[AaronBrown]

You're right. Everyone, loose or tight, wants loose players on his right and tight players on his left. When you shift, you get a tight player on your left, he gets a loose one on his right. The player who used to be on your left, now has a tight player instead of a loose player on his right. She loses. The player who used to be on his right, now has a loose player instead of a tight player on his left. He loses.

The only reason it seems impossible is when you're both in middle position, it doesn't seem to matter to anyone else at the table which of you acts first. Whichever order the two of you sit, everyone else at the table gets to see either both or neither of your actions before acting.

In practice, the pots might be larger with you acting first. You might call in situations when you would have folded if the tight player had acted first. In theory, it shouldn't make any difference to the average pot size, if we assume you both factor in the other's tendencies properly.

The difference to the table is the one hand per round when he is under the gun and you are big blind. Then the whole table gets a tight player acting first, with a loose player acting last.