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Journal of Logic and Computation Advance Access published online on April 30, 2008
Journal of Logic and Computation, doi:10.1093/logcom/exn012
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© The Author, 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Papers

Aggregating Partially Ordered Preferences

Maria Silvia Pini, Francesca Rossi and Kristen Brent Venable

Department of Pure and Applied Mathematics, University of Padova, Padova, Italy.
E-mail: mpini{at}math.unipd.it; frossi{at}math.unipd.it; kvenable{at}math.unipd.it

Toby Walsh

NICTA and UNSW, Sydney, Australia.
E-mail: tw{at}cse.unsw.edu.au


  Abstract

Preferences are not always expressible via complete inear orders: sometimes it is more natural to allow for the presence of incomparable outcomes. This may hold both in the agents' preference ordering and in the social order. In this article, we consider this scenario and study what properties it may have. In particular, we show that, despite the added expressivity and ability to resolve conflicts provided by incomparability, classical impossibility results (such as Arrow's theorem, Muller–Satterthwaite's theorem and Gibbard–Satterthwaite's theorem) still hold. We also prove some possibility results, generalizing Sen's theorem for majority voting. To prove these results, we define new notions of unanimity, monotonicity, dictator, triple-wise value-restriction and strategy-proofness, which are suitable and natural generalizations of the classical ones for complete orders.

Keywords: Social choice; preference aggregation; partially ordered preferences; strategy-proofness


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