Why Decision Theory Tells You to Eat ALL the Cupcakes

June 17, 2013 14 Comments

cupcakeImagine that you have a big task coming up that requires an unknown amount of willpower – you might have enough willpower to finish, you might not. You’re gearing up to start when suddenly you see a delicious-looking cupcake on the table. Do you indulge in eating it? According to psychology research and decision-theory models, the answer isn’t simple.

If you resist the temptation to eat the cupcake, current research indicates that you’ve depleted your stores of willpower (psychologists call it ego depletion), which causes you to be less likely to have the willpower to finish your big task. So maybe you should save your willpower for the big task ahead and eat it!

…But if you’re convinced already, hold on a second. How easily you give in to temptation gives evidence about your underlying strength of will. After all, someone with weak willpower will find the reasons to indulge more persuasive. If you end up succumbing to the temptation, it’s evidence that you’re a person with weaker willpower, and are thus less likely to finish your big task.

How can eating the cupcake cause you to be more likely to succeed while also giving evidence that you’re more likely to fail?

Conflicting Decision Theory Models

The strangeness lies in the difference between two conflicting models of how to make decisions. Luke Muehlhauser describes them well in his Decision Theory FAQ:

This is not a “merely verbal” dispute (Chalmers 2011). Decision theorists have offered different algorithms for making a choice, and they have different outcomes. Translated into English, the [second] algorithm (evidential decision theory or EDT) says “Take actions such that you would be glad to receive the news that you had taken them.” The [first] algorithm (causal decision theory or CDT) says “Take actions which you expect to have a positive effect on the world.”

The crux of the matter is how to handle the fact that we don’t know how much underlying willpower we started with.

Causal Decision Theory asks, “How can you cause yourself to have the most willpower?”

It focuses on the fact that, in any state, spending willpower resisting the cupcake causes ego depletion. Because of that, it says our underlying amount of willpower is irrelevant to the decision. The recommendation stays the same regardless: eat the cupcake.

Evidential Decision Theory asks, “What will give evidence that you’re likely to have a lot of willpower?”

We don’t know whether we’re starting with strong or weak will, but our actions can reveal that one state or another is more likely. It’s not that we can change the past – Evidential Decision Theory doesn’t look for that causal link – but our choice indicates which possible version of the past we came from.

Yes, seeing someone undergo ego depletion would be evidence that they lost a bit of willpower.  But watching them resist the cupcake would probably be much stronger evidence that they have plenty to spare.  So you would rather “receive news” that you had resisted the cupcake.

A Third Option

Each of these models has strengths and weaknesses, and a number of thought experiments – especially the famous Newcomb’s Paradox – have sparked ongoing discussions and disagreements about what decision theory model is best.

One attempt to improve on standard models is Timeless Decision Theory, a method devised by Eliezer Yudkowsky of the Machine Intelligence Research Institute.  Alex Altair recently wrote up an overview, stating in the paper’s abstract:

When formulated using Bayesian networks, two standard decision algorithms (Evidential Decision Theory and Causal Decision Theory) can be shown to fail systematically when faced with aspects of the prisoner’s dilemma and so-called “Newcomblike” problems. We describe a new form of decision algorithm, called Timeless Decision Theory, which consistently wins on these problems.

It sounds promising, and I can’t wait to read it.

But Back to the Cupcakes

For our particular cupcake dilemma, there’s a way out:

Precommit. You need to promise – right now! – to always eat the cupcake when it’s presented to you. That way you don’t spend any willpower on resisting temptation, but your indulgence doesn’t give any evidence of a weak underlying will.

And that, ladies and gentlemen, is my new favorite excuse for why I ate all the cupcakes.

Filed under Philosophy, Psychology, Rationality

What Would a Rational Gryffindor Read?

March 18, 2013 86 Comments

In the Harry Potter world, Ravenclaws are known for being the smart ones. That’s their thing. In fact, that was really all they were known for. In the books, each house could be boiled down to one or two words: Gryffindors are brave, Ravenclaws are smart, Slytherins are evil and/or racist, and Hufflepuffs are pathetic loyal. (Giving rise to this hilarious Second City mockery.)

But while reading Harry Potter and the Methods of Rationality, I realized that there’s actually quite a lot of potential for interesting reading in each house. Ravenclaws would be interested in philosophy of mind, cognitive science, and mathematics; Gryffindors in combat, ethics, and democracy; Slytherins in persuasion, rhetoric, and political machination; and Hufflepuffs in productivity, happiness, and the game theory of cooperation.

And so, after much thought, I found myself knee-deep in my books recreating what a rationalist from each house would have on his or her shelf. I tried to match the mood as well as the content. Here they are in the appropriate proportions for a Facebook cover image so that you can display your pride both in rationality and in your chosen house (click to see each image larger, with a book list on the left):

Rationality Ravenclaw Library

Rationality Gryffindor Library

Rationality Slytherin Library

Rationality Hufflepuff Library

What do you think? I’m always open to book recommendations and suggestions for good fits. Which bookshelf fits you best? What would you add?

Filed under Arts, Fiction, Rationality

Messing With Time: Why The Flash is in Hell

January 27, 2013 17 Comments

clockInterfering with time can really make a mess of things. We’ve all thought about what might happen if someone travels in time – think movies like Back to the Future, Primer, or Terminator. But let’s take the question to the next level: what if instead of changing position in time – jumping ahead or back – we changed velocities? Would it still be a disaster waiting to happen if we speed up or slow down time?

What would it even mean to change the speed of time? Reading Sean Carroll’s “From Eternity To Here”, he makes an interesting point:

“We live in a world that contains all sorts of periodic processes, which repeat a predictable number of times in comparison to certain other periodic processes. And that’s how we measure duration: by the number of repetitions of such a process. When we say that our TV program lasts one hour, we mean that the quartz crystal in our watch will oscillate 117,964,800 times between the start and end of the show (32,768 oscillations per second, 3,600 seconds in an hour).
…
“As human beings we feel the passage of time. That’s because there are periodic processes occurring within our metabolism – breaths, heartbeats, electrical pulses, digestion, rhythms of the central nervous system. We are a complicated, interconnected collection of clocks.”

So speeding up time across the universe doesn’t make much sense. Every process would still happen at the same relative rate, including our thoughts and metabolism. Modern physics tells us that there isn’t an objective frame of reference – different objects can, in fact, experience different relative times.

The real question is what would happen if we speed up our own processes relative to everything else in the universe. We wouldn’t feel any different – the “internal clocks” Carroll talks about would all still be in sync with each other – but we would notice all outside processes happening much less frequently compared to our thoughts and motions.

But much like the dilemma facing Calvin and Hobbes, which way would you go? As I read Carroll’s book, I started to ask: If you could change your relative speed, would you want to be faster or slower?

The reason to speed yourself up is obvious: you get a comparative advantage over everyone else. Imagine being able to think more, run further, and react more quickly in the same duration of “external time”. Who wouldn’t want that?

But there are advantages to slowing yourself down, too. Slowing down your body’s processes would be like stretching your life experience over a longer period of external time. Any benefit you get from the rest of the world is amplified. Randall Munroe at XKCD seems to have thought about it before in his comic about ‘Time Vultures’:

And it goes beyond food – assistants, coworkers, and fellow citizens could accomplish more. You would get to take advantage of all the medical breakthroughs, technological advances, and political developments that people come up with during your “stretched” lifespan.

As I talked with my friends about the question, many of them brought up the same point: there’s a risk in permanently changing too far. And that brings me to my last point, that Barry Allen (alter-ego of ‘The Flash’) is arguably in a special version of hell. Yes, after being struck by lightning in his lab, he was granted superhuman speed. Sounds great, but if you follow the thought process to its horrifying conclusion you get “The Ballad of Barry Allen” by Jim’s Big Ego:

I’ve got time to think about my past
As I dodge between the bullets
How my life was so exciting
Before I got this way
And how long ago it was now I never can explain
By the clock that’s on the tower
Or the one that’s in my brain

And I’m there before you know it
I’ll be gone before you see me
And I’d like to get to know you
But you’re talking much too slowly
And I know you want to thank me
But I never stick around
‘Cause time keeps dragging on…
And on…
And on

The game theory dynamics are complex. It seems like to the extent that you’re competing with others, you want to be faster. To the extent that you’re cooperating/collaborating with others, you want them to be faster. And overarching all of it, there’s a coordination factor in that you don’t want to be too different from others.

At the moment, this is all just a fun thought experiment. But I know that the next time I’m bored in a meeting or enjoying a particularly nice moment, I’ll wish I could tweak my speed just a bit.

Filed under Physics

Colbert Deconstructs Pop Music, Finds Mathematical Nerdiness Within

September 12, 2012 16 Comments

Stephen Colbert channeling Kurt Godel

And here I thought I didn’t like pop music. Turns out I just hadn’t found the songs that invoke questions about the foundations of logic and mathematics. Fortunately, Stephen Colbert brings our attention to the fascinating – and paradoxical! – pop song “That’s What Makes You Beautiful” by One Direction. Watch Stephen do his thing deconstructing the lyrics with glorious nerdy precision before we take it even further (the good part starts at 1:54 or so):

[gigya src=”http://media.mtvnservices.com/mgid:cms:item:comedycentral.com:418915″ width=”512″ height=”288″ quality=”high” wmode=”transparent” allowFullScreen=”true” ]

For those of you who can’t watch the video, here’s the nerdy part, hastily transcribed:

Their song “That’s What Makes You Beautiful” isn’t just catchy, it has a great message. “You don’t know you’re beautiful. That’s what makes you beautiful.”

First of all: great dating advice. Remember girls, low self esteem – very attractive to men. Guys always go for the low hanging fruit, easy pickings.

Second: the lyrics are incredibly complex! You see, the boys are singing “You don’t know you’re beautiful, that’s what makes you beautiful.” But they’ve just told the girl she’s beautiful. So since she now knows it, she’s no longer beautiful!

But – stick with me, stick with me, oh it goes deeper! – but she’s listening to the song, too. So she knows she’s not beautiful. Therefore, following the syllogism of the song, she’s instantly beautiful again!

It’s like an infinite fractal recursion, a flickering quantum state of both hot and not. I mean, this lyric as iterated algorithm could lead to a whole new musical genre. I call it Mobius pop, which would include One Direction and of course the rapper MC Escher.

They say the way to a man’s heart is through his stomach but honestly, talking about recursion, fractals, and flickering quantum states does far more to win my love.  We can find intellectual stimulation in anything!

And there’s more – we can go nerdier!

Stick With Me, Stick With Me, Oh It Goes Deeper

Let’s analyze the dilemma a bit further:

  1. She can’t KNOW she’s beautiful because, as Stephen points out, that leads to a logical contradiction – she would no longer be beautiful.
  2. She can’t KNOW that she isn’t beautiful, because that also leads to a logical contradiction – she would be beautiful again.
  3. It’s impossible for the girl to know that she is or isn’t beautiful, so she has to be uncertain – not knowing either way.
  4. This uncertainty satisfies the requirements: she doesn’t know that she’s beautiful, therefore, she’s definitely beautiful and can’t know it.

It turns out she’s not in a flickering state of hot and not, she’s perpetually hot – but she cannot possibly know it without logical contradiction! From an external perspective, we can recognize it as true. From within her own mind, she can’t – even following the same steps. How weird is that?

Then it hit me: the song lyrics are a great example of a Gödel sentence!

Gödel sentences, from Kurt Gödel’s famous Incompleteness Theorems, are the statements which are true but unprovable within the system.  Gödel demonstrated that every set of mathematical axioms complex enough to stand as a foundation for arithmetic will contain at least one of these statements: something that is obviously true from an outside perspective, but isn’t true by virtue of the axioms.  (He found a way to coherently encode “The axioms do not prove this sentence to be true.”)  This raises the question: what makes a mathematical statement true if not the fact that it can be derived from the axioms?

Gödel’s findings rocked the world of mathematics and have had implications on the philosophy of mind, raising questions like:

  • What does it mean to hold a belief as true?
  • What are our minds doing when we make the leap of insight (if insight it is) that identifies a Gödel sentences as true?
  • How does this set us apart from the algorithmic computers, which are plagued by their own version of Incompleteness, the Halting Problem?

I had no idea pop music was so intelligent!

Was the boy band comparing her, not to a summer’s day, but a turing-complete computer?  Were they glorifying their listeners by reminding us that, according to some interpretations of Incompleteness Theory, we’re more than algorithmic machines?  Were they making a profound statement about mind/matter dualism?

I don’t know, but apparently I should turn on the radio more often.

[For related reading, see various analyses of Mims’ “This is Why I’m Hot”]

As they say in the Sirius Cybernetics Corporation: Share and Enjoy!

Filed under Arts, Humor, Math

Be a Communications Consequentialist

June 11, 2012 23 Comments

You just hit post.  You put a lot of thought into your message, you laid it out carefully, and look forward to people’s reactions.  You start getting emails telling you that people have commented, so you excitedly check them to find… that somehow they completely and utterly misunderstood you.  It happens.

One of the worst examples I’ve seen is when American Atheists put up a tongue-in-cheek billboard quoting a Bible verse that endorsed slavery, they were misunderstood as promoting slavery themselves.  Oops.

It’s tempting to blame the audience at times like this, isn’t it?

“How did he miss where I covered that?  There’s a whole paragraph refuting that!”
“She couldn’t possibly have read all the way to the bottom of the post before commenting.”
“Did he think for half a second before opening his mouth? See the quote!”

It’s especially tempting to react that way with misunderstood sarcasm.  I nabbed a screenshot of this image getting praise which says, “Intelligent people understand sarcasm does not equal anger.  Sarcasm is cleverly disguised humor.  It’s not my fault if you ‘don’t get it’.”  That’s the tack a lot of people took after the American Atheists’ billboard – blame the offended people for being stupid.  But does it make sense to blame them?

There’s a vague sense in society that writers and readers each have certain responsibilities. Writers need to use proper spelling and grammar, state their view, and provide supporting reasons. Readers need to read the whole thing carefully and charitably. If someone doesn’t hold up their end of the bargain, any misunderstanding is their fault.

And it IS frustrating when people aren’t reading closely enough, or don’t respect your argument enough to spend the time reading it fully.

But we only have control over what we do, and there are things we can do to entice them. We need to be communications consequentialists – The question we should be asking is: am I doing what I can to maximize the chances of getting my point across?

It’s not enough to do our part and hope readers do theirs.  With a few possible exceptions (graduate-level coursework, Immanuel Kant) readers will stop reading something that’s dense and tough.  Or even worse, they’ll walk away with the wrong message.

If we’re trying to maximize our success, we need to go further and help make it easier for readers to understand us.

Ways to help readers:

Here are some steps I’ve come up with to make it easier for readers to come away understanding.  Since my talents lie in writing over artistic design work, I’ve focused on that:

  • Shorten posts. Presenting readers with an epic saga and expecting them to read it all carefully is asking a lot. Ben Radford has an interesting post bemoaning that people don’t read. It’s 1,380 words – appropriate for some audiences, not for others. If my posts get over 1,000 words, I look for ways to trim them or break them into separate posts.
     
  • Write for human brains – Your readers are human. So write in a way that humans find engaging. The Heath brothers have a good framework with the SUCCES principles: ideas are easier to grasp and remember if they’re Simple, Unexpected, Concrete, Credible, Emotional, and Story-driven. Engaged readers will be more likely to read everything, and read it attentively.
     
  • Break up large blocks of text – I still remember reading Les Miserables in class and facing a three-page-long paragraph. It’s daunting! Without paragraph indentations or images breaking up the text, I know my eyes are prone to sliding. On that note…
     
  • Place key sections where people will see them – People don’t read, they usually skim. Eye-scan studies found that people are most likely to read a horizontal stripe near the top of the page, a second stripe slightly further down, and then down along the left side – in a vague “F” pattern. Make sure that you’re using that prime real estate for engaging hooks and key points. Bulleted lists, bolded words, and subheadings also get attention.
     
  • Use subheadings if necessary – As people’s eyes skim and scan the page, descriptive subheadings can help frame the information and help readers keep the flow.
     
  • Eschew Avoid Obscure Words – See what I did there? Seriously though, while readers *can* look up new words in a dictionary, there’s a good chance they won’t. Besides, studies have found that using big words needlessly doesn’t impress people – you’ll seem more intelligent if you express yourself simply.
     
  • Doublecheck words with ambiguous meanings – You can cause a lot of trouble when you use the word ‘religion’ to mean the culture and institution, but people think you mean “the set of beliefs“.  A lot of words, even in context, can be taken multiple ways by a reader who doesn’t already know what you’re thinking. If possible, see if you can replace ambiguous words with their intended substance.
     
  • Be careful with sarcasm – I guarantee that some people will miss it.  Think about whether the joke is worth those misunderstandings (and sometimes it is.)
     

If we write long posts with unbroken blocks of dry text, ignoring everything we know about our human audience, we can predict failure. Even with these tips, success isn’t guaranteed.  But we have reason to think that things like this make readers more likely to walk away understanding us.

And that’s our goal – being understood, not finding someone to blame.

Filed under Communication

Time Travel Art: Fantastic Video

May 22, 2012 4 Comments

It takes a lot for art to excite me.  But when I stumble upon a time-travel-themed YouTube video inspired by Dr. Who and Edward Gorey… I feel the urge to share it with everyone.  Yes, it’s every bit as cool as it sounds. The video is by ‘MaryDoodles’, who produces time-lapse videos of herself painting – but this time she found a way to work time-travel into the delivery as well as the content. You’ll just have to watch it:

I found myself hitting ‘replay’ over and over, figuring out how the hell she did it, spotting new things I’d missed (did you see all the things tying the scenes together?  How about the TARDIS?), and trying to piece the plot together. Alas, she’s not giving hints about the story she intended:

The discussions on Youtube are quite fun to watch as people try and piece together the order of events and what happened. I’ve decided to hold my tongue on this matter. There is an intentional order to the story but the fact that other people are seeing different orders of events, character relations and catalysts I figured I’d just leave my opinions out of it. It’s almost like a personality test when you hear someone’s take on the video. There are those that take the “glass is half empty” approach while others say the “glass is half full”. Happy ending? Tragic ending?”

I’m still making up my mind. Curiosity is a wonderful emotion, and I think the ambiguity is actually a positive factor.

Stereotypical koans take the ambiguity too far – “What is the sound of one hand clapping?” is just a broadside assault on semantics – but this is pleasantly confusing to me, like a puzzle.

Filed under Arts, Video

Basking in Reflected Glory: Football, Self Esteem, and Pronoun Choice

February 6, 2012 13 Comments

Sports fan? This might describe you. Not a sports fan? This will help you make fun of the sports fans! Everyone else who just doesn’t care either way, here’s a neat psychology study for you.

You’ve probably noticed that when a team wins, their fans are more likely to wear their jerseys around. Since the New York Giants beat the New England Patriots 21-17 in the Superbowl last night, I’ve seen a bunch of proud Giants fans gloating on Facebook. But it’s not just the bragging, it’s the way they brag.

It turns out that sports fans will actually change the words they use based on whether their favorite team won or lost. Once again, I turn to the impeccable Mitchell and Webb to illustrate the tendency:



I love that retort: “Remember when we were chasing the Nazis in Raiders of the Lost Ark?” Movies don’t inspire the same tribal attitudes that sports do, but Mitchell’s rant does highlight the absurdity of using the word “we” in this context.

It’s not just anecdotal. Mitchell and Webb are describing an actual social phenomenon: Even if they have nothing to do with the results, fans are more likely to use “we” pronouns when their favorite team is doing well.

Robert Cialdini called it Basking in Reflected Glory. In an attempt to gain social standing, we try to associate ourselves with success.

Basking in Reflected Glory

Conducting a creative study (pdf), Cialdini and his researchers called college students and asked them how their school’s team had done in a particular game. When describing victories, 32% of the students referred to the team as “we” – “We won,” “We beat them,” etc. In contrast, only 18% used the word “we” when talking about their school’s team losing.

Makes sense, right? People wanted to be seen as part of a winning group. But it gets better.

Cialdini added a twist to his study: before asking about the football game, he asked the students six quick, factual questions. Regardless of their answers, they were either told that they’d done well (gotten five correct) or poorly (gotten only one out of six correct). He hypothesized that the students who were told they’d failed would be more likely to grasp at straws to regain social status.

When the numbers were separated out, the tendency was clear: Almost all the increase in “we” pronouns was from the students who lost prestige by being told they’d failed.

Likelihood of using “we” pronoun(%)

“Succeeded” on Test “Failed” on Test Mean
Describing Win 24% (11/45) 40% (16/40) 32% (27/85)
Describing Loss 22% (9/41) 14% (6/42) 18% (15/83)

Students who were given a dose of self-esteem didn’t change their language based on whether their team won or lost.

But students who felt embarrassed? They were much more likely to latch onto a winning team and distance themselves from a losing team.

So you know all those Giants fans posting status updates on Facebook saying “We won!” or “We’re number one”? Ask them why their self-esteem is so low that they need to Bask in Reflected Glory.

That’ll show ’em.

[Title changed after posting from “How Football Scores Actually Change The Way We Talk”]

Filed under Humor, Sociology, Sports, Video

Why Blocking Roads Can Speed Up Traffic

January 25, 2012 10 Comments

It’s so counter-intuitive that it’s called Braess’ Paradox: How can closing a road actually make everyone’s commute shorter? You would think that blocking a route would be an inconvenience, but under some circumstances it’s actually for the best.

Doesn’t sound right, does it?  Here’s the situation: Assume drivers are rational and intelligent.  I know, that’s a stretch – I grew up around DC.  But bear with me.  If there are multiple paths that people can take, they should in theory find an equilibrium between them.  If one path has less traffic and takes less time, more people will switch to it until it loses its advantage.  If one path starts longer than the others, nobody will use it until the other paths get congested enough to make it worth it.

So how can an extra path actually make the average commute time longer?  Shouldn’t an extra path just give people more options to choose from, and ultimately find the best equilibrium?

The Situation:

It turns out that when some roads are more prone to traffic than others, it can create Braess’ Paradox.  Imagine that some roads aren’t as affected by traffic – I picture these as the local roads with traffic lights. They add a fixed amount of time to your commute, say 45 minutes. The other roads are heavily dependent on traffic – these highways can either be wonderfully fast or a mess of stop-and-go congestion, depending on how many other people are on them. The average time it takes to drive on them is the number of cars over 100.


(Image modified from Wikipedia)

Let’s say there are 4000 cars driving from the start to finish. Without the connector (dotted in the diagram), an equilibrium forms where half the drivers (2000 cars) take the top route through A, and half take the bottom route through B.  The highway takes 2000/100 = 20 minutes, and the local road takes 45 minutes. So half the population spends 45 minutes on a local street, followed by 20 minutes on a highway, and the other half of the drivers spend 20 minutes on a highway, followed by 45 minutes on a local street. Everyone gets to their destination in 65 minutes. Nobody has any incentive to switch.

But what if a new connector is opened between A and B, allowing people to go straight from one highway to the other? Now everyone thinks to themselves, “Hey, why spend 45 minutes on a local street when I could spend 20 minutes on the highway? I’m going to take the route Start –> A –> B –> Finish, and shave 25 minutes off of my commute time!”

Of course, if everyone thinks that way, there are now double the cars on each highway than there were before, and it’s half as fast: now each highway takes 40 minutes, not 20 minutes. That’s still 5 minutes less than the 45 minutes it takes to drive on the local street, though, so everyone still has an incentive to take the highway.

So in the end, how has the connector affected people’s commutes? Everyone’s commute used to be 65 minutes; now, everyone’s commute is 80 minutes. And to make it stranger, there’s no better path to take – anyone considering switching to their original route would be looking at an 85 minute drive.

How does this happen?

How can opening a new, super-fast connector make commutes worse? It comes down to the price of anarchy and people’s selfish motivations.  With the connector open, each set of cars has the option to clog up the other half’s highways – saving themselves 5 minutes but adding 20 minutes to the other guys’ commute.

It’s like the prisoner’s dilemma: Each driver has the motivation to take the highways, even though it damages the overall system. Without the connector, nobody is allowed to “defect” for personal gain. In the traditional prisoner’s dilemma, it would be like a mafia boss keeping all his criminals anonymous. Without the option to rat each other out, criminals would avoid the selfish temptation and the entire system is better off.

Braess’ Paradox isn’t purely hypothetical – it has real-world implications in city planning. According to this New York Times article titled What if They Closed 42d Street and Nobody Noticed?, “When a network is not congested, adding a new street will indeed make things better. But in the case of congested networks, adding a new street probably makes things worse at least half the time, mathematicians say.”  That’s shocking. My intuitions about how traffic works were way off.

Lastly, via Presh Talkwalkar’s fantastic game theory blog, Mind Your Decisions, (which brought Braess’ paradox to my attention) there’s a great video of the paradox physically in action with springs. Check it out:

Filed under Game Theory, Paradoxes, Video

Nerdy Romance Mistakes

November 22, 2011 14 Comments

As much as I hate the stereotype that nerds are hopeless at romance (and social life in general) today’s SMBC comic cracked me up:

At first it seemed like an example of the conjunction fallacy, in which people think the general conditions are less likely than a more specific example of the conditions.  (That’s mathematically impossible.)  But the comic isn’t about probability, it’s about utility.  And you know, it’s not just a GIVEN that owning the world has net positive utility!  It would be extraordinarily time-consuming to rule the world.

Yeah, I know, it’s a stretch.

And I’m forced to plead guilty to a similar situation.  A number of years back, a girl I was dating told me she worried sometimes that she liked me more than I liked her.  My unthinking response at the time was, “Well, it’s unlikely to be exactly equal.  Someone has to like the other more.”

…

I’ve gotten much better since then.

If only I’d heard of the Maxims of Conversation earlier:

Quantity:

  • Say no less than the conversation requires.
  • Say no more than the conversation requires.

Quality:

  • Don’t say what you believe to be false.
  • Don’t say things for which you lack evidence.

Manner:

  • Don’t be obscure.
  • Don’t be ambiguous.
  • Be brief.
  • Be orderly.

Relevance:

  • Be relevant.

We tend to assume that people are following these maxims in conversation.  While my reply is true in a strict sense, it implied a whole lot more.

Ah well, live and learn.

Filed under Humor, Sociology

Coach Smith’s Gutsy Call

November 16, 2011 17 Comments

Coach Mike Smith was facing a tough decision. His Falcons were in overtime against the division-rival Saints. His team had been stopped on their own 29 yard-line and were facing fourth down and inches. Should he tell his players to punt, or go for it? A punt would be safe. Trying to get the first down would be the high-risk, high-reward play. Success would mean a good chance to win, failure would practically guarantee a loss. What play call would give his team the best chance to win?

He decided to be aggressive. He called for star running back Michael Turner to try pounding up the middle of the field.

It failed. The Saints were given the ball in easy range to score, and quickly did so. The media and fans criticized Smith for his stupid decision.

But is the criticism fair? If the play call had worked, I bet he would have been praised for his guts and brilliance. I think my favorite reaction came from ESPN writer Pat Yasinskas:

When Mike Smith first decided to go for it on fourth-and-inches in overtime, I liked the call. I thought it was gutsy and ambitious. After watching Michael Turner get stuffed, I changed my mind. Smith should have punted and taken his chances with his defense.

What a perfect, unabashed example of Outcome Bias! We have a tendency to judge a past decision solely based on the result, not on the quality of the choice given the information available at the time.

Did Coach Smith know that the play would fail? No, of course not. He took a risk, which could go well or poorly. The quality of his decision lies in the chances of success and the expected values for each call.

Fortunately, some other people at ESPN did the real analysis, using 10 years of historical data of teams’ chances to win based on factors like field position, score, time remaining, and so on:

Choice No. 1: Go for the first down

…Since 2001, the average conversion percentage for NFL teams that go for it on fourth-and-1 is 66 percent. Using this number, we can find the expected win probability for Atlanta if it chooses this option.

* Atlanta win probability if it converts (first-and-10 from own 30-yard line): 67.1 percent
* Atlanta win probability if it does not convert (Saints first-and-10 from Falcons’ 29-yard line): 18 percent.
* Expected win probability of going for the first down: 0.660*(.671) + (1-.660)*(.180) = 50.4%

Choice No. 2: Punt

* For this choice, we will assume the Falcons’ net punt average of 36 yards for this season. This means the expected field position of the Saints after the punt is their own 35-yard line. This situation (Saints with first-and-10 from their 35, in OT, etc.) would give the Falcons a win probability of 41.4%.

So by choosing to go for it on fourth down, the Falcons increased their win probability by 9 percentage points.

That’s a much better way to evaluate a coach’s decision! Based on a simple model and league averages (there are problems with both of those, but they’re better than simply trusting outcome!) the punt was not the best option. Smith made the right decision.

Well, sort of. There are different ways to go for the fourth-down conversion, and according to Brian Burke at AdvancedNFLStats, Smith chose the wrong one:

Conversion success rates on 1-yd to go runs (%)

Position 3rd Down 4th Down
FB 77 70
QB 87 82
RB 68 66
Total 72 72

In these situations, quarterback sneaks have proven much more effective than having your running back take the ball. In a perfect game-theory world, defenses would realize their weakness and focus more effort on stopping it. But for now, it remains something more offenses teams can exploit. According to the numbers, the Falcons probably could have made a better decision.

And, of, course, it was OBVIOUS to me at the time that they should have called a quarterback sneak. </hindsight bias>

Filed under Game Theory, Statistics

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