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This question is inspired by one asked at MathOverflow. (These questions at Cognitive Sciences and at Cross Validated might also be relevant.)

Are there any studies on what choices humans commonly make when asked to think of a choice "at random"?

For example, this website claims that when people are asked to think of a card (in a standard 52-card deck), they often select the nine of diamonds, the ace of spades, the queen of hearts, or the six of clubs. Or when a person is asked to think of a number between 1 and 1,000, they will often select 333.

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And therefore, they're not making choices at random. The closest I've gotten to random choices is asking a specific question about hiding in a circle or sphere. –  John Jan 27 '13 at 16:54
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It would also be interesting to know whether people could be trained to choose more "randomly". –  Jeromy Anglim Jan 28 '13 at 3:34
    
I'm not sure selecting an item at random that requires some conscientious thought is possible? The card example looks like people picking the first card which comes to mind based on familiarity, maybe considering the whole subset requires too much thought. However if a magician asked me to think of a card at random I would most likely avoid the most familiar and pick the last card which comes to mind. With numbers between 1-1000 the subset is much simpler so you may think a number involving 3's or 7's is "more random" than 500. If you have to think about it then it surely can't be random. –  MattP Feb 13 at 12:31
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Perhaps the best well-known example of asking patients to do something at random was performed by Benjamin Libet in 1983[1]. Libet asked patients to wait until a spontaneous moment and push a button as they watched an animated clockhand circle. Surprisingly, what he found was that there were about 200 ms between cerebral activity indicating the patient was about to push the button and the perception of the impulse by which they pushed the button. Libet could predict when they were "randomly" going to push the button before even they knew it, calling into question the concept of free will.

In 2008, another experiment was done by another research group, this time asking patients to "randomly" choose between left and right hand while hooked up to an fMRI[2]. Researchers were able to determine participants decisions up to 10 seconds before the participants themselves "impulsively" made their decision by analyzing the voxels of their fMRI readout.

So there is obviously a fair bit more of determinism involved in our choice making then we are able to perceive. Are brain only seems to cue us in when it's time to act.

References

[1]Libet, B., Gleason, C. A., Wright, E. W., and Pearl, D. K. (1983). Time of conscious intention to act in relation to onset of cerebral activity (readiness-potential). The unconscious initiation of a freely voluntary act. Brain, 106:623-642.

[2] Soon, C., Brass, M., Heinze, H., Haynes, J. (2008). Unconscious determinants of free decisions in the human brain. Nature Neuroscience 11, 543 - 545. http://www.nature.com/neuro/journal/v11/n5/full/nn.2112.html

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