Independence and Social Choice
Speaker
Robert Powers
Department of Mathematics, University of Louisville
https://www.math.louisville.edu/people/faculty/powers.html
Description
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.