# Aesthetic preference for even or odd numbers

In my experience most people prefer the appearance of even numbers or numbers divisible by 5.

• Is there any research which proves or disproves my theory?
• Is it all about symmetry?

I expect that people prefer the number 5 because it is half of 10 and we live in a world that primarily uses a base-10 system. e.g. I like my gamerscore on xbox-live or reputation here to be even or divisible by 5.

• I'd add that we have 5 fingers on a hand which likely also influences it's popularity. We use base-10 probably because we have 10 fingers.
– Jim
Commented May 17, 2013 at 19:04
• "Prefer" is too vague to be answered in a rigorous way. You should give some examples of what you mean by number preference or try and operationalize it in some other manner. Commented May 17, 2013 at 22:54
• I agree with zergylord, the answer to this depends on what you mean by "prefer." My best guess is that you mean that when people give quantitative estimates of various quantities, the stated estimates are more likely to be even numbers or numbers divisible by 5 compared to other numbers. But you need to confirm whether this is what you mean. Commented May 17, 2013 at 23:49
• Also, if you are interested in why participants respond with certain numbers, see this existing question Commented May 18, 2013 at 9:04
• There's a discussion of cultural differences in odd and even numbers Commented Jul 24, 2013 at 0:39

Some ancient historical precedent exists for preferring $10$, but also for $6$, so that's mixed support from Wikipedia on perfect numbers. As for honest-to-goodness modern research, here's one quick result on prevalence of round prices in marketing (Klumpp, Brorsen, & Anderson, 2005): it's higher than for non-round prices. Some other results are reviewed within, including those of Kandel, Sarig, & Wohl (2001), who claim "direct evidence that investors prefer round numbers," Harris (1991), who claims, "Stock prices cluster on round fractions," and Osler (2003), regarding whose results Klumpp and colleagues wrote, "[market] trends tend to increase after certain prices levels (specifically round prices) are crossed." Osler's own wording (with numeric list reformatting and emphasis added):

1. trends tend to reverse course at predictable support and resistance levels, and
2. trends tend to be unusually rapid after rates cross such levels.

The data are the first available on individual currency stop-loss and take-profit orders. Take-profit orders cluster particularly strongly at round numbers, which could explain the first prediction. Stop-loss orders cluster strongly just beyond round numbers, which could explain the second prediction.

Klumpp and colleagues' research claims to be a relatively new attempt to apply these ideas outside of financial market analysis...but to some extent, wheat is just another form of currency, so this is debatable.

As for substantive theoretical explanations, a good review and test of theory is freely available (Kahn, Pennacchi, & Sopranzetti, 1999). This paper mentions many circumstantial and traditional peculiarities about financial markets as motivating factors, but the ideas most interesting for our audience pertain to memory. Here's an excerpt (emphasis added):

Experimental tests performed by Schindler and Wiman (1989) find that individuals tend to recall odd-ending prices less accurately than even-ending prices, and that expressing a price as odd-ending increases the likelihood that it will be underestimated when recalled. A biological explanation for this downward bias in recalling odd-ending prices is offered by Brenner and Brenner (1982). They propose a theory of fixed storage capacity which assumes that the extra decision of rounding the initially observed number is costly, so that the cheapest transfer mechanism involves simply storing the first digit. Hence, if a prices right-most digits are not stored in memory, odd-ending prices will tend to be underestimated. If firms recognize consumers downward bias in recalling odd-ending prices, they may significantly increase the demand for their products by making odd-ending price quotes rather than slightly higher even-ending ones. Even-ending quotes will then represent pricing points where product demand experiences a discrete decline. Blinder (1991) reports some empirical support for this notion. Based on interviews with firm managers, he finds that a majority were reluctant to cross the psychological barrier of raising prices from an odd-ending quote to an even-ending one.

In summary, it seems people prefer to ignore the last available digit for conservation of memory and attentional resources. People use round numbers as arbitrary thresholds for decision making, probably because they can be simplified by dropping the lowest digit, and hence require less unnecessary cognitive elaboration to select when the decision really is arbitrary anyway. Busy people with lots of other things to worry about would probably experience cognitive dissonance when finding themselves thinking about such arbitrary decisions any harder than they have to. Since people pay more attention to that second-to-last digit, they notice when that number "rolls over", and evidently find it a suitable stimulus to trigger premeditated actions like buying and selling.

I haven't seen any particular references to five or symmetry in general, but if you look into these references further yourself, you might find more than what I've reviewed here. : On second thought, here's one (emphasis added again):

Consumers disproportionately selected round, whole-dollar, and half-dollar amounts. About 73 percent of customers tipped a round, whole-dollar amount, and an additional 8 percent rounded their tips to a half dollar. They also clustered their tips around multiples of $5. And on the occasions when the bill didn’t end in .00, nearly a quarter of diners left an unrounded tip that when added to the bill, came to a round total. This requires some mental math skills, the authors note, implying that consumers’ preferences for round prices is so strong that they’ll calculate an exact tip amount to arrive at a round total. This demonstrates that ordinary people have these preferences too, not just financial marketeers. Read the rest here (Palmquist, 2013), or at his source, a study of tipping behavior in the Journal of Economic Psychology (Lynn, Flynn, & Helion, 2013). References - Blinder, A. S. (1991). Why are prices sticky? Preliminary results from an interview study. American Economic Review: Papers and Proceedings, 81, 89–96. - Brenner, G. A., & Brenner, R. (1982). Memory and markets, or why are you paying \$2.99 for a widget? Journal of Business, 55, 147–158.
- Harris, L. (1991). Stock price clustering and discreteness. Review of Financial Studies, 4(3), 389–415. Retrieved from http://www.acsu.buffalo.edu/~keechung/TEM/Journal%20Articles/Clustering%20-%20Harris.pdf.
- Kahn, C., Pennacchi, G., & Sopranzetti, B. (1999). Bank deposit rate clustering: Theory and empirical evidence. The Journal of Finance, 54(6), 2185-2214. Retrieved from https://www.clevelandfed.org/Research/workpaper/1996/wp9604.pdf.
- Kandel, S., Sarig, O., & Wohl, A. (2001). Do investors prefer round stock prices? Evidence from Israeli IPO auctions. Journal of Banking & Finance, 25(8), 1543–1551.
- Klumpp, J. M., Brorsen, W., & Anderson, K. B. (2005). The preference for round number prices. Selected paper prepared for presentation at the Southern Agricultural Economics Association annual meetings, Little Rock, Arkansas, February 5–9, 2005. Retrieved from http://ageconsearch.umn.edu/bitstream/35537/1/sp05kl01.pdf.
- Lynn, M., Flynn, S. M., & Helion, C. (2013). Do consumers prefer round prices? Evidence from pay-what-you-want decisions and self-pumped gasoline purchases. Journal of Economic Psychology, 36, 96–102. Retrieved from http://tippingresearch.com/uploads/Round_Prices_JEP.pdf.
- Osler, C. L. (2003). Currency orders and exchange rate dynamics: an explanation for the predictive success of technical analysis. The Journal of Finance, 58(5), 1791–1820. Retrieved from Ben-Gurion University's Department of Economics.
- Schindler, R. M., & Wiman, A. R. (1989). Effects of odd pricing on price recall. Journal of Business Research, 19(3), 165–177.

There are numbers - as in groups of objects - that are easily divisible so may have the appeal of symmetry. Other numbers may align with the number system. However, there are different number systems. The ancient Egyptians counted on their fingers using the each knuckle of the four fingers sequentially, so 3 knuckles x 4 fingers allowed them to count to twelve. It's not a bad system. I think they would have liked the number 3 and possibly 3/6/9/12 as "natural" feeling numbers.

As someone who is a bit fascinated with mathematics - and maybe a slightly perverse personality - I have a bit of an attraction for numbers that are difficult: favorite number 17. It's a prime so doesn't divide and it doesn't fit anything much. There are other primes but they don't cut it. 1,2,3: too small; 5: five fingers; 7:lucky number; 11: double one; 13: unlucky number. 17 is the first number without any obvious narrative.

So you might be able to test for number preferences but what would it mean? It would be tied up with the individual's cultural milieu and number system. It is likely that counting beyond a few is a relatively recent development that only really got going with farming like 10k years ago - counting sheep and grain quantities - so a deeper/evolutionary basis probably doesn't exist.

I'm not the best man to answer the question – I don't have any reference; I do have some logic behind what I'm saying.

Many years ago, very few people were educated, very few knew how to do math, but they all had money. And they had to count it, and do some math.

If I have 10 employees, each wants 5 coins, I have 1000 coins, I pay 50 and I still have 950 to party. If I have 2243 workers, I have to pay each 227 coins and I have 19353256421 coins in my account, well then, where's my calculator? Oh, no calculator. Call my math genius slave; if you can't find him, kill every worker! :)

We love numbers that can easily be divided and multiplied, It happens to be the even numbers and the 5, because it's easy to divide by 5 and the 1, because getting 1 is easy to work with in math, and 0 of course.

\$1, \$5, \$10, \$20, \$50, \$100: pretty much all currencies in the world are like that.

Old habits die hard: you go to a restaurant, you have to pay \$13. Where's the tips? Most people will usually pay \$15. If you have to pay \$36 for what you ate, most people will pay$40 in total.

It's really about the money, because unless you're a mathematician or something, you'd use numbers for counting money mostly in your daily life.

• Some cultural specificity is implicit in the references to dollars and tips, but speaking from my own, culturally-bound perspective, this answer may be true enough in America. Commented Feb 21, 2014 at 2:26
• ...or Lebanon, I'm sure :) Commented Feb 21, 2014 at 2:34
• @NickStauner yes :P from my previous answer :) Commented Feb 21, 2014 at 2:36