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I am looking for axiomatic characterisations of dictatorial social choice/welfare functions; where a dictatorial social choice function is one that always picks the dictator’s favourite outcome, and a dictatorial social welfare function is one whose social preference always coincides with the one of the dictator.

An axiomatic characterisation of a dictatorial social choice/welfare function is a collection of axioms that uniquely identify a dictatorial social choice/welfare function. The three most famous such characterisations I can think of were provided by Arrow (1951, 1963), Gibbard (1973) & Satterthwaite (1975) and Koray (2000):

  1. [Arrow (1951, 1963)] With at least three alternatives, a social welfare function is dictatorial if and only if it satisfies unrestricted domain, Pareto-optimality and independence of irrelevant alternatives.
  2. [Gibbard (1973) & Satterthwaite (1975)] With at least three alternatives, a social choice function is dictatorial if and only if it satisfies unrestricted domain and strategy-proofness.
  3. [Koray (2000)] A social choice function satisfying unrestricted domain, unanimity and neutrality is self-selective if and only if it is dictatorial.

Can you please direct me to other results in social choice theory that uniquely characterise dictatorships?

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    $\begingroup$ I am not sure whether this answers your questions so leaving this as a comment, but you can refer to Prof. Arunava Sen's notes on social choice theory. isid.ac.in/~asen/scdoc/lecarrow_2017.pdf These notes contains a lot of the major results in social choice, so they might have the sort of results you're seeking. $\endgroup$
    – mynameparv
    May 16 at 11:08
  • $\begingroup$ Thank you very much for your comment: these notes are very nice and contain one result I wasn’t aware of (namely, that unrestricted domain, Maskin monotonicity and unanimity imply dictatorship). I also saw that the Gibbard & Satterthwaite Theorem is stated in terms of unanimity, unrestricted domain and strategy-proofness. While I see Satterthwaite used unanimity in his paper, I can’t see it in Gibbard’s. $\endgroup$
    – EoDmnFOr3q
    May 16 at 13:20

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