Abstract.
If, for strict preferences, a unique choice function (CF) is used to aggregate preferences position-wise then the resulting social welfare function (SWF) is dictatorial. This suggests that the task performed by non-dictatorial SWFs must be “more complex” than just selecting an alternative from a list using a single criterion. This is because the information required by non-dictatorial SWFs to aggregate preferences cannot be compressed into a CF. It is also shown that the attempt to reduce the working of a SWF to the working of a CF involves the adoption of certain positional requirements, whose relationship with the conditions in Arrow's theorem is established.
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Received: 28 May 2001/Accepted: 25 March 2002
My deepest gratitude to Donald G. Saari, who rescued this paper from the worst fate, and to the referee, who showed the escape route.
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Quesada, A. Positional independence in preference aggregation. Soc Choice Welfare 20, 363–370 (2003). https://doi.org/10.1007/s003550200187
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DOI: https://doi.org/10.1007/s003550200187