I figured I would mention it because Phreak said normal draft doesn't do this.
However, I duo queue with a friend frequently, we are always first/second, third/fourth, or fourth/fifth. We never get second/third. I ask whenever people are above us in champion selection, and they have always said yes to being a duo or tri queue.
Whenever I solo queue, I am almost always fourth or fifth pick, with third pick on rare occasions. Any time I'm third pick, the people below have always said no to being a duo queue. Most of the time the picks above me are either a duo or tri queue, and sometimes I get a quad queue. I do have rare games where everyone is solo though.
My point is, whenever I duo queue, my friend and I are never placed below solo queues, and whenever I solo queue, I am never placed above premades of any number. Ever.
Edit: I'll start recording my picking position for evidence. Any game where premade status isn't mentioned means they neglected to answer.
Game 1 - Fifth
Game 2 - Fourth, tri queue above
Game 3 - Fourth, tri queue above
Game 4 - Fifth, duo queue first and second pick
Game 5 - Fourth, duo queue first and second pick
Game 6 - Fourth, duo queue first and second pick
Game 7 - Fourth, tri queue above
Game 8 - **DUO QUEUE** fourth/fifth pick, tri queue above
Game 9 - Fourth, tri queue above
Game 10 - Fourth, duo queue first/second pick
Game 11 - Fifth, tri queue first three picks
Game 12 - Fifth, tri queue first three picks