Cereal Box Fun

March 10, 2008

Here are two exciting problems that I expect to see on the back of a cereal box soon. Look at this image:

16.jpg

The two horizontally-oriented lines are curved, right? Wrong! Your brain is fooled by the outward-pointing lines into seeing the straight lines as curved.

OK, here’s another one:

Which would you rather have, 1A. or 1B.?

1A. $24,000, with certainty.
1B. 33/34 chance of winning $27,000, and 1/34 chance of winning nothing.

Made your choice? Make a mental note, and move on to the second part:

Which would you rather have, 2A. or 2B.?

2A. 34% chance of winning $24,000, and 66% chance of winning nothing.
2B. 33% chance of winning $27,000, and 67% chance of winning nothing.

So, what did you choose?

If you’re like most people, you said you’d rather have 1A in the first case, and 2B in the second. But if you’re making these choices in the hopes of maximizing your expected utility, that set of choices doesn’t make sense!

Alright, enough cereal box-style writing. Basically, this latter problem is a puzzle because most people say they prefer 1A and 2B, but it is impossible to construct a utility function consistent with those choices. Think of it this way: in the first problem, you are saying that the extra $3,000 isn’t worth enough to you to justify giving away 1/34 of your chances to win $24,000. In the second problem, you are saying exactly the opposite. People with a 34% chance of winning $24,000 are willing to trade away one of those percentage points for a chance at the $27,000 payout. There is a contradiction there.

The moral of this stuff is, you’re absolutely right if you think that we don’t really explicitly use rationality to make our day-to-day decisions. Neither do our eyes and brain take in and process every pixel of every image that we see. In both decision-making and creating mental images, we take energy-saving shortcuts that will generally lead us to solutions that are accurate enough for our survival.

In the optical illusion, the lines look curved, even after we know that they are straight. In the money problem, we might still feel like 1A is better than 1B and 2B is better than 2A, even after we know that these choices are inconsistent with maximizing utility. Neither of these facts tells you much about whether our image processing or decision-making mechanisms are useful in general, since these problems are designed to uncover and exploit the weaknesses in our processing systems.

That is the danger in extrapolating too much from any experiment. Unlike cereal box problems, choices in real life are not specifically designed to fool our normal decision-making systems. Getting the curved line problem wrong doesn’t cause me to doubt everything I see, so why should making the wrong choice in the money problem cause me to doubt all my decisions? A little skepticism is healthy; no one should believe they’re infallible. Still, let’s use these extreme examples to update and improve our decision-making, not to throw out the system entirely.

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4 Responses to “Cereal Box Fun”

  1. Thomas Says:

    I agree with you that “energy saving shortcuts”, referred to as “heuristics” in Psychology, form a crucial tool of human decision making.

    I disagree with you in that I believe that there *are* in fact choices designed to fool our normal decision-making systems. Consider choices that revolve around getting Americans to consume! Spend more! Trust the experts! Get in more debt! Etc.

    For an interesting look at the history of decision-making theory, look at the history of advertising.

    Old magazine ads used to employ paragraphs of expository text in an attempt to rationally convince the consumer to choose the product in question.

    As Ad companies became more and more aware of the way that people make decisions based on impulse and association, ads became more sophisticated. They started to focus on imagery rather than words. Pictures of bliss, sex, glamor, humor…anything to get their product recognized, remembered, and tied with a good feeling. Ad companies also realized that branding was crucial; fostering long-term positive associations with your product/service is a much more effective way to draw consumers than giving a drawn-out, rational explanation of why your product is better.

    I think that Dan Ariely’s example of the sub-prime mortgage crisis (in his interview with Will Wilkinson) is a good one– since it’s so difficult to figure out what an optimal amount for your mortgage is, people were easily swayed into making disastrous decisions.

    Of course this tomfoolery was also built upon the myth of affluence that is the American Dream; houses with white picket fences for all!

  2. David Says:

    Okay, so this is an old post I guess, but I was just directed over here by Thomas!

    I get the impression (from this blog as well as from comments on Thomas’s) that you are driven by rationalism. That’s well and good, but in some cases I think strict rationalism loses some vital context…misses the forest for the trees, if you will. I’d like to try to argue that your money riddle is an example of this.

    You say that it makes no sense to give up the 1/34 chance in the second example if you wouldn’t do it in the first. You go on to call this the “wrong answer,” et cetera. I disagree wholeheartedly. Yes, in both cases the ‘B’ answer sacrifices a 1/34 chance in exchange for a potential gain of $3000. But the contexts of the offers are VASTLY different.

    -In the first, it is a difference between 100% and 97%: however negligible that 3% may seem to you, keep in mind that there is a titanic difference in context between a whole and a fraction of a whole. In essence, the problem can be boiled down to this: you are given 24000, and the choice to wager on a 97% chance of winning 3000, with a 3% chance of LOSING that 24000. That is the significance of the difference between a whole and a fraction of a whole. The question becomes, are you willing to gamble?

    -In the second, the question is entirely different. There is no choice to gamble; in participating, you are gambling already. It is just a matter of choosing your stakes. One option gives a 1% decrease in odds (1/34 less, if you must) for a $3000 increase in payout. If you’re looking at that 1/34 figure, it appears to be the same question as before. But here’s that context I’ve been promising: you’re still gambling in both cases! No matter which choice you make, you could walk away with nothing. In this case, it matters much more how greatly you value a 1/34 chance.

    I could go on about how the first question presents a 3% drop in odds versus a 1% drop, or how the context may reasonably change for certain people when you know there is a roughly 2/3 chance of either choice failing, but it doesn’t really matter. My point is that in one case you have a “mystery box” proposition (you can have this prize you see here, or trade it in for the mystery box!) whereas the in the second case you are gambling. Though odds are involved in both cases, they are two entirely different games. Thus, I maintain that the “typical” human response to these two propositions is perfectly reasonable one, and in no way wrong.

    I go to such length to respond to an old post because while I respect a strict adherence to rationalism, there are cases where it can convince you that you are categorically right, when in fact it ignores VITAL CONTEXT from the situation.

    Kudos on the well thought-out entries in this forum, though!


  3. Hi David,

    Thanks for the response. This post is a bit old, but it’s one of my favorites, so I’m happy to be able to keep talking about it.

    This post was part of a debate between Thomas and myself that started over the matter of whether smoking is rational or irrational. This is an important question for economists, because they make most of their recommendations based on the idea that if everyone is rational, you don’t need to do anything to make other people happy: they will make themselves happy. In the case of smoking, we don’t need to do anything about people who smoke or don’t smoke, because their choices reflect what is best for them. By showing that rational actors will find what is best for themselves, economists try to undermine the rationale behind “paternalistic” laws from people who would say, e.g. “We’re going to ban you from smoking because it will make you better off.” Economists would respond “If a smoking ban would truly make me better off, I wouldn’t have been smoking in the first place.”

    Fundamentally, then, this is a debate about whether we should routinely do something to protect people from their own bad decisions. Your argument in favor of people who choose 1A and 2B makes you an unwitting supporter of my side (evil laugh) by showing just how difficult it is to even identify bona fide “bad” decisions. Thomas and I went through the exact same thing on the smoking debate, in which Thomas argued that smoking is a bad decision, and I argued that it isn’t, at least not always. If you can’t even show that someone is making a bad decision, it’s extremely difficult to argue that you can improve on it.

    Behavioral economists, in contrast to classical economists, try to show that people make decisions that violate normal rationality assumptions. The fact of these violations is often used to advocate for policies to change people’s behavior. Your point (and mine) is that economists may be a lot worse than they think they are at knowing what changes in behavior would bring about a real improvement. Most people are already getting it right, most of the time. I definitely wouldn’t go so far as to say that people never make mistakes; I doubt you would either, even though you don’t believe this money problem to demonstrate a genuine mistake. The point of bringing up the money problem was not to show that people are irrational and make bad decisions. Rather, I was trying to show that, even though I can create a puzzle that fools people’s decision-making intuition and put the puzzle on the back of a cereal box, when we’re talking about real life situations, our decision-making intuition is actually very good.

    As I said, the point I was trying to make (people are pretty good at making decisions) is more important to me than arguing over this specific decision. Nevertheless, here is a good discussion of the problem itself.

  4. tripinchina Says:

    No way David’s on your side, cuz I want him on my side!

    Economists assume that people act rationally, i.e. according to their preferences. But I say that there are a host of social, psychological, and environmental factors (read: CONTEXT) that influence how people act. Hence not only is smoking not rational as such, but indeed no behavior can be thought of as “rational” in the economic sense.

    The assumption of the previous existence of economic “laws” or “facts”, construed by eonomists, is untenable when confronted with what we know about the behavior of humans, especially those who have not been integrated into economic society (ancient societies and cultures as well as contemporary indigenous folk.)

    Yet economic theory refuses to yield to the facts of non-economic life. Moreover, economics strives to subordinate to its rule and to subsume under its logic every other form of social interaction in every society it invades. The transformation of autonomous men and women with their infinite variety of human concerns into rationally-acting “homo economicus” is a precondition for the emergence of economic society, which goes hand with the political designs of the bourgouise (who were the new dominant class when “Wealth of Nations” was written.)

    The economic “laws” of the classical economists were deductive inventions which transfromed the newly observed patterns of social behavior, adapted with the emergence of economic society, into unviersal axioms designed to carry on a new political project (which continues under the rubric of “development”).

    So as long are you’re going to characterize my position, characterize it thusly: I don’t support paternalistic laws or government intervention into my private affairs BUT I also take umbrage with the rationalist economic lens as a whole because it’s woefully innacruate and politically biased. Ha-rumph.


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