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?
One way in which I've observed some very smart and numerate people falling for this fallacy is when they run out of cash in bars and are forced to take money out of those rip-off ATMs that charge $3 or so per transaction. People will often take a larger amount of money than necessary, rationalizing that the rip-off isn't that bad if it's only a small percentage of the amount (I've heard this "reasoning" expressed loudly several times). This despite the fact that tomorrow they'll walk by their own bank's ATM from which they can take money without any fees, so there's absolutely no benefit from taking more money than necessary from the expensive one.
I am myself not immune to this feeling, even though I'm perfectly aware it's completely irrational. I would feel awful if I paid $3 to take out a twenty and then took $100 without a fee next day, but paying $3 to take $120 feels much less bad.
The question is whether it's worth $3 to you at that moment to avoid a) starting a tab, b) walking to the nearest no-fee ATM, or c) not drinking for the rest of the night.
Sometimes it is and sometimes it isn't, but you're bang on that the amount of cash you get out doesn't make a difference.