A couple years ago, Aaron Swartz blogged about what he called the "percentage fallacy":
There’s one bit of irrationality that seems like it ought to be in behavioral economics introduction but mysteriously isn’t. For lack of a better term, let’s call it the percentage fallacy. The idea is simple:
One day I find I need a blender. I see a particularly nice one at the store for $40, so I purchase it and head home. But on the way home, I see the exact same blender on sale at a different store for $20. Now I feel ripped off, so I drive back to the first store, return the blender, drive back to the second store, and buy it for $20.
The next day I find I need a laptop. I see a particularly nice one at the store for $2500, so I purchase it and head home. But on the way home, I see the exact same laptop for $2480. “Pff, well, it’s only $20,” I say, and continue home with the original laptop.
I’m sure all of you have done something similar — maybe the issue wasn’t having to return something, but spending more time looking for a cheaper model, or fiddling with coupons and rebates, or buying something of inferior quality. But the basic point is consistent: we’ll do things to save 50% that we’d never do to save 1%.
He recently followed up with a speculation that this may explain some irrational behaviour normally attributed to hyperbolic discounting:
In a famous experiment, some people are asked to choose between $100 today or $120 tomorrow. Many choose the first. Meanwhile, some people are asked to choose between $100 sixty days from now or $120 sixty-one days from now. Almost everyone choose the laster. The puzzle is this: why are people willing to sacrifice $20 to avoid waiting a day right now but not in the future?
The standard explanation is hyperbolic discounting: humans tend to weigh immediate effects much more strongly than distant ones. But I think the actual psychological effect at work here is just the percentage fallacy. If I ask for the money now, I may have to wait 60 seconds. But if I get it tomorrow I have to wait 143900% more. By contrast, waiting 61 days is only 1.6% worse than waiting 6 days. Why not wait an extra 2% when you get 16% more money for it?
Has anyone done a test confirming the percentage fallacy? A good test would be to show people treat the $100 vs. $120 tradeoff as equivalent to the $1000 to $1200 tradeoff.
Is this a real thing? Is there any such research? Is there existing evidence that does especially support the usual hyperbolic discounting explanation over this?
The "percentage fallacy" is a real thing, and it does get covered in standard JDM/behavioral economics. See the classic Kahneman & Tversky jacket-calculator study, for instance. K&T also cite a study which shows that if you compare the prices of a consumer good at various stores, the standard deviation in price is roughly proportional to the price of the good.
I don't think it has a handy name, but the money version ($20 out of $2500 or $40) usually gets covered under mental accounting, as reflecting the shape of the value function (diminishing marginal sensitivity). It also gets connected more broadly to Weber's Law in psychophysics, which basically says that people's perceptions of a continuous quantity (including weight, brightness, etc.) follow a log scale - e.g., if someone is holding a weight and you add more weight to it, the smallest change that they'll notice is proportional to the total amount of weight that they're holding.
There has been some research applying this to temporal discounting, including a recent paper by Zauberman & colleagues (pdf).
Zauberman, G. B., Kim, K., Malkoc, S., & Bettman, J. R. (2009). Discounting time and time discounting: Subjective time perception and intertemporal preferences. Journal of Marketing Research, 46, 543–556.
I usually refer to this as "thinking logarithmically".