my daughter's teacher has only one fine tuner on her E string. She said, and i read some where, that smaller violins (e.g., 1/32, 1/8, 1/4, etc) are harder to tune so the fine tuner would help tuning the string to the right note, whereas the bigger violins are easier to tune. i didn't ask for the reason, but my guess is it has to do with the pegs, the strings length, steel strings, etc. Most smaller size violins have steel strings.

Here, I found it:

Violins are tuned by turning the pegs in the pegbox under the scroll, or by adjusting the fine tuner screws at the tailpiece. All violins have pegs; fine tuners (also called fine adjusters) are optional. Most fine tuners consist of a metal screw that moves a lever attached to the string end. They permit very small pitch adjustments much more easily than the pegs. By turning one clockwise, the pitch becomes sharper and turning one counterclockwise, the pitch becomes flatter.

Fine tuners on all four of the strings are a practical necessity for playing steel-core strings, and some players use them with synthetic strings as well. Since modern E strings are steel, a fine tuner is typically fitted for that string. Fine tuners are not used with gut strings, which are more elastic than steel or synthetic-core strings and do not respond adequately to the very small movements of fine tuners.

(source: http://en.wikipedia.org/wiki/V.....lin#Tuning)

The fiddlerman has two fine tuner -- one on his E string and one on his A string, you could see them on his video on how to change string.