Proposed Canon
As shown Erf-b2-p4, it appears that Dittomancy amplifies bonuses and duplicates units.
Jetstone's Dittomancer has a tendency to say everything twice. For example, "Yeah, yeah. I know, I know", or "It's... It's foolamancy! Foolamancy!". Where each word or phrase is said twice, in keeping with the doubling theme. He also appears to rhyme when precise repeats are not what he wishes to say. The interaction of Dittomancy with Rhyme-o-mancy is still unknown.
- Empower Special
Can double special bonuses, like Leadership.
- Multiply Ranged Attack
Can increase the number of ranged attacks from a set of specified units, either double or quadruple.
- Duplicate Unit
Can duplicate a unit completely (this unit is called a Double. The duplicate last for one turn and disappears if croaked. The Double will even count as the ruler being alive if the original is croaked.
 Known Dittomancers
A dittomancer has been seen multiplying the number of arrows in an archer stack's volley. This may be a physical manifestation of multiplying the archers' combat stat. Dittomancers may also be able to double other stats, such as hits or move.
Dittomancers have been shown to able to make copies of other units, in a fashion similar to croakamancy. Eg, the more attention spent on each individual unit, the more like the original it will be. It may be possible to duplicate an entire army, but the resulting copies would likely have very low stats and last only for a single turn.
The phrase "Double or Nothing" may apply here. It is possible that in the attempt to use Dittomancy i.e. to "double down" that failure of the magic might result in the loss of the unit which the Dittomancy is attempting to duplicate.
Dittomancy may combine with Hat Magic to triplicate effects - a "hat trick", as it were.
 Real World References
"Ditto" is a term that has many iterations, all of which involve duplication, repetition, or copying.
The original Tuscan word (cir 1625) meant "in the stated month or year" and was used in place of repeating the same date. (Speculatively, this implies Date-a-mancy may be tied to Dittomancy ) By 1678 it was in use in English to mean "same as above," from which we get the "ditto mark" (or "), placed under a word or phrase it is used to repeat.
The Ditto corporation made simple printing devices called spirit duplicators (because they used alcohol), or "Ditto machines" which produced "ditto sheets," or copies.
Ditto was used famously in the film Ghost to mean, roughly, "I feel the same way."
Multiple fictional characters that involve copying or twins, etc. are named ditto.