Why Decision Theory Tells You to Eat ALL the Cupcakes

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.

How has Bayes’ Rule changed the way I think?

People talk about how Bayes’ Rule is so central to rationality, and I agree. But given that I don’t go around plugging numbers into the equation in my daily life, how does Bayes actually affect my thinking?
A short answer, in my new video below:

 

 

(This is basically what the title of this blog was meant to convey — quantifying your uncertainty.)

What Would a Rational Gryffindor Read?

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?

Messing With Time: Why The Flash is in Hell

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.

Colbert Deconstructs Pop Music, Finds Mathematical Nerdiness Within

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):

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!

Will moving to California make you happier?

I pass dozens of brilliantly-colored flowers like this on my daily walk to work. (Photo credit: B Mully, Flickr)

I might have to disagree with a Nobel Laureate on this one.

According to Daniel Kahneman, Nobel prize-winning psychologist and author of the excellent Thinking Fast and Slow, the answer is “No.” A recent post on Big Think describes how Kahneman asked people to predict who’s happier, on average, Californians or Midwesterners. Most people (from both regions!) say, “Californians.” That’s because, Kahneman explains, the act of comparison highlights what’s saliently different between the two regions: their climate. And on that dimension, California’s a pretty clear winner.

And indeed, Californians report loving their climate and Midwesterners loathing theirs. Yet despite that, the overall life satisfaction in the two regions turns out to be nearly identical, according to a 1998 survey by Kahneman. Climate just isn’t that important to happiness, it turns out. The fact that it greatly influences people’s predictions of relative happiness in California vs. the Midwest stems from something called the “Focusing illusion,” Kahneman explains – a bias he sums up with the pithy, “Nothing in life is as important as you think it is when you are thinking about it.”

So far, I have no beef with this interpretation. What I *do* object to is the conclusion, which Kahneman implies and Big Think makes explicit, that “moving to california won’t make you happy.”

I moved from New York, NY to Berkeley, CA, earlier this year, and — having read Kahneman — I didn’t expect the climate to make a noticeable difference in my mood. And yet, every day, when I would leave my house, I found my spirits buoyed by the balmy weather and the clear blue sky. I noticed, multiple times daily, how beautiful the vegetation was and how fresh, fragrant, and — well – un-Manhattanlike the air smelled. It made a noticeable difference in my mood nearly every day, and continues to, six months after I moved.

I was a little surprised that my result was so different from Kahneman’s. And then I realized: Most of those Californians in his study have always been Californians. They grew up there; they didn’t move from the Midwest (or Manhattan) to California. So it’s understandable that their climate doesn’t make a big impact on their happiness, because they have no standard of comparison. They’re not constantly thinking to themselves — as I have been — “Man, it’s so *nice* not to have to shiver inside a bulky winter coat!” or “Man, it’s such a relief not to smell garbage bags sitting out on the sidewalk,” or “Wow, it’s quite pleasant not to be sticky with sweat.”

I’m only one data point, of course, and it’s possible that if you studied people who moved from the Midwest to CA, you’d find that their change in happiness was in fact no different than that of people who moved from CA to the Midwest. But at least, I think it’s important to note that that’s not the study Kahneman did. And that, as a general rule in reading (or conducting!) happiness research, it’s important to remember that the happiness you get from a state depends on your previous states.

How to Raise a Rationalist Kid

In honor of Father’s Day, I talk about the things Jesse’s and my parents did that helped make us intellectually curious and interested in rationality.

Follow

Get every new post delivered to your Inbox.

Join 487 other followers

%d bloggers like this: