Movement+initiative.

Initiative. dats all i have to say.
just investigate a little bit :D

A person can have 999999999 initiative and be in position 4 and still not move first if their enemy is in a position 1 with 1 initiative stat . . .
Position matters first.
THEN it comes down to initiative.

This is assuming neither side is using kurotsuchi.....
But yes, it goes higher init pos 1, lower init pos 1, higher init pos 2, lower init pos 2 etc

This isn't quite true, I have been in position 1 and be interrupted by an earth main in level 120 ninja exam.

Enemy earth main was in position 2. So there is a way to move faster in a different position, it just requires a lot more initiative. I like to think of the positions as a passive boost to initiative. (Albeit a massive boost)

Nope. Position matters more than initiative. That's why aggressive PVP teams put their combo starter on the 1st position and stack them with the highest refines. I've seen teams using kimmimaro/Hinata on the 1st position lose to people with lower power because the guy they are facing had their combo on the first slot and thus went first.

I'm not arguing that Position doesn't matter more than initiative. I have seen people in position 9 act before position 7. Position does matter more but initiative can make them move quicker than a higher position.

No, it can't. In pve npcs can have super-prompt, like in the Hidan SA, Chikushodo will go first, even her normal attack before your prompt mystery. But in pvp it's impossible, you will never go before move 1 guy with your move 2 guy even if you have thousands of init more, unless the move 1 guy has slow debuff.

Oh, no, it's not that position.
Perhaps it's better worded as "move 1"
It goes from 1 to 4, as in the order of your ninjas relative to each other, not the 1-9
So that exam thing you were talking about, he's probably position 2 move 1, which is same as position 1 move 1 or position 6 move 1.

Then they should fix AI because it never respects the order and ends up throwing the AI first
It is one of the reasons why many do not like survival or fights against AI

I have never had any troubles with it. As long as you spam your mystery the turn before, everything works fine. It's throwing AI when you are hestitating to use a move.