Robert Powers
(Department of Mathematics, University of Louisville)
Independence and Social Choice
Abstract
A new version of independence (I+) is proposed for social welfare
functions based
on the following notion of agreement. Two weak orders and
' on a
finite set S agree on a pair {x,y}, denoted by
|+{x,y} = '|+{x,y},
if |{x,y} =
'|{x,y} and [z * x and z * y for some
z in S] if and only if [z' (')* x and
z' (')* y for some
z' in S]. The last part says that x and y are strictly under
z with respect to exactly when x and y are strictly under
z'
with respect to '. The idea is that there may be an
alternative that is preferred
over x and y and one should keep track of this additional information.
There exist
nondictatorial social
welfare functions that satisfy (I+) and Pareto allowing one to avoid the
Arrow paradox. In fact, our main
result is a description of the social welfare functions that satisfy
(I+), Pareto, and
nondictatorship.
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