One store is having a half-price sale – everything is 50% off. Another is advertising 30% off everything, stackable with a 25% off coupon.

Quick, which is the better deal?

If you do the math, half-price is preferable, since 30% off plus 25% off doesn’t actually equal 55% off. Even if you know how to crunch the numbers, though, a new study finds that double discounts are more appealing, even if they don’t represent the better deal.

Surprise, surprise: The dual impact of double discounting on consumer preferences” appears in the newest edition of Elsevier’s Journal of Retailing. Its authors set out to show that double discounts are more effective in attracting deal-seeking shoppers, even when two discounts add up to be less than one.

The researchers point to prior studies that considered double discounts as a math problem. As in the above example, shoppers might incorrectly add percentage discounts and think they’re getting a bigger discount than they really are.

But this study aimed to take the math out of the equation. “Might emotions also play a key role in how double discounting impacts consumers?” the authors asked.

The answer, they discovered, was yes.

After conducting a series of tests with shoppers, they found that “given the relative rarity of double discounts, consumers will feel surprise in response to receiving a double discount.” And a positive surprise is more likely to result in a positive shopping experience. The emotional boost you might feel about getting an additional discount layered on top of an existing deal is, in many cases, enough to prompt a purchase – even if a single discount up front offers a lower price.

That can be true even if a double discount is not presented as a math problem. Imagine going to the grocery store with a $2 coupon in hand. You’re not sure you’ll buy the promoted product, but you’ll decide when you get there. Now imagine going to the store with a mere $1 coupon. When you get there, you find out there’s an additional $1 store coupon you can stack with yours.

A double discount! Even though the total savings of $2 are exactly the same, this study argues that shoppers are more likely to feel positively about the double discount, and are therefore more likely to make a purchase.

In fact, they’re more likely to make multiple purchases. “Double discounting is also shown to impact consumer willingness to purchase other non-promoted products on the same shopping trip,” the study found. That’s because “consumers feel more loyal to the retailer offering the double discount and experience greater shopping momentum.”

So what can we do with this knowledge? Retailers armed with this information might be able to trick us with some sleight of hand. “The results suggest that retailers can use a smaller promotion when using double discounts and generate greater likelihood of buying than by using a larger single price promotion,” the researchers pointed out.

But they shouldn’t get greedy and overdo it. Retailers should “avoid the overuse of double discounts, as that can mitigate the surprise response among consumers and reduce their willingness to purchase.” In other words, it’s the surprise that gets our attention and our business – when a double discount is no longer a surprise, it no longer has the same impact.

Previous studies have produced similar results when it comes to surprise discounts. Nearly a quarter century ago, a study published in the Journal of Marketing Research found that “surprise coupons,” or “unanticipated coupons encountered while in the grocery store,” not only increase the likelihood that a shopper will purchase that specific product, but “this unexpected savings will increase the number of unplanned purchases made on the shopping trip.” So saving money on one product, can prompt you to spend more money overall.

Both studies indicate that, when it comes to effective promotions, appealing to our emotions is more important than appealing to our math skills. So the next time you have the chance to stack savings for a double discount, keep your emotions in check and your calculator handy – so psychological trickery doesn’t prompt you to spend more and save less than you think.

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