Arrow's Impossibility Theorem: Preference Diversity in a Single-Profile World
AbstractIn this paper we provide two simple new versions of Arrow’s impossibility theorem, in a model with only one preference profile. Both versions are transparent, requiring minimal mathematical sophistication. The first version assumes there are only two people in society, whose preferences are being aggregated; the second version assumes two or more people. Both theorems rely on assumptions about diversity of preferences, and we explore alternative notions of diversity at some length. Our first theorem also uses a neutrality assumption, commonly used in the literature; our second theorem uses a neutrality/monotonicity assumption, which is stronger and less commonly used. We provide examples to illustrate our points.
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 Brown University, Department of Economics in its series Working Papers with number 2008-8.
Date of creation: 2008
Date of revision:
Contact details of provider:
Postal: Department of Economics, Brown University, Providence, RI 02912
Arrow's Theorem; single-profile;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-10-21 (All new papers)
- NEP-CDM-2008-10-21 (Collective Decision-Making)
- NEP-HPE-2008-10-21 (History & Philosophy of Economics)
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.:
- Kenneth J. Arrow, 1950. "A Difficulty in the Concept of Social Welfare," Journal of Political Economy, University of Chicago Press, vol. 58, pages 328.
- Pollak, Robert A, 1979. "Bergson-Samuelson Social Welfare Functions and the Theory of Social Choice," The Quarterly Journal of Economics, MIT Press, vol. 93(1), pages 73-90, February.
- Parks, Robert P, 1976. "An Impossibility Theorem for Fixed Preferences: A Dictatorial Bergson-Samuelson Welfare Function," Review of Economic Studies, Wiley Blackwell, vol. 43(3), pages 447-50, October.
- Roberts, Kevin W S, 1980. "Social Choice Theory: The Single-profile and Multi-profile Approaches," Review of Economic Studies, Wiley Blackwell, vol. 47(2), pages 441-50, January.
- Marc Fleurbaey & Philippe Mongin, 2004.
"The News of the Death of Welfare Economics is Greatly Exaggerated,"
- Marc Fleurbaey & Philippe Mongin, 2005. "The news of the death of welfare economics is greatly exaggerated," Social Choice and Welfare, Springer, vol. 25(2), pages 381-418, December.
- Blau, Julian H & Deb, Rajat, 1977. "Social Decision Functions and the Veto," Econometrica, Econometric Society, vol. 45(4), pages 871-79, May.
- Campbell, Donald E. & Kelly, Jerry S., 2002. "Impossibility theorems in the arrovian framework," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 1, pages 35-94 Elsevier.
- Reny, Philip J., 2001. "Arrow's theorem and the Gibbard-Satterthwaite theorem: a unified approach," Economics Letters, Elsevier, vol. 70(1), pages 99-105, January.
- Kemp, Murray C & Ng, Yew-Kwang, 1976. "On the Existence of Social Welfare Functions, Social Orderings and Social Decision Functions," Economica, London School of Economics and Political Science, vol. 43(169), pages 59-66, February.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Brown Economics Webmaster).
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.