| The problem with players going in a set order is that player 3 might not be able to come up with something on the spot to fix what player 2 said, whereas the next player in line has a great idea.
On the other hand, this simply serves to postprones the problem, as at some point the player has to act.
It did feel a little weird when I was running a social skill challenge, because after the first couple of players had acted (the ones who are more "outspoken" in character), a few players was left that took longer to come up with what to do/say.
I would argue that it is easier to go first, so the best option might be to direct who speaks first, and ensure it is the people that like to stay in the background. This might also lead to some complicated situations for the more "outspoken" players to fix (and hence, challenging them). | 
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