Attack order is inconsistent (doubles random battle (dev)).
Turn 2: Mr. Mime was faster (hidden power - priority +0) than Electivire (earthquake - priority +0)
Turn 3: Mr. Mime was slower (thunderbolt - priority +0) than Electivire (earthquake - priority +0)
Something perhaps noteworthy is that my Combusken with speed boost was in battle when Mr. Mime was faster. However none of the sources suggest that changes the attack order in the real game.
Link:
http://www.pokemonshowdown.com/replay/doublesrandombattledev8535511
Log:
Turn 2
The foe's Combusken used
Flare Blitz!
Electivire lost 59% of its health!
The foe's Combusken is damaged by recoil!
The foe's Mr. Mime used
Hidden Power!
Electivire lost 21% of its health!
Electivire used
Earthquake!
[DEBUG] natural immunity.
It doesn't affect Xatu...
A critical hit! It's super effective! The foe's Combusken lost 79% of its health!
The foe's Mr. Mime lost 37% of its health!
The foe's Combusken fainted!
Xatu used
Roost!
Xatu regained health!
The foe's Mr. Mime restored HP using its Leftovers!
The foe's Mr. Mime was hurt by poison!
Sixish sent out Emboar!
Turn 3
Electivire used
Earthquake!
[DEBUG] natural immunity.
It doesn't affect Xatu...
It's super effective! The foe's Emboar lost 56% of its health!
The foe's Mr. Mime lost 22% of its health!
The foe's Mr. Mime fainted!
Xatu used
Psychic!
It's super effective! The foe's Emboar lost 44% of its health!