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I want to say this would be hilarious if true. But the thing is it can’t be hilarious even if its true because, not knowing for sure whether its true or a hoax its too easily hoaxed and its exactly the kind of thing that would be hoaxed and having that in your mind when you watch it makes it not funny even if its true. There is a trough in the funny curve as we move along the x-axis between the two local optima of overtly made-up (e.g. an SNL fake commercial) at the left end-point and true with subjective probability 1 on the right end-point. Its getting near impossible to make it that far to the right, indeed the farthest we can get still puts us below the local optimum at the left.
(Capotain curl: Kottke.)
A great story on The Morning News about a guy who is trying to preserve his spoiler-free existence in the face of meddling Internets, bus riders, and Amazon delivery guys:
Well, don’t you worry. This book will be on your doorstep tomorrow afternoon, ready to read.
I, of course, could read the book–YOUR book–right now.
And I gotta admit, it WOULD be fun to be one of the first people in the world to know how it all ends.
Hmm. So, maybe I’ll just read the last page…
OH MY GOD I CANNOT BELIEVE IT!! IT WAS ALL A DREAM???!
Hah hah. I’m just yanking your chain. That’s not how it ends. Or maybe it IS, and I’m just saying it’s not so you’ll be doubly surprised when you finish it. You never know.
I really did read the last page, though. The final word is “haberdashery.” You can verify that when you get the book. Tomorrow. A full day after I had it.
I gotta tell ya, though: Now that I know how it ends, I kind of want to read the whole thing. If I start right now, I could probably finish it and get this book in the mail to you by Wednesday. You wouldn’t mind waiting a few extra days, would you?
Also, I dog-ear pages to save my place. I hope that’s OK.
j/k. I wouldn’t really read this book. 1,000 words about fairies? Yeah, no. Besides, who has the time? Some of us have to work for a living. For instance, I bust my hump 60 hours a week schlepping your books around.
Besides, I’d rather see the movie anyway. That chick who plays Hermione is smoking hot. I’d quidditch, if you know what I’m sayin’.
Including analysis of the ncessary and sufficient epistemic conditions for an arbitrary statement to qualify as a spoiler:
- Did your comment spoil my reading experience? Yes.
- Was my experience any less spoiled because you didn’t know your comment was true? No.
- Was my experience any less spoiled because you really, truly, honestly, swear to God didn’t mean to spoil the experience for anyone? No.
- Was my experience any less spoiled because I knew your comment was true only by accident? Nope again.
Read it. (Spoiler alert.)
Wile E. Coyote runs off a cliff but gravity doesn’t seem to work on him. He just keeps on running, suspended in air, a supernatural feat. But here’s the tragedy: he is capable of this feat only because he doesn’t know he’s doing it. And it’s exactly the moment he realizes there is no ground beneath his feet that he comes crashing down into the canyon below. There is never an instant where he is both flying and aware that he is flying.
It’s the fearless who succeed. But take two people who are equally talented and ask which one is more likely to be fearless. It’s the one who is less worried about failure. But if we turn that around then what it says is that the guy for whom failure hurts the most is the one that’s going to fail.
Everyone has gone through something like this: you take on some new challenge like playing chess or the piano. You work hard at it because initially two things are true: a) when you see other people who do it well you sense the feeling of pride and satisfaction you would have if you could do it well too, and b) at the beginning you cannot yet do it well. Then after lots of hard work finally you can do it too. But somewhere along the way something changed. Mastering it meant discovering that it’s not such an impressive feat after all. Now that you can do it you see that there is a method to it, it’s not magic like you thought.
Could it be that the causality actually works in the opposite direction: those skills that you eventually do master, you master them because you stop thinking of them as magic as start to think of them as routine methodical tricks.
Is it even possible for someone to be great at something and be in as much awe of himself as the rest of us failures are of him?
This guy wrote a column about The Hunger Games and gave away many details of the plot, some of them big-time spoilers. Then he wrote a column about how he was actually doing his readers a favor because spoilers actually increase the enjoyment of the book. For example
The suggestion is that there is a trade-off in the pleasures available to first-time readers or viewers on the one hand, and “repeaters” (as they are called in the scholarly literature) on the other. First-time readers or viewers, because they don’t know what’s going to happen, have access to the pleasures of suspense — going down the wrong path, guessing at the identity of the killer, wondering about the fate of the hero. Repeaters who do know what is going to happen cannot experience those pleasures, but they can recognize significances they missed the first time around, see ironies that emerge only in hindsight and savor the skill with which a plot is constructed. If suspense is taken away by certainty, certainty offers other compensations, and those compensations, rather than being undermined by a spoiler, require one.
The positive case for spoilers is even stronger if you are persuaded by those who argue, in the face of common sense, that suspense survives certainty. This is called “the paradox of suspense” and it is explained by A. R. Duckworth: “1. Suspense requires uncertainty. 2. Knowledge of the outcome of a narrative, scene or situation precludes any uncertainty. 3. [Yet] we feel suspense in response to fictions we know the outcomes of” (“The Paradox of Suspense II—The Problem,” The Journal of Film, Art and Aesthetics, Jan. 14, 2012).
and some other related arguments. Even if you accept these arguments, they amount to saying that there is a qualitative difference between the spoiled reading and the fresh reading and you want to have both. But this does not vindicate the spoilage. The problem with the spoiler is that it deprives you of the fresh reading. Spared the spoiler, or suitably alerted, you could have had both.
Now maybe you have time for only one reading. And so the counterargument could be that if the spoiled reading is in fact better than the fresh one then the spoiler saves you the effort of self-spoiling (settle down Beavis!) and gets you straight to the good, i.e. spoiled, stuff.
But notice what this says about the author of the novel. The author invented this whole story. She created the entire spoil-fodder. Indeed the spoiler only exists because the author chose not to “spoil” it himself by informing the reader right away what’s going to happen later. Either that is because this makes for a better story, or because the author is incompetent. In other words, putting a naked spoiler into your column and claiming that it makes the story better is tantamount to saying that the author is a hack. Not
If “The Hunger Games” is so shallow that it can be spoiled by a plot revelation, the alert doesn’t save much. If “The Hunger Games” is a serious accomplishment, no plot revelation can spoil it.
Deerstalker dash: Alex Frankel.
Do memories depreciate slowly, bit by bit, or do they remain constant for some time and then wiped out completely? For short term visual memory its the latter:
Which is exactly what happened: Zhang & Luck found that participants were either very precise, or they completely guessed; that is, they either remembered the square’s color with great accuracy, or forgot it completely. It was almost as if their memories behaved like files on a computer: Your Microsoft Word documents don’t lose letters over time, and your digital photos don’t yellow; rather, they continue to exist until you move them into the trash—where they are wiped out all at once.
But for long term memories its the former. Check out this Scientific American article that surveys some recent research on the shelf life of memories.
Here’s a model of self-confidence. People meet you and they decide if they admire/respect/lust after you. You can tell if they do. When they do you learn that you are more admirable/respectable/attractive than you previously knew you were. Knowing this increases your expectation that the next person will react the same way. That means that when you meet the next person you are less nervous about how they will judge you. This is self-confidence.
Your self-confidence makes a visible impression on that next person. And it’s no accident that your self-confidence makes them admire/respect/lust after you more than they would if you were less self-confident. Because your self-confidence reveals that the last person felt the same way. When trying to figure out whether you are someone worthy of admiration respect or lust, it is valuable information to know how other people decided because people have similar tastes on those dimensions.
And of course it works in the opposite direction too. People who are judged negatively lose self-confidence and their unease is visible to others and makes a poor impression.
For this system to work well it must escape herding and prevent manipulation. Herding would be a problem if confident people ignore that others admire them only because they are confident and they allow these episodes to further fuel their confidence. I believe that the self-confidence mechanism is more sophisticated than this. Celebrities complain about being unable to have real relationships with regular people because regular people are unable to treat celebrities like regular people. A corollary of this is that a celebrity does not gain any more confidence from being mobbed by fans. A top-seeded tennis player doesn’t gain any further boost in confidence from a win over a low-ranked opponent who wilts on the court out of awe and intimidation.
Herding may be harder to avoid on the downside. If people who lack confidence are shunned they may never get the opportunity to prove themselves and escape the confidence trap.
And notwithstanding self-help books that teach you tricks to artificially boost your self-confidence, I don’t think manipulation is a problem either. Confidence is an entry, nothing more. When you are confident people are more willing to get to know you better. But once they do they will learn whether your self-confidence is justified. If it isn’t you may be worse off than if you never had the entry in the first place.
Someone asks you a question and you have an intuitive understanding of precisely what is being asked. If you are not a game theorist you stop there and answer.
If you are a game theorist you start to analyze the question and discover that, as with all language there is some ambiguity. There’s more than one way to answer the question, the answer could be very detailed or just straightforward, the question might actually be rhetorical, there may be some implicit message to you in the question.
You begin to analyze how else she might have posed the same question. The fact that she chose this particular wording over another gives you clues about what precisely she is getting at. By a process of elimination this leads you to refine your interpretation of the question.
But if you are just a mediocre game theorist its pretty likely your analysis is totally wrong and you are worse off than if you hadn’t ever thought to analyze it. Indeed there is a good reason that your intuitive interpretation was the right one. Because the language evolved that way. And the evolution was probably so complex that there is no way a mediocre game theorist could have traced through the path of evolution to deduce that interpretation.
This is like how drugs can be found from compounds that have evolved in the plant and animal kingdom despite the fact that science has no way of knowing how to synthesize those.
And of course pretty much all of us are mediocre game theorists at best.
A rundown of various tricks restaurants use when arranging items on a menu. Including The Anchor, Siberia, Boxes and Bracketing. A sampling:
4. In The Vicinity
The restaurant’s high-profit dishes tend to cluster near the anchor. Here, it’s more seafood at prices that seem comparatively modest.
5. Columns Are Killers
According to Brandon O’Dell, one of the consultants Poundstone quotes in Priceless,it’s a big mistake to list prices in a straight column. “Customers will go down and choose from the cheapest items,” he says. At least the Balthazar menu doesn’t use leader dots to connect the dish to the price; that draws the diner’s gaze right to the numbers. Consultant Gregg Rapp tells clients to “omit dollar signs, decimal points, and cents … It’s not that customers can’t check prices, but most will follow whatever subtle cues are provided.”
Check this out. Five numbers appear on a screen in different locations. They remain visible for 210 milliseconds and then they are obscured. The subject must then touch the locations in increasing order of the numbers that appeared there. That’s pretty much impossible. Here’s a human subject who is highly trained and does an impressive job but still fails miserably.
Now check out how nonchalantly this chimpanzee does it.
I didn’t even know they could count. Note that the 5 numbers are random integers between 1 and 9. So the chimp is processing a binary relation in short-term memory, not to mention reading at a super-human rate. There are more videos here. I saw these at Colin Camerer’s talk last week at Arthur Robson‘s conference on the Biological Basis of Preferences.
Have two subjects play matching pennies. They will face each other but separated by a one-way mirror. Only one subject will be able to see the other’s face. He can only see the face, not anything below the chin.
Each subject selects his action by touching a screen. Touch the screen to the West to play Heads, touch the screen on the East to play Tails. (East-West rather than left-right so that my Tails screen is on the same side as your Tails screen. This makes it easier to keep track.)
You have to touch a lighted region of the screen in order to have your move registered and the lighted region is moving around the screen. This is going to require you to look at the screen you want to touch. But you can look in one direction and then the other and touch only the screen you want. Your hands are not visible to the other subject.
How much more money is earned by the player who can see the other’s eyes?
(Conversation with Adriana Lleras-Muney)
Skip ahead to about 13:00. It seems a little too neatly staged but it’s still hilarious.
Hardee heave: Emil Temnyalov
Subjects video chat with each other. In one treatment subject A sees her own image in a small window in the corner of the chat, and in the other treatment (the control) there is no small window and she sees only the chat partner.
Subject B is not told about the two treatments and is simply asked to report how attractive subject A is. We want to know whether attractiveness is higher in the self-image treatment versus the control treatment.
This gets at a few different issues but the one I am curious about is this: do people know what it is about them that makes them attractive to others?
Also, we would want to track eye movements during the chat.
If you’re a psychologist, the news has to make you a little nervous—particularly if you’re a psychologist who published an article in 2008 in any of these three journals:Psychological Science, the Journal of Personality and Social Psychology,or the Journal of Experimental Psychology: Learning, Memory, and Cognition.
Because, if you did, someone is going to check your work. A group of researchers have already begun what they’ve dubbed the Reproducibility Project, which aims to replicate every study from those three journals for that one year. The project is part of Open Science Framework, a group interested in scientific values, and its stated mission is to “estimate the reproducibility of a sample of studies from the scientific literature.” This is a more polite way of saying “We want to see how much of what gets published turns out to be bunk.”
We should do this in economics. But there is a less confrontational way to do it. Top departments in experimental economics attract PhD students who want hands on experience in the lab. These are departments like NYU and CalTech. They would benefit the profession, their students, and the reputation of their PhD programs, i.e. everybody concerned, if they were to add as a requirement that every student receiving a PhD must pick one recently published experimental article and attempt to replicate it.
Thanks to Josh Gans for the pointer.
Funded by the U.S. Department of Health and Human Services, a panel of experts in psychology and economics, including Nobel laureate Daniel Kahneman, began convening in December to try to define reliable measures of “subjective well-being.” If successful, these could become official statistics.
Alan Krueger, Angus Deaton and Justin Wolfers have cameos in the article.
In Britain, Prime Minister David Cameron has embraced the idea, and last year the government began asking survey respondents things like “Overall, how happy did you feel yesterday?” and “Overall, how satisfied are you with your life nowadays?” The U.K. Economic and Social Research Council is also funding the U.S. panel’s $370,000 budget. In France, President Nicolas Sarkozy in 2008 launched a commission including two Nobel winners, Joseph Stiglitz and Amartya Sen, which opined that the “time is ripe for our measurement system to shift emphasis from measuring economic production to measuring people’s well-being.”
Far ahead in such measures, however, is the tiny Himalayan kingdom of Bhutan, which has embraced the notion of “Gross National Happiness” as a national goal and has created a commission to achieve it.
Sandeep wrote one of our most popular posts on this topic. There was a survey that showed some correlation between pre-marital cohabitation and divorce. Sandeep said its probably just a selection effect.
First, suppose one partner is reluctant to get married and has doubts about the relationship. More information would be helpful to decide whether to stay together or break up. If the couple cohabit, that will give them valuable information. On the other hand, couples who are more confident about their relationship are more likely to get married straight away. Hence, more stable couples are less likely to live together before marriage than less stable couples. Living together per se is not the problem. The real problem is that a deeper source of instability is correlated with cohabitation.
Second – and this theory is implicit in the research – more religious couples are less likely to get divorced and less likely to live together before marriage. Again, selection explains the data and not cohabiting per se.
Now the Internet is back again with a new theory: ”sliding in.”
She was talking about what researchers call “sliding, not deciding.” Moving from dating to sleeping over to sleeping over a lot to cohabitation can be a gradual slope, one not marked by rings or ceremonies or sometimes even a conversation. Couples bypass talking about why they want to live together and what it will mean.
As in, no-sliding-in before marriage. Because if you do, you might actually get locked in:
Sliding into cohabitation wouldn’t be a problem if sliding out were as easy. But it isn’t. Too often, young adults enter into what they imagine will be low-cost, low-risk living situations only to find themselves unable to get out months, even years, later. It’s like signing up for a credit card with 0 percent interest. At the end of 12 months when the interest goes up to 23 percent you feel stuck because your balance is too high to pay off. In fact, cohabitation can be exactly like that. In behavioral economics, it’s called consumer lock-in.
Does this make any sense? Isn’t a couple who goes straight to the sliding in before getting married ultimately just as locked in as a couple who completely abstains from sliding in until they are locked in by the bonds of wedlock?
You are categorically opposed to some policy. She on the other hand is utilitarian and while she believes the policy is effective based on her current information she could be persuaded otherwise. You would like to persuade her if you could and in fact you have some information that might but it’s not guaranteed.
She opens the debate about the policy, states her arguments in favor and invites you to give any arguments against. But you are not interested in her information. You are categorically opposed to the policy and nothing would persuade you otherwise.
Moreover you are not even going to engage in the debate by trying to persuade her with your information. Because to do so would be to implicitly acknowledge that this is a debate that could be won by the side with the stronger argument. That entails the risk that she and any observer might judge her arguments to be stronger and take an even firmer position in favor.
You are better off shutting down that front of the debate and insisting that it must be decided as a matter of principle, not utilitarianism.
At some point, you likely received a present from a prepaid gift card from the person who wasn’t exactly sure what you’d want. Residents of New Jersey may not be able to buy them for much longer. American Express has pulled its gift cards from the state, and other big industry players are threatening to do the same. They oppose a new law that would allow New Jersey to claim unused gift card balances after two years. NPR’s Joel Rose reports.
As you may know, huge sums of money are loaded onto gift cards that are never redeemed. The gift card “industry” leverages a wedge between your overly optimistic belief that you will not lose your gift card and the vendor’s knowledge that with quite high probability you will. Is it welfare improving to prevent the vendor from profiting from this wedge? Whatever welfare theory you are basing your conclusion on, it is not revealed preference, so what is it? (Never mind that it’s the greedy government essentially trying to capture the same wedge. Let’s assume for the sake of argument the unspent balance was automatically remitted to the purchaser of the card.)
Why doesn’t market competition already erode these profits? (“Try our gift cards instead. You will get any unpaid balance back, indeed with interest.”)
Related question. Peet’s coffee has shrunk the size of their gift cards so that they are even easier to lose. They do give you the choice whether you want a large gift card or a small one. Are they being nice?
Twitter has finally acknowledged a long-suspected bug that makes users automatically unfollow accounts for no apparent reason, and now that it’s working on a fix, many would rather keep the bug to cover the awkwardness of manually unfollowing people. Time to admit you’re just sick of your friends’ updates, folks.
Of course, Twitter power users like Reuters’ Anthony De Rosa don’t really want to automatically lose followers, but it’s sort of funny for him to tweet ”one benefit of the unfollow bug is it gives me an excuse if someone gets upset i unfollowed them.” De Rosa’s far from the only one. It seems likehundreds reacted with the same sentiment on hearing the news. That’s because it’s true that sometimes you keep following some idiot just because you don’t want the drama of dropping them. Look at how many people publiclycomplain about losing a follower. Well, tweeters, it’s time for us to take responsibility for our actions just a little bit more. Take a cue from The Awl’s Choire Sicha and embrace the hate.
In basketball the team benches are near the baskets on opposite sides of the half court line. The coaches roam their respective halves of the court shouting directions to their team.
As in other sports the teams switch sides at halftime but the benches stay where they were. That means that for half of the game the coaches are directing their defenses and for the other half they are directing their offenses.
If coaching helps then we should see more scoring in the half where the offenses are receiving direction.
This could easily be tested.
Here’s a simple model of the slippery slope. You have to adopt a position on an issue and defend your position to yourself and your critics. The spectrum of positions ranges from the left-most extreme to the right-most extreme and you have to decide whether to take one of these extreme positions or some moderate point in the interior.
Defending a moderate position is a delicate balancing act. It’s a very special set of utility functions which attain their maximum right at that point, and you need to convince your critics that the right utility function happens to be one of those. Any slight perturbation of a utility function in that set will push you to the left or right so your critics have an easy task. And once you’ve lost the first battle your credibility is damaged.
The easiest positions to defend are the extreme ones. At an extreme position you have a binding constraint. To defend your extremist position it is enough to say that you are such an extremist that you would like to move even farther to the right if that were possible. The set of utility functions that have an optimum somewhere to the right of the right boundary is a large set. You can perturb such a utility function and the extremist position will still be optimal.
The same logic explains why a few special interior positions can be robust to the slippery slope. Think of a kinked budget constraint. A large set of utility functions achieve their optimum at a kink.
In the study, male fruit flies that had mated repeatedly for several days showed no preference for alcohol-spiked food. On the other hand, spurned males and those denied access to females strongly preferred food mixed with 15 percent alcohol. The researchers believed the alcohol may have satisfied the flies’ desire for physical reward.
Over the course of your life you have to decide your position on a number of philosophical/social/political issues. You are open-minded so you collect as much data as you can before forming an opinion. But you are human and you can only remember so many facts.
There will come a time when the data you have collected make a very strong case for one particular position on issue A, say the right-wing position. When that happens you are pretty sure that there is never going to be enough evidence to overturn your position.
That’s not because you are closed-minded. That’s because you are very open-minded and based on the weight of all the evidence you collected and processed as objectively as a person can do, you have concluded that its very likely that this is the right position on A. And the fact that this is very likely the right position on A does not just imply but is indeed equivalent to saying that you attach very low probability to the future occurrence of strong evidence in the other direction.
Now that means that there’s not much point in collecting any more information about A. And indeed there’s not much point in remembering the detailed information that led you to this conclusion. The only reason for doing that would be to weigh it against future evidence but we’ve already established that this is unlikely to make any difference.
So what you optimally, rationally, perfectly objectively do is allow yourself to forget everything you know about A including all the reasons that justify your strongly-held views on A and to just make an indelible mental note that “The right-wing position on A is the correct one no matter what anyone else says and no matter what evidence to the contrary should come along in the future.”
The reason this is the rational thing to do is that you have scarce memory space. By allowing those memories to fade away you free up storage space for information about issues B, C, and D which you are still carefully collecting information on, forming an objective opinion about, in preparation for eventually also adopting a well-informed dogmatic opinion about.
Here is an excellent rundown of some soul searching in the neuroscience community regarding statistical significance. The standard method of analyzing brain scan data apparently involves something akin to data mining but the significance tests use standard single-hypothesis p-values.
One historical fudge was to keep to uncorrected thresholds, but instead of a threshold of p=0.05 (or 1 in 20) for each voxel, you use p=0.001 (or 1 in a 1000). This is still in relatively common use today, but it has been shown, many times, to be an invalid attempt at solving the problem of just how many tests are run on each brain-scan. Poldrack himself recently highlighted this issue by showing a beautiful relationship between a brain region and some variable using this threshold, even though the variable was entirely made up. In a hilarious earlier version of the same point, Craig Bennett and colleagues fMRI scanned a dead salmon, with a task involving the detection of the emotional state of a series of photos of people. Using the same standard uncorrected threshold, they found two clusters of activation in the deceased fish’s nervous system, though, like the Poldrack simulation, proper corrected thresholds showed no such activations.
How can a guy who never misses a field goal miss an easy one at a crucial moment?
Still, a semiconsensus is developing among the most advanced scientists. In the typical fight-or-flight scenario, scary high-pressure moment X assaults the senses and is routed to the amygdala, aka the unconscious fear center. For well-trained athletes, that’s not a problem: A field goal kick, golf swing or free throw is for them an ingrained action stored in the striatum, the brain’s autopilot. The prefrontal cortex, our analytical thinker, doesn’t even need to show up. But under the gun, that super-smart part of the brain thinks it’s so great and tries to butt in. University of Maryland scientist Bradley Hatfield got expert dart throwers and marksmen to practice while wearing a cumbersome cap full of electrodes. Without an audience, their brains show very little chatter among regions. But in another study, when dart throwers were faced with a roomful of people, the pros’ neural activity began to resemble that of a novice, with more communication from the prefrontal cortex.
When I was in the 6th grade I won our school’s spelling bee going away. The next level was the district-wide spelling bee, televised on community access cable. My amygdala tried to insert an extra `u’ into the word tongue and I was out in the first round.
Teller as in Penn &. He’s out to teach neuroscientists a thing or two about deception.
I’m all for helping science. But after I share what I know, my neuroscientist friends thank me by showing me eye-tracking and MRI equipment, and promising that someday such machinery will help make me a better magician.
I have my doubts. Neuroscientists are novices at deception. Magicians have done controlled testing in human perception for thousands of years.
I remember an experiment I did at the age of 11. My test subjects were Cub Scouts. My hypothesis (that nobody would see me sneak a fishbowl under a shawl) proved false and the Scouts pelted me with hard candy. If I could have avoided those welts by visiting an MRI lab, I surely would have.
I was having coffee outside and I saw ants crawling on my feet so I moved to another table.
Then I rewound my stream of consciousness about 30 seconds and I was able to recall that in fact there was a little more going on than that. I was daydreaming while sipping my coffee and I felt ticklishness on my toes and ankles. That made me look down and that’s when I saw the ants.
Now the fact that I had to rewind to remember all of this says something interesting. Had I looked down and not seen ants, i.e. if it turned out it was just the precious Singapore wind blowing on my cozy bare feet, then this episode would never have penetrated my conscious mind. I would have gone on daydreaming without distraction.
The subconscious mind pays attention to a million things outside of our main line of being and only when it detects something worth paying attention to does it intervene in some way. There are two very common interventions. One is to react at a subconscious level. I.e. shooing a fly while I go on daydreaming. Another is to commandeer consciousness and force a reaction. I.e. pay attention to an attractive potential mate passing by.
Both of these involve the subconscious mind making a decisive call as to what is going on, what is its level of significance, and how to dispense with it. It’s all or nothing: let the conscious mind go on without interruption or completely usurp conscious attention.
But the ant episode exemplifies a third type. My subconscious mind effectively said something like this :”I am not sure what is going on here, but I have a feeling that its something that we need to pay attention to. But to figure that out I need the expertise and private information available only to conscious visual attention and deliberation. I am not telling you what to do because I don’t know, I am just saying you should check this out.”
And so a tiny slice of consciousness gets peeled off to attend to that and only on the basis of what it sees is it decided whether the rest has to be distracted too.
As you sit in your office working, reading, etc., the random email arrival process is ticking along inside your computer. As time passes it becomes more and more likely that there is email waiting for you and if you can’t resist the temptation you are going to waste a lot of time checking to see what’s in your inbox. And it’s not just the time spent checking because once you set down your book and start checking you won’t be able to stop yourself from browsing the web a little, checking twitter, auto-googling, maybe even sending out an email which will eventually be replied to thereby sealing your fate for the next round of checking.
One thing you can do is activate your audible email notification so that whenever an email arrives you will be immediately alerted. Now I hear you saying “the problem is my constantly checking email, how in the world am i going to solve that by setting up a system that tells me when email arrives? Without the notification system at least I have some chance of resisting the temptation because I never know for sure that an email is waiting.”
Yes, but it cuts two ways. When the notification system is activated you are immediately informed when an email arrives and you are correct that such information is going to overwhelm your resistance and you will wind up checking. But, what you get in return is knowing for certain when there is no email waiting for you.
It’s a very interesting tradeoff and one we can precisely characterize with a little mathematics. But before we go into it, I want you to ask yourself a question and note the answer before reading on. On a typical day if you are deciding whether to check your inbox, suppose that the probability is p that you have new mail. What p is going to get you to get up and check? We know that you’re going to check if p=1 (indeed that’s what your mailbeep does, it puts you at p=1.) And we know that you are not going to check when p=0. What I want to know is what is the threshold above which its sufficiently likely that you will check and below which is sufficiently unlikely so you’ll keep on reading? Important: I am not asking you what policy you would ideally stick to if you could control your temptation, I am asking you to be honest about your willpower.
Ok, now that you’ve got your answer let’s figure out whether you should use your mailbeep or not. The first thing to note is that the mail arrival process is a Poisson process: the probability that an email arrives in a given time interval is a function only of the length of time, and it is determined by the arrival rate parameter r. If you receive a lot of email you have a large r, if the average time spent between arrivals is longer you have a small r. In a Poisson process, the elapsed time before the next email arrives is a random variable and it is governed by the exponential distribution.
Let’s think about what will happen if you turn on your mail notifier. Then whenever there is silence you know for sure there is no email, p=0 and you can comfortably go on working temptation free. This state of affairs is going to continue until the first beep at which point you know for sure you have mail (p=1) and you will check it. This is a random amount of time, but one way to measure how much time you waste with the notifier on is to ask how much time on average will you be able to remain working before the next time you check. And the answer to that is the expected duration of the exponential waiting time of the Poisson process. It has a simple expression:
Expected time between checks with notifier on =
Now let’s analyze your behavior when the notifier is turned off. Things are very different now. You are never going to know for sure whether you have mail but as more and more time passes you are going to become increasingly confident that some mail is waiting, and therefore increasingly tempted to check. So, instead of p lingering at 0 for a spell before jumping up to 1 now it’s going to begin at 0 starting from the very last moment you previously checked but then steadily and continuously rise over time converging to, but never actually equaling 1. The exponential distribution gives the following formula for the probability at time T that a new email has arrived.
Probability that email arrives at or before a given time T =
Now I asked you what is the p* above which you cannot resist the temptation to check email. When you have your notifier turned off and you are sitting there reading, p will be gradually rising up to the point where it exceeds p* and right at that instant you will check. Unlike with the notification system this is a deterministic length of time, and we can use the above formula to solve for the deterministic time T at which you succumb to temptation. It’s given by
Time between checks when the notifier is off =
And when we compare the two waiting times we see that, perhaps surprisingly, the comparison does not depend on your arrival rate r (it appears in the numerator of both expressions so it will cancel out when we compare them.) That’s why I didn’t ask you that, it won’t affect my prescription (although if you receive as much email as I do, you have to factor in that the mail beep turns into a Geiger counter and that may or may not be desirable for other reasons.) All that matters is your p* and by equating the two waiting times we can solve for the crucial cutoff value that determines whether you should use the beeper or not.
The beep increases your productivity iff your p* is smaller than
This is about .63 so if your p* is less than .63 meaning that your temptation is so strong that you cannot resist checking any time you think that there is at least a 63% chance there is new mail waiting for you then you should turn on your new mail alert. If you are less prone to temptation then yes you should silence it. This is life-changing advice and you are welcome.
Now, for the vapor mill and feeling free to profit, we do not content ourselves with these two extreme mechanisms. We can theorize what the optimal notification system would be. It’s very counterintuitive to think that you could somehow “trick” yourself into waiting longer for email but in fact even though you are the perfectly-rational-despite-being-highly-prone-to-temptation person that you are, you can. I give one simple mechanism, and some open questions below the fold.
As the director of recruiting for your department you sometimes have to consider Affirmative Action motives. Indeed you are sympathetic to Affirmative Action yourself and even on your own your recruiting policy would internalize those motives. But in fact your institution has a policy. You perceive clear external incentives coming from that policy.
Now this creates a dilemma. For any activity like this there is some socially optimal level and it combines your own private motivations with any additional external interests. But the dilemma for you is how these should be combined. One possibility is that the public motive and your own private interest stem from completely independent reasons. Then you should just “add together” the weight of the external incentives you feel plus those of your own. But it could be that what motivates your Dean to institutionalize affirmative action is exactly what motivates you. In this case he has just codified the incentives you would be responding to anyway, and rather than adding to them, his external incentives should perfectly crowd out your own.
There is no way of knowing which of these cases, or where in between, the true moral calculation is. That is a real dilemma, but I want to think of it as a metaphor for the dilemma you face in trying to sort out the competing voices in your own private moral decisions.
Say you have a close friend and you have an opportunity to do something nice for them, say buy them a birthday gift. You think about how nice your friend has been to you and decide that you should be especially nice back. But compared to what? Absent that deliberative calculation you would have chosen the default level of generosity. So what your deliberation has led you to decide is that you should be more generous than the default.
But how do you know? What exactly determined the default? One possibility is that the default represents your cumulative wisdom about how nice you should be to other people in general. Then your reflection on this particular friend’s particular generosity should increment the default by a lot. But surely that’s not the relevant default. He’s your friend, he’s not just an arbitrary person (you would even be considering giving a gift to an arbitrary person.) No doubt your instinctive inclination to be generous to your friend already encodes a lot of the collected memory and past reflection that also went into your most recent conscious deliberation. And as long as there is any duplication, there should be crowding out. So you optimally moderate the enthusiasm that arises from your conscious calculation.
But how much? That is a dilemma.
A question raised over dinner last week. A group of N diners are dining out and the bill is $100. In scenario A, they are splitting the check N ways, with each paying by credit card and separately entering a gratuity for their share of the check. In scenario B, one of them is paying the whole check.
In which case do you think the total gratuity will be larger? Some thoughts:
- Because of selection bias, it’s not enough to cite folk wisdom that tables who split the check tip less (as a percentage): At tables where one person pays the whole check that person is probably the one with the deepest pockets. So field data would be comparing the max versus the average. The right thought experiment is to randomly assign the check.
- Scenario B can actually be divided into two subcases. In Scenario B1, you have a single diner who pays the check (and decides the tip) but collects cash from everyone else. In Scenario B2 the server divides the bill into N separate checks and hands them to each diner separately. We can dispense with B1 because the guy paying the bill internalizes only 1/Nth of the cost of the tip so he will clearly tip more than he would in Scenario A. So we are really interested in B2.
- One force favoring larger tips in B2 is the shame of being the lowest tipper at the table. In both A and B2 a tipper is worried about shame in the eyes of the server but in B2 there are two additional sources. First, beyond being a low tipper relative to the overall population, having the server know that you are the lowest tipper among your peers is even more shameful. But even more important is shame in the eyes of your friends. You are going to have to face them tomorrow and the next day.
- On the other hand, B2 introduces a free-rider effect which has an ambiguous impact on the total tip. The misers are likely to be even more miserly (and feel even less guilty about it) when they know that others are tipping generously. On the other hand, as long as it is known that there are misers at the table, the generous tippers will react to this by being even more generous to compensate. The total effect is an increase in the empirical variance of tips, with ambiguous implications for the total.
- However I think the most important effect is a scale effect. People measure how generous they are by the percentage tip they typically leave. But the cost of being a generous tipper is the absolute level of the tip not the percentage. When the bill is large its more costly to leave a generous tip in terms of percentage. So the optimal way to maintain your self-image is to tip a large percentage when the bill is small and a smaller percentage when the bill is large. This means that tips will be larger in scenario B2.
- One thing I haven’t sorted out is what to infer from common restaurant policy of adding a gratuity for large parties. On the one hand you could say that it is evidence of the scale effect in 5. The restaurant knows that a large party means a large check and hence lower tip percentage. However it could also be that the restaurant knows that large parties are more likely to be splitting the check and then the policy would reveal that the restaurant believes that B2 has lower tips. Does anybody know if restaurants continue to add a default gratuity when the large party asks to have the check split?
- The right dataset you want to test this is the following. You want to track customers who sometimes eat alone and sometimes eat with larger groups. You want to compare the tip they leave when they eat alone to the tip they leave when part of a group. The hypothesis implied by 3 and 5 is that their tips will be increasing order in these three cases: they are paying for the whole group, they are eating alone, they are splitting the check.
(Thanks to those who commented on G+)
Here’s a card game: You lay out the A,2,3 of Spades, Diamonds, Clubs in random order on the table face up. So that’s 9 cards in total. There are two players and they take turns picking up cards from the table, one at a time. The winner is the first to collect a triplet where a triplet is any one of the following sets of three:
- Three cards of the same suit
- Three cards of the same value
- Ace of Spaces, 2 of Diamonds, 3 of Clubs
- Ace of Clubs, 2 of Diamonds, 3 of Spades
Got it? Ok, this game can be solved and the solution is that with best play the result is a draw, neither player can collect a triplet. See if you can figure out why. (Drew Fudenberg got it almost immediately [spoiler.]) Answer and more discussion are after the jump.