Rational ignorance is why we don't check our supermarket receipts

Last week, news.com.au reported:

WHEN you go shopping, do you casually throw your receipt in with the groceries, neglecting to read it over?

Or, worse, do you decline to print one out and walk away, ignorant what you’ve paid for all those carefully-selected items?

If you answered “yes”, you could be ripping yourself off, with scanning errors causing supermarkets to overcharge for everyday items — and many shoppers failing to detect, or act upon the mistakes to recoup what they are owed.

A survey of 2,141 Australians by comparison site finder.com.au found that two in five people had been overcharged at the till in the past year.

But one-quarter said they didn’t bother checking their dockets and, of those who did, they would only bother going for a refund if they were overcharged by more than $10.

There is a good reason why supermarket shoppers don't check their receipts. It takes time and effort to check those receipts, and the chances that the time and effort you spend pays off by your finding an error in your favour is low.

To illustrate, let's construct a plausible numerical scenario. Let's say that "two in five people" have been overcharged once each in the past year (as noted in the quote above), making a 40 percent chance that you've been overcharged once in the past year [*]. So, on average each person has been overcharged 0.4 times in the last year (some have been overcharged more times, and some have been overcharged fewer times). Let's assume each person goes to the supermarket roughly once per week (say 50 times per year). So, on average each shopper is being overcharged 0.4 times in 50 shopping trips, or a 0.8 percent chance that any given shopping trip results in an overpayment. Now let's generously assume that in each shopping trip where a shopper is overcharged, they are overcharged by $10 [**]. The expected value of checking every supermarket receipt is 0.8% x $10 = $0.08 (yes, that's EIGHT CENTS). This is the expected (or average) benefit you would gain from carefully checking every supermarket receipt to make sure you haven't been overcharged.

If the cost, in terms of time and effort, of carefully checking a supermarket receipt is more than $0.08, a rational person wouldn't do so. You would be better off to remain rationally ignorant of whether you overpaid the supermarket. Even at the minimum wage, $0.08 is the pay for about 18 seconds. Taking the minimum wage as the cost of people's time, you wouldn't want to spend any more than 18 seconds scrutinising each supermarket receipt. If your implicit value of time is higher than the minimum wage, you'd want to spend even less time than that.

You might argue that people are loss averse, so that they value losses much more than gains. Losing money to overcharging is a loss, so we should value the expected loss at much more than $0.08. However, it isn't a loss if you don't know about it! You're still better off being rationally ignorant, even if you're loss averse (maybe especially if you're loss averse).

I'm not surprised supermarket shoppers don't carefully scrutinise their receipts to check for overpayments on every item. It simply doesn't pay off for us.

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[*] Probably some people had been overcharged multiple times, but I don't think that will make much difference to this example.

[**] Probably most instances of overcharging are much less than $10. In my experience, overpayments I have caught in my own shopping trips (usually because I happened to be looking at the screen when the item was scanned and remembered the price) have been a couple of dollars at most.