Why Decision Theory Tells You to Eat ALL the Cupcakes
June 17, 2013 14 Comments
Imagine 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.
It’s a fun argument, but I think we all know the REAL reasons you posted this were 1) publicity for Yudkowsy’s new paper and 2) to create a whole new mess of people arguing over Newcomb’s Paradox. Well I WON’T FALL INTO YOUR TRAP YOU MONSTER!
(but it’s totally option 2)
I will neither confirm nor deny that my primary motive was to delight in the confusion that ensues when people read about Newcomb’s Paradox and decision theory contradictions.
Doesn’t this post leave out 1) the positive/negative impacts of eating the cupcake and 2) the net change in long-term willpower capacity based on the decision.
t would appear that the post assumes eating the cupcake is a negative outcome, but the decision model doesn’t seem to weigh the ramifications against the potential savings of willpower.
indulging would not only imply that you may have less willpower, but may actually reduce your willpower capacity. Not indulging would likely increase your total willpower capacity long term.
Ugh. Typos. Sorry – I can’t figure out how to edit posts quite yet.
You’re absolutely right – I had more information about the psychology of willpower and the long-term effects, but those paragraphs got cut as I shifted to a stronger focus on decision theory.
For one thing, exercising willpower does strengthen your will in the long run. There are also interesting links between consuming calories and having more willpower… Both of these are factors but didn’t make it into the post.
Plus, cupcakes are delicious and increase your utility. This cannot be overstated.
True. And no matter how many cupcakes you refuse, you change not one whit whether you were predestined to be one of the long-lived elect. http://en.wikipedia.org/wiki/Limited_atonement
I would make a case for a sort of “hypothetical-evidential decision theory” which allows for having one’s choice influenced not purely by real-world evidence, but also about one’s best prediction about the results of a hypothetical statistical test more carefully tailored to match your own situation, even if that test hasn’t been performed. In the cupcake case, though it may be true in general that people who eat randomly offered cupcakes at non-mealtimes have less willpower, if we hypothetically imagine testing a extremely large sample of people and situations, and restricting our attention to the specific subset of cases where people were aware of the effect of glucose on willpower and were specifically choosing to eat sugary foods in situations when they knew they needed more willpower for other tasks (and avoided eating them in other situations, except maybe a pre-decided dessert times if they were at a healthy weight), then in that more narrow sample, there might be no significant correlation between cupcake-eating and low willpower.
Note that the reasoning that makes me think this is likely does incorporate causal considerations, even though I am still ultimately basing my choice on what I believe would be the empirical results of the experiment–specifically, I assume that those who eat random cupcakes usually tend to do so because of the hedonistic appeal, not for instrumental reasons like boosting willpower, so that people who did eat cupcakes for instrumental reasons would give atypical results compared to the larger group of cupcake-eaters. But of course, I would be open to revising my choice if new evidence suggested that even with people who only ate random cupcakes in situations where they had other important tasks, and avoided them otherwise, this group still had lower willpower than those who always avoided cupcakes. And I think this “hypothetical-evidential decision theory” would support the same choice as the standard evidential version when faced with Newcomb’s paradox, since there’s no reason to think the ideal predictor would be less successful when dealing with a collection of people tailored to be similar to myself in their knowledge of (and opinions about) decision theory.
No paradox–Given your reason for eating the cupcake (which explains away the hypothesis that you have little willpower), AND that eating the cupcake should leave you with more willpower, learning that you ate the cupcake should be evidence in favor of you finishing your task.
Newcombe’s Paradox has an analog in Calvinism’s predestination. At birth you are either saved or not, but still you choose to do good works in hopes that you are amongst the the saved. Or at least to signal to the people in your community that you are probably going to heaven.
But I wonder if the Marshmallow Test (to which I assume you are alluding) really shows what it purports to. It could be the case that children who do better in life are not those with better self control, but those with less of a sweet tooth (and who coincidentally didn’t really want a marshmallow to start with). So for me, it could be the urge to read and post half baked ideas, not the cupcake, that really tries my willpower.
Hello, Jesse. Another plausible model might be physiological. An endocrinologist, for instance, might say that eating the cupcake is a way to attenuate cortisol in anticipation of the upcoming “big task.” We know, of course, that people often eat in response to stress. Cupcakes are high on the list of so-called “comfort foods” — certainly for me.
A walk in the woods will restore your depleted directed attention which is linked to among other things willpower and better cognitive processing, is less fattening, and the effects will probably last longer as blood sugar quickly plummets.. This is the Attention Restoration Theory (ART) of Stephen Kaplan at the University of Michigan.
Karen
Karen, I’m pretty skeptical that Kaplan ART has achieved something that amounts to a theory. It seems to me to be loaded down with a lot of the naturalistic fallacy. In the study I skimmed (http://la570.willsull.net/Built_Environment_%26_Health/Stress_files/ulrichetal1991.pdf), they contrasted “unthreatening natural environments” with “urban settings.” It seems to me that they cooked the books at exactly that point. For it to be significant, they’d have to run the images of urban environments through the exact same filter they used to select the supposedly unthreatening natural images. I mean, we can all imagine very threatening natural images, which they definitely decided to keep out. Have they shown anything other than the very unremarkable idea that unthreatening things are less stressful than threatening things? Or that breaks are a good idea? The notion that willpower, however, is a finite resource is an important one, and should be incorporated into your decision process.
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Suppose you’re on a diet, as I always am. If you skip the cupcake, you feel awesome, like you could take over the world. If you eat it, you feel like a fat slob with low willpower. So you actually have more willpower if you skip the cupcake.
But then you’re skinny and everyone with low willpower hates you.