Condorcet Jury Theorem: The Dependent Case

Author Info

Listed author(s):
• Bezalel Peleg
• Shmuel Zamir
Registered author(s):

Abstract

We provide an extension of the Condorcet Theorem. Our model includes both the Nitzan-Paroush framework of “unequal competencies” and Ladha’s model of “correlated voting by the jurors”. We assume that the jurors behave “informatively”, that is, they do not make a strategic use of their information in voting. Formally, we consider a sequence of binary random variables X = (X 1 ,X 2 , ...,X n , ...) with range in {0,1} and a joint probability distribution P. The pair (X,P) is said to satisfy the Condorcet Jury Theorem (CJT) if lim n→∞ P(∑X i >n/2)=1. For a general (dependent) distribution P we provide necessary as well as sufficient conditions for the CJT. Let p i = E(X i ), p n = (p 1 + p 2 , ...+ p n )/n and X n = (X 1 +X 2 , ...+X n )/n. A consequence of our results is that the CJT is satisfied if lim√n( p n -1/2)=∞ and ∑ i ∑ j≠i Cov(X i ,X j ) ≤ 0 for n > N 0 . The importance of this result is that it establishes the validity of the CJT for a domain which strictly (and naturally) includes the domain of independent jurors. Given (X,P), let p = liminf p n , and p = limsup p n . Let y = liminf E( X n - p n ) 2 , y * = liminf E| X n - p n | and y * = limsup E| X n - p n |. Necessary conditions for the CJT are that p ≥1/2 + 1/2 y ∗ , p ≥ 1/2 + y , and also p ≥ 1/2 + y ∗ . We exhibit a large family of distributions P with liminf 1/n(n-1) ∑ i ∑ j≠i Cov(X i ,X j ) > 0 which satisfy the CJT. We do that by ‘interlacing’ carefully selected pairs (X,P) and (X′,P′). We then proceed to project the distributions P on the planes ( p , y ∗ ) and ( p , y ), and determine all feasible points in each of these planes. Quite surprisingly, many important results on the possibility of the CJT are obtained by analyzing various regions of the feasible set in these planes.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://ratio.huji.ac.il/sites/default/files/publications/dp477.pdf

Bibliographic Info

Paper provided by The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem in its series Discussion Paper Series with number dp477.

as
in new window

 Length: 22 pages Date of creation: Mar 2008 Handle: RePEc:huj:dispap:dp477 Contact details of provider: Postal: Feldman Building - Givat Ram - 91904 JerusalemPhone: +972-2-6584135Fax: +972-2-6513681Web page: http://www.ratio.huji.ac.il/Email: More information through EDIRC

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as
in new window

1. Myerson, Roger B., 1998. "Extended Poisson Games and the Condorcet Jury Theorem," Games and Economic Behavior, Elsevier, vol. 25(1), pages 111-131, October.
2. Ladha, Krishna K., 1995. "Information pooling through majority-rule voting: Condorcet's jury theorem with correlated votes," Journal of Economic Behavior & Organization, Elsevier, vol. 26(3), pages 353-372, May.
3. Jean-François Laslier & Jörgen Weibull, 2008. "Committee decisions: Optimality and Equilibrium," Working Papers halshs-00121741, HAL.
4. Roger B. Myerson, 1998. "Population uncertainty and Poisson games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 375-392.
5. Wit, Jorgen, 1998. "Rational Choice and the Condorcet Jury Theorem," Games and Economic Behavior, Elsevier, vol. 22(2), pages 364-376, February.
6. Daniel Berend & Jacob Paroush, 1998. "When is Condorcet's Jury Theorem valid?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(4), pages 481-488.
Full references (including those not matched with items on IDEAS)

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Corrections

When requesting a correction, please mention this item's handle: RePEc:huj:dispap:dp477. 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: (Tomer Siedner)

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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.