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Wednesday, April 02, 2003

Blinkered perspectives

Yesterday, I saw attending a very interesting seminar by Alberto Bisin presenting joint work with Jess Benhabib. Roughly he presented a model of impulse buying with the idea that to avoid the temptation to buy people have to devote some of their limited attention to saying “be thrifty be thrifty” to themselves. I am pleased that economists are talking to psychologists and neuro-biologists (and listening to what they say). I’m not the only one. The seminar was one of the biggest hits I ever saw (ended with applause !). I have some thoughts

“say to themselves” is meant almost literally. In particular, I was taught in a freshman introductory psychology course 25 years ago that short term memory is very limited and verbal. Very limited in that we seem to have only 7 file handles (files = 7 in config.sys for people old enough to remember an operating system which was comprehensible). Verbal in that people make errors confusing things named by words that sound the same even if the information is presented with pictures and recollection is illustrated by pushing buttons.

It is true that to over-ride an impulse (well to try to over-ride an impulse) I talk to myself. One of the great bits of evidence from the psych literature is that overweight people can resist nibbling if they are remembering a 3 digit number but not if they are remembering a 7 digit number (see the magic number 7). They had to remember for 5 minutes or so. They weren’t warned that they would be tempted with food.

The guess is in the heads of the 3 digit non-nibblers is “’6’’4’’7’ don’t eat ’6’’4’’7’ don’t eat ’6’’4’’7’ don’t eat ’6’’4’’7’ don’t eat“’6’’4’’7’ don’t eat …” while in the heads of the the 7 digit nibblers was “6 4 7 3 5 2 4 ; 6 4 7 3 5 2 4, 6 4 7 3 5 2 4 , hey why is my stomach full ???”.

Another interesting analogy was between dynamically inconsistent time preference and perspective. That is things seem much more important if they are in the very near future just as things seem larger if they are close to us. The idea is that, as we evolved (and as we grow up) we learn to correct for this. Bisin had an interesting example of how his young son didn’t believe in perspective.

This reminded me of Inevitable Illusions : How Mistakes of Reason Rule Our Minds by Massimo Piattelli-Palmarini. Piattelli Palmarini likes to describe the systematic biases which influence people’s reasoning about probability as cognitive illusions. That is, these biases are similar to optical illusions in that they are virtually universal, systematic, persist even among those who consider them to be errors and can be fought only with concentration.

Now a typical optical illusion is not the fact that far away things seem smaller. This does not confuse adults anyway. They are the opposite -- Automatic over corrections for perspective. A simple experiment is to stare at a bright light. This temporarily exhausts the rod cells in a spot on the retina. This creates a blurred image which for me switches from green to purple as I blink. Now look at something close and at something far away (it helps to rapidly blink to see the spot). The spot seems bigger if it is superimposed on something far away. This is an image which corresponds to a constant area on the retina, because it is a constant area of the retina. The correction between geometric perspective and subjective distance is instant, effortless and automatic. It does not involve a voice in our head saying “that’s not small it’s far away”. In contrast, to avoid falling for optical illusions based on this feature of our non-verbal brain, we (or at least I) think “watch out it’s a trick” and force ourselves to measure.

This brings us up to 3 struggling mechanisms
1. something very automatic, for vision our eye and light following the rules of optics.
2. Something almost as automatic involving our brain but not requiring attention which corrects for the bias do to 1.
3. Sometimes something learned which involves a voice in our head and requires concentration to correct for 2 when it leads us astray.

Now back to time preference. I suggest that the very automatic process is that future rewards seem less important than immediate rewards. This is not as simple as light in an eye but it is clearly ancient and automatic. I suggest that the second automatic correction mechanism is the set of biases noted by Kahneman Twersky and followers. I think we are not up to 3 yet.

But how do I get from time to probability and back ? Piattelli Palmarini’s star example is “the Monte Hall paradox” from “Let’s Make a Deal” an old game show. The last step in the game show was guess which of these 3 boxes contains the big prize. The contestant guessed one. The assistant (Carol Marol or was she on truth and consequences) opened one of the other two boxes showing that it didn’t contain the big prize. Monte Hall offered the contestant the chance to switch to pick the remaining unopened unselected box. No one ever did. I admit I watched this show and agreed with the contestants. We all made a mistake.

The chance of winning guessing and sticking is, of course, one in 3. The chance of winning guessing and switching must be 2 in 3. This follows from Bayes formula. Say the contenstant picks 1 and they open 2. The prize is in 1 or 3. If the big prize is in 3, the chance they open 2 is 1 since they don’t open the box with the big prize. If the prize is in 1, the chance they open 2 is ½ as they chose which unguessed box to open at random. Bayes formula says chance of winning by staying is 1/3 by switching is 2/3. For some silly reason Bayes formula is not taught in elementary school, but it is simpler to see they should switch, since it is clear that one can always win either by staying or switching and the probability of winning by staying must be 1/3. So why didn’t anyone switch ?

A pseudo explanation is that we fear regret – to have had it and given it away. To me this is like saying morphine causes sleep because it has a dormative virtue.

Maybe we make the Monte Hall blunder because there is an automatic don’t change horses in midstream, stick to your guns, many other clich├ęs mechanism which has evolved or been learned to help us fight dynamic inconsistency. That is, we have all decided to do something involving effort or abstinence in the future, all noticed that it seems a bad plan when the time for effort comes, all learned to be firm in our purpose. Perhaps even without learning we have evolved a no backsliding reflex. Now on “let’s make a deal,” the temptation to switch is not based on dynamic inconsistency. The (evidently weak) temptation is based on new evidence. Still there is the reflex don’t switch as if there were a voice saying “don’t give in to temptation to stray from the path you have chosen “ but which evidently require neither such a voice in our head nor conscious self control.


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