This article explicitly constructs and classifies all arrovian voting systems on three or more alternatives. If we demand orderings to be complete, we have, of course, Arrow's classical dictator theorem, and a closer look reveals the classification of all such voting systems as dictatorial hierarchies. If we leave the traditional realm of complete orderings, the picture changes. Here we consider the more general setting where alternatives may be incomparable, that is, we allow orderings that are reflexive and transitive but not necessarily complete. Instead of a dictator we exhibit a junta whose internal hierarchy or coalition structure can be surprisingly rich. We give an explicit description of all such voting systems, generalizing and unifying various previous results.
|Date of creation:||Aug 2006|
|Date of revision:||03 Oct 2006|
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- KIRMAN, Alan P. & SONDERMANN, Dieter, .
"Arrow's theorem, many agents, and indivisible dictators,"
CORE Discussion Papers RP
-118, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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"Social choice theory and the "Centre de Mathématique Sociale". Some historical notes,"
Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers)
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