The Psychology of the Stimulus in a Game of Numbers
A numbers game reveals the psychology behind the stimulus package.
March. 1, 2009 — -- An intriguing mathematical-psychological game sheds a little light on the size of the stimulus package recently passed by Congress. In particular it illustrates the truism that passing legislation calls for an understanding of the interplay between politics and economics.
First, note that most economists believe that the $800 billion ($0.8 trillion) stimulus is too small to do the job. They say the package needs to be much greater to close the $2.9 trillion gap between what the Congressional Budget Office forecasts the economy is capable of producing over the next three years and what it's likely to produce without the stimulus.
Further argument and arm-twisting might reduce the gap further, but several iterations probably would be required to get something sufficiently effective. Recognizing political realities is essential, however. If the stimulus package presented had been significantly bigger, it likely would have failed.
Now for the game which I sometimes present to my classes.
Consider a situation in which people in a large group are each asked to independently choose a number (not necessarily a whole number) between 0 and 100. They are further directed to pick the number that they think will be closest to 80 percent of the average number chosen by the group.
The one who comes closest will receive $10,000 for his efforts. (This latter offer I don't make to my students.) Stop for a bit and think what number you would pick.
Some in the group might reason that if people choose numbers at random, the average number chosen is likely to be 50 and so these people would guess 40, which is 80 percent of 50. Others, looking around at the thoughtful looks on people's faces, might anticipate that many of them will reason in the same way and guess 40 too, and so they would guess 32 (or perhaps a bit higher), which is 80 percent of 40.
Still others, seeing the intense concentration of other smart people in the group, might anticipate that they will guess 32 (or so) for the same reason and so they would guess 25.6 (or a bit higher), which is 80 percent of 32.
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