Binary Effectivity Rules
AbstractA social choice rule is a collection of social choice correspondences, one for each agenda. An effectivity rule is a collection of effectivity functions, one for each agenda. We prove that every monotonic and superadditive effectivity rule is the effectivity rule of some social choice rule. A social choice rule is binary if it is rationalized by an acyclic binary relation. The foregoing result motivates our definition of a binary effectivity rule as the effectivity rule of some binary social choice rule. A binary social choice rule is regular if it satisfies unanimity, monotonicity, and independence of infeasible alternatives. A binary effectivity rule is regular if it is the effectivity rule of some regular binary social choice rule. We characterize completely the family of regular binary effectivity rules. Quite surprisingly, intrinsically defined von Neumann-Morgenstern solutions play an important role in this characterization.
Download InfoIf 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.
Bibliographic InfoPaper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp378.
Length: 16 pages
Date of creation: Oct 2004
Date of revision:
Publication status: Published in Review of Economic Design, 2006, vol. 10, pp. 167-181.
social choice correspondences; effectivity functions; Nakamura’s number; von Neumann-Morgenstern solutions;
Other versions of this item:
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-01-02 (All new papers)
- NEP-DCM-2005-01-02 (Discrete Choice Models)
- NEP-DCM-2005-01-04 (Discrete Choice Models)
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.:
- Moulin, Herve, 1985. "From social welfare ordering to acyclic aggregation of preferences," Mathematical Social Sciences, Elsevier, vol. 9(1), pages 1-17, February.
- Peleg, Bezalel & Peters, Hans & Storcken, Ton, 2002. "Nash consistent representation of constitutions: a reaction to the Gibbard paradox," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 267-287, March.
- Hans Keiding & Bezalel Peleg, 2002. "Representation of effectivity functions in coalition proof Nash equilibrium: A complete characterization," Social Choice and Welfare, Springer, vol. 19(2), pages 241-263, April.
- Moulin, H. & Peleg, B., 1982.
"Cores of effectivity functions and implementation theory,"
Journal of Mathematical Economics,
Elsevier, vol. 10(1), pages 115-145, June.
- Moulin, Hervé & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Economics Papers from University Paris Dauphine 123456789/13220, Paris Dauphine University.
- Bezalel Peleg, 1997. "Effectivity functions, game forms, games, and rights," Social Choice and Welfare, Springer, vol. 15(1), pages 67-80.
- Peleg,Bezalel & Peters,Hans, 2005.
"Nash consistent representation of effectivity functions through lottery models,"
030, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- Peleg, Bezalel & Peters, Hans, 2009. "Nash consistent representation of effectivity functions through lottery models," Games and Economic Behavior, Elsevier, vol. 65(2), pages 503-515, March.
- Bezalel Peleg & Hans Peters, 2005. "Nash Consistent Representation of Effectivity Functions through Lottery Models," Discussion Paper Series dp404, The Center for the Study of Rationality, Hebrew University, Jerusalem.
- Bezalel Peleg & Shmuel Zamir, 2013. "Representation of constitutions under incomplete information," Discussion Paper Series dp634, The Center for the Study of Rationality, Hebrew University, Jerusalem.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ilan Nehama).
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.