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Looking for the title and author of a sci-fi short story wherein an Earth spaceship with telepathic crew encounters an alien spaceship. The telepathic crew try to convince the aliens that the ship's cat is in charge...

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This is almost definitely "Trouble with Treaties" by Katherine MacLean & Tom Condit as mentioned in this previous answer. It was originally published in 1959 in the anthology Star Science Fiction Stories No. 5 so it definitely qualifies as "vintage."

It's been a long time since I read it, but as best I recall the (human) telepath figures out that the aliens think the humans aren't forceful/dominating enough to be as apparently advanced as they are, and unless there's some evidence of a more powerful race in charge of the humans, that the aliens will simply take them over. The humans hatch a plot to pretend that the ship's cat is secretly in charge of them - and the cat so powerful that the humans don't even realize it's in charge.

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