A&W's third pound burger
This rests on one telling: a memoir, a tradition, a story someone put on record. Where the wider point has independent support, the entry says so. The specifics remain one person's account, and they should be held that way.
In the 1980s A&W believed it had found the move that would beat McDonald's. The Quarter Pounder had become an icon, so A&W answered with a third pound burger. More meat for the same price, and in taste tests people preferred it. In the market it failed, and for a while nobody inside the company could explain why. As A&W's former owner later told the story, the research surfaced something that has been repeated in marketing departments ever since. Customers felt cheated, and their reasoning was that three is smaller than four, so a third of a pound must be less than a quarter. The burger with more meat lost because its fraction looked smaller. This account comes from one man's memoir rather than published research, so treat the specific story with some caution. The underlying difficulty people have comparing fractions is separately well documented.
Customers judge your offer in about half a second with whatever mental shortcut is closest to hand, rather than evaluating it against objective truth, and the shortcut does its own arithmetic. That is worth sitting with before you assume a better product will win on its merits. For the person deciding in half a second, the way something is expressed, named or numbered is a large part of the value they think they are getting, rather than decoration sitting on top of it.
Whatever the truth of the A&W account, the discipline it points at is checkable in your own numbers. Prices, pack sizes, plan names and discounts all get compared against a competitor's version in the same few seconds, using whatever comparison is quickest. A fraction has to be converted before it can be ranked against another fraction, and a price per item has to be converted before it can be ranked against a price per hundred grams. Every conversion you leave for the buyer is a moment where they can rank you wrong. Before publishing a number, put it beside the number a customer will see next to it and check whether the better one is obvious without arithmetic.
The same mechanism, running on a product rather than a number, is Diamond Shreddies.
Source: Alfred Taubman recounted this in his memoir Threshold Resistance, 2007. A single account rather than published research. The underlying difficulty with fractions is separately documented.
John Allen Paulos, 1988
On how badly people handle numbers, and what it costs when nobody notices.
Draw your own card. It does not take long, and it rewards taking your time.