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Why can't (or shouldn't) economists answer normative questions?

Normative questions are those which:

affirm how things should or ought to be, how to value them, which things are good or bad, which actions are right or wrong. Normative is usually contrasted with positive (i.e. descriptive, explanatory, or constative) claims when describing types of theories, beliefs, or propositions. Positive statements are factual statements that attempt to describe reality.

Normative questions may include:

  • What is the right amount of money to spend on healthcare?
  • How do we reduce the unfairness of income inequality?
  • Is it better for the few to sacrifice for the many?

The main reason that economists (and this site) steer clear of normative questions is that they are difficult to answer in a way that has academic rigour. Experienced philosphers and economists will usually attempt to rephrase any question so that it is positive so that an answer can be arrived at and research conducted.

People tend to think normatively, though. Things can feel "right" or "wrong".

My question: is there a clear and decisive answer (or research) to the question as to why it is difficult (or even irresponsible) for economists to answer normative questions and, by extension, is it possible to use normative questions to arrive at a positive result?