Risky business (2)
In my previous blog, I described a study showing how different levels of risk or uncertainty resulted in different patterns of brain activity. I also posed the question of whether there is a less emotional and/or more useful to respond to uncertainty. Here I open the fan of possibilities for you to examine.
But first let me pose a quest question: Suppose the same experiment is done with an added condition. The experimenter gives the same instructions as in the original uncertainty condition. “You get $10 for drawing a red card. Some of the cards are red.”
As you will recall, the uncertainty condition left the participants uncertain about the best strategy, activated emotional brain parts, and led them to be more cautious than they were when the experimenter told them the percentage of red cards in the deck. The new condition I propose is this: The experimenter offers to let the participant examine the deck and count the cards for a price of, say, $12. How would you expect that offer to affect the results?
(Psychology students note: The above experiment could be run without the fMRI to study the acceptable price, the effect on conservatism strategy, and the relation of individual differences on acceptable price.)
Now to the fan of possibilities, assuming the original uncertainty condition. Here are some viewpoints the participant could take to reduce the uncertainty (and presumably the level of the emotional response).
Viewpoint: statistician (Vulcan). If I have no information about the number of red cards, I start by assuming that that all numbers are equally probable. The experimenter said “some red cards.” That expression implies any number from 2 to 20. It would be to my advantage to draw a cord if the expected value of a draw exceeds the $3 I am spending to draw. If 30% of the cards are red, the expected value of the draw is $3. Since the deck has 20 cards, 30% is 6 cards. Any number from 7 to 20 favors drawing. An number from 2 to 5 favors taking the sure thing. Only 4 numbers favor the sure thing.
My initial analysis thus favors drawing. But I also note that drawing is equivalent to buying information on cards at $3 per test. My best strategy is to buy that information and use it to estimate the odds.
Viewpoint: strategist (Vulcan and Empath). I agree with the analysis of the statistician, but I will not assume that all numbers are equally probable. The experimenter chose the number for the objectives of the experiment.
Obviously, I can estimate the frequency of red cards by drawing cards at $3 each. If I get mostly cards of one kind or the other, I will quickly conclude that the deck is loaded in favor of one choice or the other. The number that will keep me uncertain over the greatest number of trials is 10 red cards (50% odds).
Despite my insightful analysis, I reach the same conclusion as the statistician.
Viewpoint: Explorer. I don’t see anything dangerous here. I will get a little money for very little effort. If I take the sure thing, I will collect $72 and learn nothing. If I draw cards, I will find out whether drawing pays better than $3. If it doesn’t, I can change strategies. But my view is that I was buying information, not throwing away money.
Viewpoint: pragmatist. I am not going to overthink this problem. I can expect to come out of this with more money than I brought in. The best case is $240. The worst case is nothing. These values are small compared to my tuition at Caltech. I will do what feels most comfortable and be content with the result. I’d rather spend my brain power thinking about my calculus test tomorrow.
How would a participant be affected by adopting one of these viewpoints? You probably have an opinion already. I will post my speculation in a later blog.
But first let me pose a quest question: Suppose the same experiment is done with an added condition. The experimenter gives the same instructions as in the original uncertainty condition. “You get $10 for drawing a red card. Some of the cards are red.”
As you will recall, the uncertainty condition left the participants uncertain about the best strategy, activated emotional brain parts, and led them to be more cautious than they were when the experimenter told them the percentage of red cards in the deck. The new condition I propose is this: The experimenter offers to let the participant examine the deck and count the cards for a price of, say, $12. How would you expect that offer to affect the results?
(Psychology students note: The above experiment could be run without the fMRI to study the acceptable price, the effect on conservatism strategy, and the relation of individual differences on acceptable price.)
Now to the fan of possibilities, assuming the original uncertainty condition. Here are some viewpoints the participant could take to reduce the uncertainty (and presumably the level of the emotional response).
Viewpoint: statistician (Vulcan). If I have no information about the number of red cards, I start by assuming that that all numbers are equally probable. The experimenter said “some red cards.” That expression implies any number from 2 to 20. It would be to my advantage to draw a cord if the expected value of a draw exceeds the $3 I am spending to draw. If 30% of the cards are red, the expected value of the draw is $3. Since the deck has 20 cards, 30% is 6 cards. Any number from 7 to 20 favors drawing. An number from 2 to 5 favors taking the sure thing. Only 4 numbers favor the sure thing.
My initial analysis thus favors drawing. But I also note that drawing is equivalent to buying information on cards at $3 per test. My best strategy is to buy that information and use it to estimate the odds.
Viewpoint: strategist (Vulcan and Empath). I agree with the analysis of the statistician, but I will not assume that all numbers are equally probable. The experimenter chose the number for the objectives of the experiment.
Obviously, I can estimate the frequency of red cards by drawing cards at $3 each. If I get mostly cards of one kind or the other, I will quickly conclude that the deck is loaded in favor of one choice or the other. The number that will keep me uncertain over the greatest number of trials is 10 red cards (50% odds).
Despite my insightful analysis, I reach the same conclusion as the statistician.
Viewpoint: Explorer. I don’t see anything dangerous here. I will get a little money for very little effort. If I take the sure thing, I will collect $72 and learn nothing. If I draw cards, I will find out whether drawing pays better than $3. If it doesn’t, I can change strategies. But my view is that I was buying information, not throwing away money.
Viewpoint: pragmatist. I am not going to overthink this problem. I can expect to come out of this with more money than I brought in. The best case is $240. The worst case is nothing. These values are small compared to my tuition at Caltech. I will do what feels most comfortable and be content with the result. I’d rather spend my brain power thinking about my calculus test tomorrow.
How would a participant be affected by adopting one of these viewpoints? You probably have an opinion already. I will post my speculation in a later blog.
posted by Selby Evans at 8:30 AM
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