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No, not everyone bases morals on rationality. Consequentialists do but not everyone is a consequence based thinker. I used to think like you but I realize not everyone is going to accept this. In fact if you look at the data the majority of people on the earth don't think this way.

Not everyone does, but machines and AI will. Unless you are suggesting we build AI that thinks irrationally.

No not at all. The AI is logical (not rational). The person who asked the question, trained the AI, tells the AI it's values, has to be rational for the AI to provide a rational answer.