A non-dictatorial compromise

Abstract aggregations are defined and pertinent conditions of decisiveness, anonymity, unanimity, independence of irrelevant alternatives (stronger than the Arrowian) and non-dictatoriality (logically independent of the Arrowian) are developed for aggregations of choices. The mode is identified as a compromise aggregating variable societies of choices into a social choice, and it is shown (Theorem 4.1) to satisfy these conditions. This non-dictatorial compromise is then characterized (Theorem 5.1) in terms of three axioms paralleling those characterizing the approval voting of Sertel 7].This paper has benefited from helpful discussions with a number of colleagues and students, who are hereby thanked without being implicated for any remaining failings. In particular, earlier versions received the useful comments of participants at the Eighth and Ninth Bosphorus Workshops on Industrial Democracy, July 1983 and August 1984, Boaziçi University, Istanbul: most notably, Nick Baigent, Faruk Gül and Dennis Mueller. The help of Ünal Zenginobuz is also gratefully acknowledged. Finally, an anonymous referee's suggestions led to the addition of clarifying notes relating the notions of independence of irrelevant alternatives and of non-dictatoriality here to the usual Arrowian ones, and it is due to this referee's instigation that the characterization of the mode in Sect. 5 was produced.