Abstract
A fixed agenda social choice correspondence Φ on outcome set X maps each profile of individual preferences into a nonempty subset of X. If Φ satisfies an analogue of Arrow's independence of irrelevant alternatives condition, then either the range of Φ contains exactly two alternatives, or else there is at most one individual whose preferences have any bearing on Φ. This is the case even if Φ is not defined for any proper subset of X.
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Campbell, D.E., Kelly, J.S. Independent social choice correspondences. Theor Decis 41, 1–11 (1996). https://doi.org/10.1007/BF00134113
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DOI: https://doi.org/10.1007/BF00134113