the 45 degree line at age 63.
(Yes Gary was my classmate at Berkeley when I was 20-something and he was 40-something.)
The less you like talking on the phone the more phone calls you should make. Assuming you are polite.
Unless the time of the call was pre-arranged the person placing the call is always going to have more time to talk than the person receiving the call simply because the caller is the one making the call. So if you receive a call but you are too polite to make an excuse to hang up you are going to be stuck talking for a while.
So in order to avoid talking on the phone you should always be the one making the call. Try to time it carefully. It shouldn’t be at a time when your friend is completely unavailable to take your call because then you will have to leave a voicemail and he will eventually call you back when he has plenty of time to have a nice long conversation.
Ideally you want to catch your friend when they are just flexible enough to answer the phone but too busy to talk for very long. That way you meet your weekly quota of phone calls at minimum cost in terms of time actually spent on the phone. What could be more polite?
Matthew Rabin was here last week presenting his work with Erik Eyster about social learning. The most memorable theme of their their papers is what they call “anti-imitation.” It’s the subtle incentive to do the opposite of someone in your social network even if you have the same preferences and there are no direct strategic effects.
You are probably familiar with the usual herding logic. People in your social network have private information about the relative payoff of various actions. You see their actions but not their information. If their action reveals they have strong information in favor of it you should copy them even if you have private information that suggests doing the opposite.
Most people who know this logic probably equate social learning with imitation and eventual herding. But Eyster and Rabin show that the same social learning logic very often prescribes doing the opposite of people in your social network. Here is a simple intuition. Start with a different, but simpler problem. Suppose that your friend makes an investment and his level of investment reveals how optimistic he is. His level of optimism is determined by two things, his prior belief and any private information he received.
You don’t care about his prior, it doesn’t convey any information that’s useful to you but you do want to know what information he got. The problem is the prior and the information are entangled together and just by observing his investment you can’t tease out whether he is optimistic because he was optimistic a priori or because he got some bullish information.
Notice that if somebody comes and tells you that his prior was very bullish this will lead you to downgrade your own level of optimism. Because holding his final beliefs fixed, the more optimistic was his prior the less optimistic must have been his new information and its that new information that matters for your beliefs. You want to do the opposite of his prior.
This is the basic force behind anti-imitation. (By the way I found it interesting that the English language doesn’t seem to have a handy non-prefixed word that means “doing the opposite of.”) Suppose now your friend got his prior beliefs from observing his friend. And now you see not only your friend’s investment level but his friend’s too. You have an incentive to do the opposite of his friend for exactly the same reason as above.
This assumes his friend’s action conveys no information of direct relevance for your own decision. And that leads to the prelim question. Consider a standard herding model where agents move in sequence first observing a private signal and then acting. But add the following twist. Each agent’s signal is relevant only for his action and the action of the very next agent in line. Agent 3 is like you in the example above. He wants to anti-imitate agent 1. But what about agents 4,5,6, etc?
If you are like me and you believe that thinking is better path to success than not thinking, its hard not to take it personally when an athlete or other performer who is choking is said to be “overthinking it.” He needs to get “untracked.” And if he does and reaches peak performance he is said to be “unconscious.”
There are experiments that seem to confirm the idea that too much thinking harms performance. But here’s a model in which thinking always improves performance and which is still consistent with the empirical observation that thinking is negatively correlated with performance.
In any activity we rely on two systems: one which is conscious, deliberative and requires “thinking.” The other is instinctive. Using the deliberative system always gives better results but the deliberation requires the scarce resource of our moment-to-moment attention. So for any sufficiently complex activity we have to ration the limited capacity of the deliberative system and offload many aspects of performance to pre-programmed instincts.
But for most activities we are not born with an instinctive knowledge how to do it. What we call “training” is endless rehearsal of an activity which establishes that instinct. With enough training, when circumstances demand we can offload the activity to the instinctive system in order to conserve precious deliberation for whatever novelties we are facing which truly require original thinking.
An athlete or performer who has been unsettled, unnerved, or otherwise knocked out of his rhythm finds that his instinctive system is failing him. The wind is playing tricks with his toss and so his serve is falling apart. Fortunately for him he can start focusing his attention on his toss and his serve and this will help. He will serve better as a result of overthinking his serve.
But there is no free lunch. The shock to his performance has required him to allocate more than usual of his deliberative resources to his serve and therefore he has less available for other things. He is overthinking his serve and as a result his overall performance must suffer.
(Conversation with Scott Ogawa.)
I coach my daughter’s U12 travel soccer team. An important skill that a player of this age should be picking up is the instinct to keep her head up when receiving a pass, survey the landscape and plan what to do with the ball before it gets to her feet. The game has just gotten fast enough that if she tries to do all that after the ball has already arrived she will be smothered before there is a chance.
Many drills are designed to train this instinct and today I invented a little drill that we worked on in the warmups before our game against our rivals from Deerfield, Illinois. The drill makes novel use of a trick from game theory called a jointly controlled lottery.
Imagine I am standing at midfield with a bunch of soccer balls and the players are in a single-file line facing me just outside of the penatly area. I want to feed them the ball and have them decide as the ball approaches whether they are going to clear it to my left or to my right. In a game situation, that decision is going to be dictated by the position of their teammates and opponents on the field. But since this is just a pre-game warmup we don’t have that. I could try to emulate it if I had some kind of signaling device on either flank and a system for randomly illuminating one of the signals just after I delivered the feed. The player would clear to the side with the signal on.
But I don’t have that either and anyway that’s too easy and quick to read to be a good simulation of the kind of decision a player makes in a game. So here’s where the jointly controlled lottery comes in. I have two players volunteer to stand on either side of me to receive the clearing pass. Just as I deliver the ball to the player in line the two girls simultaneously and randomly raise either one hand or two. The player receiving the feed must add up the total number of hands raised and if that number is odd clear the ball to the player on my left and if it is even clear to the player on my right.
The two girls are jointly controlling a randomization device. The parity of the number of hands is not under the control of either player. And if each player knows that the other is choosing one or two hands with 50-50 probability, then each player knows that the parity of the total will be uniformly distributed no matter how that individual player decides to randomize her own hands.
And the nice thing about the jointly controlled lottery in this application is that the player receiving the feed must look left, look right, and think before the ball reaches her in order to be able to make the right decision as soon as it reaches her feet.
We beat Deerfield 3-0.
I loved that show. She died last month. Here are 30 selected episodes. Definitely check out the Keith Jarett one.
- Facebook’s business problem is that it is the social network of people you see in real life. All the really interesting stuff you want to do and say on the internet is stuff you’d rather not share with those people or even let them know you are doing/saying.
- What is the rationale for offsides in soccer that doesn’t also apply to basketball?
- If the editors of all the journals were somehow agreeing to publish each others’ papers what patterns would we look for in the data to detect that?
- I need to know in advance the topic of the next 3 Gerzensee conferences so that I can start now writing papers on those topics in hopes of getting invited.
Suppose you are writing a referee report and you are recommending that the paper be rejected. You have a long list of reasons. How many should you put in your report? If you put only your few strongest arguments you run the risk that the author (or editor) finds a response to those and accepts the paper.
You will have lost the chance to use your next few strongest arguments to their full effect, even if there is a second round. The reason has to do with a basic friction of rhetoric. Nobody really knows what’s true or false, but the more you’ve thought about it the better informed you are. So there is always a signaling aspect to rhetoric. Even if the opponent can’t find a counterargument, when it is known that you rank your argument low in terms of persuasiveness, your argument will as a result be in fact less persuasive. Your ranking reveals that you believe that the probability is high that a counterargument could be found, even if by chance this time it wasn’t.
On the other hand you also don’t want to put all of your arguments down. The risk here is that the author refutes all but your strongest one or two arguments. Then the editor may conclude that your decision to reject was made on the basis of that long list of considerations and now that a large percentage of them have been refuted this seals the case in favor. Had you left out all the weak arguments your case would look stronger.
It may even be optimal to pick a non-interval subset of arguments. That is you might give your strongest argument, leave out the second strongest but include the third strongest. The reason is that you care not just about the probability that any single one of your arguments is refuted but the probability that a large subset of your arguments survive. And here correlation matters. It may be that a refutation of the strongest argument is likely also to partially weaken the second-strongest. You pick the third because it is orthogonal to the first.
Grocery chain Trader Joe’s has opened up a legal can of whup ass on its self-professed “best customer,” Pirate Joe’s.
Vancouver, British Columbia shopkeeperMichael Hallatt, claims to have spent more than $350,000 at Trader Joe’s in the past two years. Trader Joe’s would like him to stop shopping there. What gives?
Hallatt, makes frequent drives across the border to shop the U.S. stores, then resells popular Trader Joe’s branded products in his own store, cannily called Pirate Joe’s.
Various commentators are at a loss to explain why Trader Joe’s would cut off its best customer. But isn’t it obvious? Trader Joe’s always had the option of opening a store in Vancouver. Because it never did, it must be that it would not be profitable. Now the joint profits between Trader Joe’s and Pirate Joe’s cannot be higher than the profit that Trader Joe’s would have earned if it opened its own store. At worst Trader Joe’s could just replicate what Pirate Joe’s is doing, but probably it could do it more efficiently. So Trader Joe’s which earns only a share of the joint TJ/PJ profit must be less profitable than it would be if it opened its own store in Vancouver which it has already calculated to be unprofitable.
Here is a nice essay on the idea that “over thinking” causes choking. It begins with this study:
A classic study by Timothy Wilson and Jonathan Schooler is frequently cited in support of the notion that experts, when performing at their best, act intuitively and automatically and don’t think about what they are doing as they are doing it, but just do it. The study divided subjects, who were college students, into two groups. In both groups, participants were asked to rank five brands of jam from best to worst. In one group they were asked to also explain their reasons for their rankings. The group whose sole task was to rank the jams ended up with fairly consistent judgments both among themselves and in comparison with the judgments of expert food tasters, as recorded in Consumer Reports. The rankings of the other group, however, went haywire, with subjects’ preferences neither in line with one another’s nor in line with the preferences of the experts. Why should this be? The researchers posit that when subjects explained their choices, they thought more about them.
The upcoming Northwestern home game versus Ohio State has now sold out. Danny Ecker at Crain’s Chicago Business has the post-mortem:
Sales so far show the school was effective in its experimental“Purple Pricing” offer for about 5,000 single-game seats for the game.
The modified Dutch auction system, which guarantees that buyers don’t pay any more for tickets than anyone else in their section, ended up selling out at $195, $151 and $126 for seats on the sideline, corner and end zones, respectively.
On the secondary market, sideline seats have sold for an average of $190, corner seats for $135 and end-zone seats for $127. That suggests that fans haven’t been able to flip them for a profit — at least, not yet.
Suppose you and a friend of the opposite sex are recruited for an experiment. You are brought into separate rooms and told that you will be asked some questions and, unless you give consent, all of your answers will be kept secret.
First you are asked whether you would like to hook up with your friend. Then you are asked whether you believe your friend would like to hook up with you. These are just setup questions. Now come the important ones. Assuming your friend would like to hook up with you, would you like to know that? Assuming your friend is not interested, would you like to know that? And would you like your friend to know that you know?
Assuming your friend is interested, would you like your friend to know whether you are interested? Assuming your friend is not interested, same question. And the higher-order question as well.
These questions are eliciting your preferences over you and your friend’s beliefs about (beliefs about…) you and your friend’s preferences. This is one context where the value of information is not just instrumental (i.e. it helps you make better decisions) but truly intrinsic. For example I would guess that for most people, if they are interested and they know that the other is not that they would strictly prefer that the other not know that they are interested. Because that would be embarrassing.
And I bet that if you are not interested and you know that the other is interested you would not like the other to know that you know that she is interested. Because that would be awkward.
Notice in fact that there is often a strict preference for less information. And that’s what makes the design of a matching mechanism complicated. Because in order to find matches (i.e. discover and reveal mutual interest) you must commit to reveal the good news. In other words, if you and your friend both inform the experimenters that you are interested and that you want the other to know that, then in order to capitalize on the opportunity the information must be revealed.
But any mechanism which reveals the good news unavoidably reveals some bad news precisely when the good news is not forthcoming. If you are interested and you want to know when she is interested and you expect that whenever she is indeed interested you will get your wish, then when you don’t get your wish you find out that she is not interested.
Fortunately though there is a way to minimize the embarrassment. The following simple mechanism does pretty well. Both friends tell the mediator whether they are interested. If, and only if, both are interested the mediator informs both that there is a mutual interest. Now when you get the bad news you know that she has learned nothing about your interest. So you are not embarrassed.
However it doesn’t completely get rid of the awkwardness. When she is not interested she knows that *if* you are interested you have learned that she is not interested. Now she doesn’t know that this state of affairs has occurred for sure. She thinks it has occurred if and only if you are interested so she thinks it has occurred with some moderate probability. So it is moderately awkward. And indeed you know that she is not interested and therefore feels moderately awkward.
The theoretical questions are these: under what specification of preferences over higher-order beliefs over preferences is the above mechanism optimal? Is there some natural specification of those preferences in which some other mechanism does better?
Update: Ran Spiegler points me to this related paper.
A firm has a basic goal: maximize profits. And then it has day-to-day decisions. It is far too complicated to every day try to trace through the consequences of those basic decisions on the fundamental objective of maximizing profits. A manager who tried to do that would spend so much time thinking that by the time he figured it out the day would be over and he’d have to start thinking again about tomorrow’s decision.
So firms don’t hire managers like that. Managers cling to intermediate goals, like say maximize market share. The best intermediate goals are the ones that are easy to monitor and which do a pretty good job of proxying for the underlying goal. These intermediate goals eventually become part of the culture of the firm and knowledge of their connection to the underlying goal can get lost. The manager can’t distinguish between intermediate goals and fundamental goals.
Now a consultant comes in to advise the manager. A consultant’s job is to show the manager how best to pursue his goals. So the very first thing a consultant should do is find out what the manager’s goals are. And here’s where the dilemma arises. The consultant might actually be smart enough to figure out that the manager’s goals are just intermediate goals. Does he say “De Gustibus” and advise the manager on how to pursue his goals even if he can see that in this particular instance it works against what the manager should really be maximizing?
Or does he have enough ambition in his job as advisor to try to convince the manager that his goals are all wrong, that he should really be maximizing something else? I honestly wonder what the smart consultant does in these situations.
More generally, in everyday life we have arguments about what’s the right thing to do. A lot of the time these arguments are confounded by the inability to distinguish whether we are arguing about the right course of action given our common goals (an argument that can be settled) or whether we have really just chosen different intermediate goals (loggerheads.)
Presh Talwalker tells us about this study of parking strategies:
They observed two distinct strategies: “cycling” and “pick a row, closest space.” They compared the results. “What was interesting,” [Professor Andrew Velkey found], “was although the individual cycling were spending more time driving looking for a parking space, on average they were no closer to the door, time-wise or distance-wise, than people using ‘pick a row, closest space.’”
And commenters are inferring that hunting for the best spot is a sub-optimal strategy. But those that are searching for the best parking spot are not interested in reducing their expected parking time, rather they care about the second moment. When we have an appointment there is a deadline effect: our payoff drops precipitously if we arrive past the deadline. Faced with such a payoff function we are typically wiling to increase our expected parking time if in return we can at least increase the probability of getting lucky with a really good spot. “Pick a row, closest space” guarantees we will be a bit late. “Cycling” may increase the average searching time but at least gives us a chance of being on time.