A Note on Selecting Maximals in Finite Spaces
AbstractGiven a choice problem, the maximization rule may select many alternatives. In such cases, it is common practice to interpret that the final choice will end up being made by some random procedure, assigning to any maximal alternative the same probability of being chosen. However, there may be reasons based on the same original preferences for which it is suitable to select certain maximal alternatives over others. This paper introduces two choice criteria induced by the original preferences such that maximizing with respect to each of them may give a finer selection of alternatives than maximizing with respect to the original preferences. Those criteria are built by means of several preference relations induced by the original preferences, namely, two (weak) dominance relations, two indirect preference relations and the dominance relations defined with the help of those indirect preferences. It is remarkable that as the original preferences approach being complete and transitive, those criteria become both simpler and closer to such preferences. In particular, they coincide with the original preferences when these are complete and transitive, in which case they provide the same solution as those preferences.
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 Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History) in its series Working Papers in Economic Theory with number 2012/06.
Length: 16 pages
Date of creation: Feb 2012
Date of revision:
Contact details of provider:
Postal: Francisco Tomás y Valiente, 5, 28049 Madrid
Web page: http://www.uam.es/departamentos/economicas/analecon/default.html
More information through EDIRC
maximal elements; maximization; acyclical preferences; rational choice; choice function; refinements of maximization rule.;
Find related papers by JEL classification:
- C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
- D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-02-20 (All new papers)
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.:
- Begoña Subiza & Josep Peris, 2005.
"Condorcet choice functions and maximal elements,"
Social Choice and Welfare,
Springer, vol. 24(3), pages 497-508, 06.
- Begoña Subiza & Josep Peris, 2000.
"Choice Functions: Rationality re-Examined,"
Theory and Decision,
Springer, vol. 48(3), pages 287-304, May.
- Begoña Subiza & Josep Peris, 2005. "Strong maximals: Elements with maximal score in partial orders," Spanish Economic Review, Springer, vol. 7(2), pages 157-166, 06.
- Fishburn, Peter C, 1991. " Nontransitive Preferences in Decision Theory," Journal of Risk and Uncertainty, Springer, vol. 4(2), pages 113-34, April.
- Susanne Fuchs-Seliger & Oliver Mayer, 2003. "Rationality without Transitivity," Journal of Economics, Springer, vol. 80(1), pages 77-87, 08.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Raúl López-Pérez).
If references are entirely missing, you can add them using this form.