It's the Same Five Dollars!

Z_M_Davis

From Tversky and Khaneman's "The Framing of Decisions and the Psychology of Choice" (Science, Vol. 211, No. 4481, 1981):

The following problem [...] illustrates the effect of embedding an option in different accounts. Two versions of this problem were presented to different groups of subjects. One group (N = 93) was given the values that appear in parentheses, and the other group (N = 88) the values shown in brackets.

[...] Imagine that you are about to purchase a jacket for ($125) [$15], and a calculator for ($15) [$125]. The calculator salesman informs you that the calculator you wish to buy is on sale for ($10) [$120] at the other branch of the store, located 20 minutes drive away. Would you make the trip to the other store?

The response to the two versions of [the problem] were markedly different: 68 percent of the respondents were willing to make an extra trip to save $5 on a $15 calculator; only 29 percent were willing to exert the same effort when the price of the calculator was $125. [...] A closely related observation has been reported [...] that the variability of the prices at which a given product is sold by different stores is roughly proportional to the mean price of that product. The same pattern was observed for both frequently and infrequently purchased items. Overall, a ratio of 2:1 in the mean price of two products is associated with a ratio of 1.86:1 in the standard deviation of the respective quoted prices. If the effort that consumers exert to save each dollar on a purchase [...] were independent of price, the dispersion of quoted prices should be about the same for all products.

This one's a killer. Money is supposed to be fungible, but these observations really highlight how difficult it is to really behave as if you believed that. So, aspiring rationalists, how might we combat this in ourselves? Maybe it would help to consciously convert between money and time: if you value your time at 25 $/hr, then the cost of a twenty-minute drive is 25 $/hr * (1/3) hr = $8.33 > $5, so you buy the calculator in front of you in either case. So this heuristic at least takes care of the calculator problem, although I would guess it fails miserably in other contexts, I currently know not which.

Another takeaway lesson is to ignore advertisements boasting that a product is currently such-and-such percent off. We don't care about the percentage! How many minutes are you saving?

From Tversky and Khaneman's "The Framing of Decisions and the Psychology of Choice" (Science, Vol. 211, No. 4481, 1981):

The following problem [...] illustrates the effect of embedding an option in different accounts. Two versions of this problem were presented to different groups of subjects. One group (N = 93) was given the values that appear in parentheses, and the other group (N = 88) the values shown in brackets.

[...] Imagine that you are about to purchase a jacket for ($125) [$15], and a calculator for ($15) [$125]. The calculator salesman informs you that the calculator you wish to buy is on sale for ($10) [$120] at the other branch of the store, located 20 minutes drive away. Would you make the trip to the other store?

The response to the two versions of [the problem] were markedly different: 68 percent of the respondents were willing to make an extra trip to save $5 on a $15 calculator; only 29 percent were willing to exert the same effort when the price of the calculator was $125. [...] A closely related observation has been reported [...] that the variability of the prices at which a given product is sold by different stores is roughly proportional to the mean price of that product. The same pattern was observed for both frequently and infrequently purchased items. Overall, a ratio of 2:1 in the mean price of two products is associated with a ratio of 1.86:1 in the standard deviation of the respective quoted prices. If the effort that consumers exert to save each dollar on a purchase [...] were independent of price, the dispersion of quoted prices should be about the same for all products.

Another takeaway lesson is to ignore advertisements boasting that a product is currently such-and-such percent off. We don't care about the percentage! How many minutes are you saving?

I've come across this problem before - what the problem really is is the inappropriate use of proportional savings ($5 is a higher proportion of $15 than of $125) when the attention should be on the absolute savings ($5 in either case) because of the way the problem was framed. The way the problem was presented in this post actually obscures this point.

What use of proportional / absolute savings exactly is appropriate? Can you be more specific in which point is obscured by the framing?

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It's the Same Five Dollars!

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It's the Same Five Dollars!

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