It all depends on independence
Eliaz (2004) has established a "meta-theorem" for preference aggregation which implies both Arrow's Theorem (1963) and the Gibbard-Satterthwaite Theorem (1973, 1975). This theorem shows that the driving force behind impossibility theorems in preference aggregation is the mutual exclusiveness of Pareto optimality, individual responsiveness (preference reversal) and non-dictatorship. Recent work on judgment aggregation has obtained important generalizations of both Arrow's Theorem (List and Pettit 2003, Dietrich and List 2007a) and the Gibbard-Satterthwaite Theorem (Dietrich and List 2007b). One might ask, therefore, whether the impossibility results in judgment aggregation can be unified into a single theorem, a meta-theorem which entails the judgment-aggregation analogues of both Arrow's Theorem and the Gibbard-Satterthwaite Theorem. For this purpose, we study strong monotonicity properties (among them non-manipulability) and their mutual logical dependences. It turns out that all of these monotonicity concepts are equivalent for independent judgment aggregators, and the strongest monotonicity concept, individual responsiveness, implies independence. We prove the following meta-theorem: Every systematic non-trivial judgment aggregator is oligarchic in general and even dictatorial if the collective judgment set is complete. However, systematicity is equivalent to independence for blocked agendas. Hence, as a corollary, we obtain that every independent (in particular, every individually responsive) non-trivial judgment aggregator is oligarchic. This result is a mild generalization of a similar theorem of Dietrich and List (2008), obtained by very different methods. Whilst Eliaz (2004) and Dietrich and List (2008) use sophisticated combinatorial and logical arguments to prove their results, we utilize the filter method (cf. e.g. Dietrich and Mongin, unpublished) and obtain a much simpler and more intuitive derivation of our meta-theorem.
|Date of creation:||15 Aug 2011|
|Contact details of provider:|| Postal: Postfach 10 01 31, 33501 Bielefeld|
Web page: http://www.imw.uni-bielefeld.de/
More information through EDIRC
When requesting a correction, please mention this item's handle: RePEc:bie:wpaper:412. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Bettina Weingarten)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.