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):
- trends tend to reverse course at predictable support and resistance levels, and
- 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. [Edit]: 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).
- 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.
- Palmquist, M. (2013, November 21). The psychology of pricing: Customers prefer round numbers. Strategy + Business. Retrieved from http://www.strategy-business.com/blog/The-Psychology-of-Pricing-Customers-Prefer-Round-Numbers?gko=f4877.
- Schindler, R. M., & Wiman, A. R. (1989). Effects of odd pricing on price recall. Journal of Business Research, 19(3), 165–177.