Once upon the time, in April, I had it figured out precisely, but as bugs were fixed, things changed.
Here's the way to think about it.
1. In order to move, an unit needs to gather a certain amount of energy. At the beginning of the battle, everyone has 0 energy, baring traits (impulsive, for example)
2. Every tick (you can think of them as combat rounds) every unit generates energy corresponding to its initiative.
3. Every tick, the energy of units is checked, and those that have gathered enough, move.
4. Next tick. I.e. go to 2.
Once again, this is not necessarily how the game works. This is a model that worked in April.
A few things that you can conclude from my model:
1. An unit with half the initiative moves about half as often.
2. Because energy gathering 'overshoots', the order can change in unexpected ways.
3. When initiatives are close, it takes a long time for a faster unit to get one whole turn on another, slower one.
4. If initiatives and ticks fall just right, a slightly slower unit can move twice while a faster unit gets no turn.