The results for the third Doppole survey are in, and now we know why Doppole get the caps they get. It's... it's random.
https://www.surveymonkey.com/results/SM-XSFPN5RL/>There is a pool of possible Doppole caps, each with its own rarity. A Doppole gets a random cap chosen from this pool.Note that which Poké Balls are in this pool, and the odds of getting each one, haven't been decided yet.