Counting in base 12 is much better than base 10. 12 has prime factors {2,2,3}, so you get 2,3,4 and 6 as integer divisors, not just 2 and 5. That's why dozens stuck as a counting unit on so many things, namely time (all the way back from Egyptians).
You can even count using your fingers. Just count using your thumb pointing at each of the finger joints and the finger tip (you have two joints and one tip per finger and four fingers excluding the thumb). Actually, that's how Egyptians counted and that's why you get 12 hours in the realm of day and 12 hours in the realm of night.
The only drawback is multiplication tables. If I tend to forget the multiplication table for 7 and 8, memorizing tables for 11 and 12 would be nightmarish :-)
P.S. This is obviously tongue-in-cheek. While it may be marginally better, switching costs mean the optimal course of action is to stay at the local maximum and avoid switching.
I've done some extensive analysis of number systems (almost enough to write a book on the subject) and come to the conclusion that the best are senary (6) and quaternary (4). Six has all the benefits of twelve, save the extra divisor of 2 (and thus 4), but that is easily remedied by use of the square (36) when required. Quaternary may seem an odd choice, but the square is 16, so one naturally learns hexadecimal without doing hardly any extra work --you just pair up the digits.
If your curious, duodecimal and octal come in after these and decimal falls to fifth place, which is fitting since its main advantage is divisibility by 5. :-)
Interesting. I always thought base 16 was the only suitable number system. Base 2 is the only justifiable one, since base 1 is not much fun. Squaring base 2 twice to get a fair amount of information in a single column seems to just make sense. What are the downsides of 16?
I haven't heard many arguments against dozens. In fact, there are some groups that specifically argue for duodecimal systems. I'd be interested to hear your position in more detail.
My main problem is that it's longer than "tens". And I have 10 fingers. And I use base-10 for everything, including counting the dozens. It's just more logical (and I say that without reading through the wiki page, so sorry if whatever I say doesn't make any sense with that in mind. I'm not good with words).
It's only logical because that's what overwhelmingly likely what you grew up using. There are duodecimal finger counting systems. (Counting to 12 isn't even all that impressive, considering counting each finger as a binary digit results in 1024.)
Also, "9 dozen" is the same in either base. "10 dozen" would become "ᘔ dozen", "11 dozen" to "3 dozen", and "12 dozen" to "10 dozen".
Finally, a dozen dozen is a gross and a dozen gross is a great gross, which at 1728 would be a likely replacement for "ton".
