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An impossibility theorem for allocation aggregation

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

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Abstract

In axiomatic approaches to expert opinion aggregation, so-called 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 anti-holistic 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 s-x 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 s-allocations to an independence condition allows only for dictatorial or imposed (i.e., constant) aggregation.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Wagner, Carlwagner@math.utk.edu
Shattuck, Markshattuck@math.utk.edu
Keywords: allocation aggregation, dictatorship, judgment aggregation, probability
Subjects: Specific Sciences > Economics
Depositing User: Carl Wagner
Date Deposited: 04 Nov 2012 22:26
Last Modified: 04 Nov 2012 22:26
Item ID: 9382
URI: http://philsci-archive.pitt.edu/id/eprint/9382

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