I am not a fan of a shared position. Not that I think that both of the winners wouldn't get along, but it would take too long to get things done, since everything has to be discussed.
When you have a tie between candidate A and B when there are three candidates, the solution seems simple: new elections where only the two tied winners participate, but in the event of a tie when only two candidates were running, I must admit that I see no other acceptible solution other than new elections (which of course carries the risk of yet another tie). For the reason stated above I'm no fan of shared positions and 'flipping a coin' seems in no way fair to me. I am also not a big fan of having the GC decide, because basically the GC gets to choose which of the two candidates gets the position. And even though whether candidate A or B wins can also very well depend on one single vote, the voting itself is anonymous (that is to say: the voters don't know who the other voters chose).
So although I recognize the potential problem with this, I'd still say: re-elections until a winner comes out on top.
-Mischa