To do a favor for someone expecting a favor in return.
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To do a favor for someone with the expectation that they will return the favor in the future.
Scratch my back and I'll scratch yours describes a mutually beneficial arrangement where each party helps the other.
It is used to describe reciprocal favors, sometimes with a slightly transactional or even corrupt connotation.
"Quid Pro Quo"
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A formal or explicit exchange where something is given only in return for something else
"Mutual Back-scratching"
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The same concept as scratch each other's backs — a reciprocal arrangement of favors
"Scratch Someone's Back"
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Doing a favor for someone with the expectation of a reciprocal favor in return