An Advised Indirect-Utility Ranking of Opportunity Sets

There is a substantial strand of literature about ranking the subsets of a set of alternatives, usually referred to as opportunity sets. We investigate a model that is dependent on the preference of a grand set of alternatives. In this framework, the indirect-utility criterion ranks the opportunity sets by the following rule: a subset A is weakly preferred to another subset B if and only if A contains at least one preference maximizing element from A∪B. This criterion leads to the indifference of each subset of alternatives to a singleton; symmetry appears at this stage, as the property holds true for any one of the maximizers in A. Conversely, suppose that a ranking of opportunity sets satisfies the property that each opportunity set is indifferent to a singleton contained within it. Then, we prove that such a ranking must use a generalized form of the indirect-utility criterion, where maximization is applied to a selection of the alternatives. Altogether, these results produce a characterization of the advised indirect-utility criterion for ranking opportunity sets.

[1]  Walter Bossert,et al.  Ranking Opportunity Sets: A n Ax-iomatic Approach , 1994 .

[2]  W. Bossert,et al.  Ranking Sets of Objects , 2001 .

[3]  Karol Sikora,et al.  Pareto Optimal Decisions in Multi-Criteria Decision Making Explained with Construction Cost Cases , 2020, Symmetry.

[4]  Klaus Nehring,et al.  Continuous Extensions of an Order on a Set to the Power Set , 1996 .

[5]  Paola Manzini,et al.  Sequentially Rationalizable Choice , 2007 .

[6]  T. Bergstrom.  Maximal elements of Acyclic Relations on Compact Sets , 1975 .

[7]  J. Alcantud.  Characterization of the existence of maximal elements of acyclic relations , 2002 .

[8]  F. Quartieri.  Existence of maximals via right traces , 2021 .

[9]  Somdeb Lahiri,et al.  Justifiable preferences over opportunity sets , 2003, Soc. Choice Welf..

[10]  José Carlos Rodriguez Alcantud,et al.  The Indirect-Utility Criterion for Ranking Opportunity Sets over Time , 2019, Symmetry.

[11]  José Carlos Rodriguez Alcantud,et al.  Sequential rationalization of multivalued choice , 2015, Math. Soc. Sci..

[12]  C. Puppe.  An Axiomatic Approach to “Preference for Freedom of Choice” , 1996 .

[13]  David M. Kreps.  A REPRESENTATION THEOREM FOR "PREFERENCE FOR FLEXIBILITY" , 1979 .

[14]  Peter C. Fishburn,et al.  Even-chance lotteries in social choice theory , 1972 .

[15]  D. Bouyssou,et al.  Utility Maximization, Choice and Preference , 2002 .

[16]  鈴村 興太郎,et al.  Rational Choice, Collective Decision And Social Welfare (位相幾何学と経済学) , 1980 .

[17]  Matthew Ryan.  Path independent choice and the ranking of opportunity sets , 2014, Soc. Choice Welf..

[18]  Tuğçe Çuhadaroğlu,et al.  Choosing on influence , 2015 .

[19]  C. Kops.  (F)Lexicographic shortlist method , 2018 .

[20]  M. Walker,et al.  On the existence of maximal elements , 1977 .

[21]  Miguel A. Ballester,et al.  Choice by sequential procedures , 2013, Games Econ. Behav..

[22]  Sen-Kuei Liao,et al.  A Hybrid MCDM Model to Select Optimal Hosts of Variety Shows in the Social Media Era , 2020, Symmetry.

[23]  Walter Bossert,et al.  Choice under complete uncertainty: axiomatic characterizations of some decision rules , 2000 .

[24]  Roberto Lucchetti,et al.  Ranking objects from a preference relation over their subsets , 2018, Soc. Choice Welf..

[25]  Kemal Yildiz,et al.  Every Choice Function is Pro-Con Rationalizable , 2018, Operations Research.

[26]  Alfio Giarlotta,et al.  Choice resolutions , 2020, Social Choice and Welfare.

[27]  Ritxar Arlegi.  A note on Bossert, Pattanaik and Xu's “Choice under complete uncertainty: axiomatic characterization of some decision rules” , 2002 .