Abstract
We show that the class of social welfare functions that satisfy a weak independence condition identified by Campbell (J Econ 12:259–272, 1976) and Baigent (J Econ 47(4):407–411, 1987) is fairly rich and freed of a power concentration on a single individual. This positive result prevails when a weak Pareto condition is imposed. Moreover, under weak independence, an impossibility of the Wilson (J Econ 5:478–486, 1972) type vanishes.
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