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I believe the rationale is that in the LLMs’ training data, higher-quality information is available in places where people are polite. The LLM is just copying that statistical fact.

It is interpreted as positive/affirmative against the correctness or relevance of the previous output. Telling it 'That is correct' will achieve a very similar effect (as will saying 'No'/'That isn't relevant'/etc. would in the converse.)

This cracks me up. For decades only INTERCAL demanded an appropriate level of politeness. It was a great joke, and we all laughed.

Now it’s an actual real thing that the computer performs the task better when you ask nicely! (I am also polite and professional whenever I talk to ChatGPT)