This puzzle is part of the Puzzling Stack Exchange Advent Calendar 2024. The accepted answer to this question will be awarded a bounty worth 50 reputation.
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Santa’s reindeer got bored waiting for Christmas. They decided to try roleplaying. Each chose characters as close as possible to their origins. Which did they choose, and how?
You know Donder and Vixen and Cupid and Comet,
Dancer and Blitzen and Prancer and Dasher,
But do you recall?
The most remarkable reindeer of them all?
Rudolph the—
Dasher glared at Rudolph. “That’s not how the song goes. It doesn’t even rhyme!”
Rudolph snorted. “I think this order actually makes a lot of sense. And I’m not taking criticism from a poisoner…”
“Takes one to know one! And if you’re putting us in ‘order’, surely I should be first?! Why on earth is Donder first?”
“He’s common. Plebian. I’m special, one in a billion, so obviously I’m last.”
Dancer trotted over. “But if we’re going by rarity, why am I fifth? Just,” he waved a hoof vaguely at the air, “I would’ve thought it was me, then Donder, then, uh, wait, are any of you even—”
“I’m still confused,” cut in Comet. “Why aren’t Cupid and I the same? Could you explain again?”
“Because then everyone might think you two were dating,” Vixen called as he admired his good looks in a mirror.
“Well, I think we'd be a pair of real diamonds! Oh, so romantic.” Cupid sighed.
“You’re pretty near each other anyways. There’s, what, one seat between yours at the table? I’m stuck in the effing bottom,” whined Prancer.
“If we’re going by our table places, shouldn’t I be first?” asked Blitzen.
“For crying out loud, forget the table. You know what, I’ve had enough of this…” Rudolph stomped away. “Give me some space, or I’m really going to start something.”
“Hey, blowing things up is my job!” Donder yelled after him.
A complete answer will explain the role each reindeer chose, the rule behind their choices, and how you know this to be the case from the conversations that just took place.
Thank you @Stiv for playtesting!