If there is any effect I would imagine it would be miniscule and not exploitable.
Rating system commutative?

Oh! That makes sense. Thanks!

No, in correspondence the rating changes when the game is complete and uses your most recent rating and rating deviation (RD) value. You can get an estimate of the change at any point, but the ratings at game end are used for the calculations.

No, in correspondence the rating changes when the game is complete and uses your most recent rating and rating deviation (RD) value. You can get an estimate of the change at any point, but the ratings at game end are used for the calculations.
Would this imply that the order you win/lose games, would in fact matter?

Yes, you can gain a few more points by winning / losing games in a different order.
If you have a choice, I think you want to lose first and then win, not the other way around.
You can also check if your opponent is about to win or lose some games. Better to let their rating get higher before you win or lose to them

Llama44 is correct. RD increases over time. The higher your RD, the more points gained or lost. So stretching out a losing game only ensures that you will lose more points when it ends, because your RD will be higher.

I didn't think of RD, I guess that's true. I guess if your RD is very high (a new player) then it's better to win first. But if your RD is stable, I think it's better to lose first.
Fore example lets imagine all 3 players are rated the same. If you win/lose you gain/lose 10 points.
Now your next win/loss you're either
higher rated and lose (means you lose more than 10) -- or
lower rated and win (means you win more than 10)
So you should:
lose 10, then gain more than 10 -- not
win 10, then lose more than 10
So it's better to lose first.
Hypothetically let's say you are a X rated player playing correspondence and you are winning against a Y rated player and losing against a Z rated player. (X, Y, Z) arbitrary ratings.
According to chess.com's ELO rating system, is your net rating change the same in the following scenarios?
1. Win Y and then lose Z
2. Lose Z and then win Y
I'm interested in this to see if it affects player's behaviors in game (Postponing clear draws for example, or trying to stretch out a losing game as long as possible.)
Thanks!