In this paper we consider the classical problem of dividing a land among many agents so that everybody is satisfied with the parcel she receives. In the literature, it is usually assumed that all the agents are endowed with cardinally comparable, additive, and monotone utility functions. In many economic and political situations violations of these assumptions may arise. We show how a family of cardinally comparable utility functions can be obtained starting directly from the agents’ preferences, and how a fair division of the land is feasible, without additivity or monotonicity requirements. Moreover, if the land to be divided can be modelled as a finite dimensional simplex, it is possible to obtain envy-free (and a fortiori fair) divisions of it into subsimplexes. The main tool is an extension of a representation theorem of Gilboa and Schmeidler (1989).
|Date of creation:||2007|
|Contact details of provider:|| Postal: Via Real Collegio, 30, 10024 Moncalieri (To)|
Web page: http://www.carloalberto.org/
More information through EDIRC
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.:
- Francis Su, "undated". "Rental Harmony: Sperner's Lemma in Fair Division," Claremont Colleges Working Papers 1999-10, Claremont Colleges.
- Berliant, Marcus & Thomson, William & Dunz, Karl, 1992. "On the fair division of a heterogeneous commodity," Journal of Mathematical Economics, Elsevier, vol. 21(3), pages 201-216.
- Ichiishi, Tatsuro & Idzik, Adam, 1999. "Equitable allocation of divisible goods," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 389-400, December.
- Gilboa, Itzhak & Schmeidler, David, 1989.
"Maxmin expected utility with non-unique prior,"
Journal of Mathematical Economics,
Elsevier, vol. 18(2), pages 141-153, April.
- Itzhak Gilboa & David Schmeidler, 1989. "Maxmin Expected Utility with Non-Unique Prior," Post-Print hal-00753237, HAL.
- L. Randall Wray & Stephanie Bell, 2004. "Introduction," Chapters, in: Credit and State Theories of Money, chapter 1 Edward Elgar Publishing.
- Fabio Maccheroni & Fabio Maccheroni & Massimo Marinacci & Massimo Marinacci, 2003. "How to cut a pizza fairly: Fair division with decreasing marginal evaluations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(3), pages 457-465, 06.
- Massimo Marinacci & Fabio Maccheroni, 2002. "How to cut a pizza fairly: fair division with descreasing marginal evaluations," ICER Working Papers - Applied Mathematics Series 23-2002, ICER - International Centre for Economic Research.
- Berliant, Marcus & Dunz, Karl, 2004. "A foundation of location theory: existence of equilibrium, the welfare theorems, and core," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 593-618, August.
- Berliant, M.C. & Dunz, K., 1991. "A Foundation of Location Theory : Exstence of Equilibrium, the Welfare Theorems and Core," RCER Working Papers 298, University of Rochester - Center for Economic Research (RCER).
- Philippe Robert-Demontrond & R. Ringoot, 2004. "Introduction," Post-Print halshs-00081823, HAL. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:cca:wpaper:58. 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: (Giovanni Bert)
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.