The Tyranny of Round Numbers

Interested in a concept I feel seriously must exist in an already cohered form, but which I am yet unable, through crowd-sourcing and search keywords, to find stable precedent for.

Tim Taylor at Economist's View discusses some version of this idea, termed "round number bias," though without an examination of its breadth and variety of effect.

Taylor reports that consumers often stop filling their gas tanks at rounded dollar amounts, or will give even-dollar tips to waiters. He also notes that baseball coaches seem to arbitrarily make decisions about players based on round-number cutoffs:

Another set of examples of round number bias come from Devin Pope and Uri Simonsohn in a 2011 paper that appeared in Psychological Science (22: 1, pp. 71-79): "Round Numbers as Goals: Evidence from Baseball, SAT Takers, and the Lab." They find, for example, that if you look at the batting averages of baseball players five days before the end of the season, you will see that the distribution over .298, .299, .300, and .301 is essentially even–as one would expect it to be by chance. However, at the end of the season, the share of players who hit .300 or .301 was more than double the proportion who hit .299 or .298. What happens in those last five days? They argue that batters already hitting .300 or .301 are more likely to get a day off, or to be pinch-hit for, rather than risk dropping below the round number. Conversely, those just below .300 may get some extra at-bats, or be matched against a pitcher where they are more likely to have success. Pope and Simonsohn also find that those who take the SAT test and end up with a score just below a round number–like 990 or 1090 on what used to be a 1600-point scale–are much more likely to retake the test than those who score a round number or just above. They find no evidence that this behavior makes any difference at all in actual college admissions.

"Round number bias" falls short of describing the ways and extent to which round numbers exert tyranny over our lives. Entire industries are ravaged by inflation because of round numbers, and it isn't solely due to cognitive bias. In a cash-based business — a food stand, a convenience mart, a dollar pizza window — where customer and seller convenience alike mean time, and time means money, defying round numbers is expensive, giving change bad business. This is to say nothing of the way fixed-price chains in general have seen their profits ebb and flow according to the value of ten cents, a quarter, or a dollar, over the past century (though consumers' interest in such stores are, I concede, largely the product of Taylor's round number bias in isolate).

Cuisine is tyrannized too: Just as art is optimized for artists as much as audiences, recipes are optimized as much for a dish's preparation and preparer as for its consumption and consumer. Ease of recording, remembering, and measuring out a recipe affects the creation and transmission of a recipe (its fitness, in the evolutionary — rather than aesthetic — sense). Seven-thirteenths of a tablespoon might be a better amount of salt to add, but half a tablespoon will win out on the recipe sheet every time.

Sports are full of these kind of semi-arbitrary distinctions, which become influential in punditry and fan followings. Nike's bid to break the four-minute mile received massive media attention; for decades prior, many believed the four-minute mile to be an unbreakable barrier, though why four minutes instead of 3:59 or 4:01 was the point at which human impossibility set in was never fully established. Russell Westbrook's triple-double average in the NBA regular season won him the MVP award this season; falling slightly short of double digits across four categories instead of three is a more impressive achievement, but lacks the crystallized marker of achievement that is the triple-double.

And think finally of the difference, in dating prospects and online profile number-fudging, between two men each standing 70.5 inches tall — one, American, whose height is measured in feet; the other, European, whose height is measured in meters.

The tyranny of round numbers is fundamentally a map/territory issue: it is the influence of territorially arbitrary but cartographically significant markers on territory decisions. But it is also a tyranny with benefits — convenience and the easing of cognitive strain — and which provides a clear cut-off point without which our evaluations of the world would require sliding-scale statistical analysis.

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