An infinite version of Arrow's theorem in the effective setting (Q1108914)

The author studies the well-known Arrow problem in the theory of voting for the case when both the set of voters and the set of alternatives are infinite. He investigates the question of whether ``infinitory versions of Arrow's theorem exist that are absolutely within ZF and for which algorithms exist to determine the identities of dictators'' (ZF stands for Zermelo-Fraenkel's set of axioms in set theory). The author asserts that ``... in the case of a society that is fully recursive over the ring of all algebraic integers of a number field we have also shown that a primitive recursive algorithm exists to determine the dictators...''.