Wagner, Carl and Shattuck, Mark
(2012)
An impossibility theorem for allocation aggregation.
[Preprint]

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PS_Arch_An_impossibility_theorem_for_alllocation_aggregation.docx_with_authors.docx
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Abstract
In axiomatic approaches to expert opinion aggregation, socalled independence conditions have been ubiquitous. Such conditions dictate that the group value assigned to each decision variable should depend only on the values assigned by individuals to that variable, taking no account of values that they assign to other variables. This radically antiholistic stricture on the synthesis of expert opinion severely limits the set of allowable aggregation methods. As we show, the limitations are particularly acute in the case of three or more variables which must be assigned nonnegative real values summing to a fixed positive real number s. For if the subset V of [0,s] comprising the allowable values of the variables satisfies the closure conditions (i)0 is an element of V ; (ii) if x is an element of V, then sx is an element of V ; and (iii) if x and y are elements of V and x+y is an element of [0,s], then x+y is an element of V, then, if V is finite, which is always the case in practice, subjecting the aggregation of such sallocations to an independence condition allows only for dictatorial or imposed (i.e., constant) aggregation.
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