Median-based extensions of an ordering over a set to the power set: An axiomatic characterization☆
References (16)
- et al.
Extending an order on a set to the power set: Some remarks on Kannai and Peleg's approach
J. Econom. Theory
(1984) Comments on the Kannai-Peleg impossibility theorem for extending orders
J. Econom. Theory
(1984)- et al.
A uniqueness result for extending orders; with application to ccollective choice as inconsistency resolution
J. Econom. Theory
(1984) An extension of Fishburn's theorem on extending orders
J. Econom. Theory
(1984)- et al.
A note on the extension of an order on a set to the power set
J. Econom. Ttheory
(1984) Preference relations
J. Math. Psychol.
(1979)The manipulability of social mechanisms that do not leave too much to chance
Econometrica
(1977)- et al.
On some axioms for ranking sets of alternatives
J. Econom. Theory
(1983)
Cited by (43)
Sufficient conditions making lexicographic rules over the power set satisfy extensibility
2023, Journal of Mathematical PsychologyConditional expected utility criteria for decision making under ignorance or objective ambiguity
2018, Journal of Mathematical EconomicsCitation Excerpt :A significant literature, surveyed for instance in Barberà et al. (2004), has analyzed such situations. With the notable exceptions of Baigent and Xu (2004) and Nitzan and Pattanaik (1984), most of the decision making criteria studied in this literature are based on the best and the worst consequences of the decisions or on associated lexicographic extensions. There are two obvious limitations of such “extremist” rankings.
Power set extensions of dichotomous preferences
2016, Mathematical Social SciencesCitation Excerpt :In these problems, the probabilities of the outcomes generated by each action are totally unknown or ignored. Therefore, each individual decision is simply described by the set of outcomes that it generates (see, among others, Arlegi, 2003, 2007, Barberà et al., 1984, Barberà and Pattanaik, 1984, Bossert et al., 2000 and Nitzan and Pattanaik, 1984). If it is assumed that the future uncertain outcomes are dichotomous (as in Bogomolnaia et al., 2005) and that assumption is considered within an environment of complete uncertainty, the problem to be analyzed collapses again into the formal structure that we propose.
Uniform expected utility criteria for decision making under ignorance or objective ambiguity
2012, Journal of Mathematical PsychologySequentially consistent rules of choice under complete uncertainty
2007, Journal of Economic TheoryFreedom, opportunity and uncertainty: A logical approach
2006, Journal of Economic Theory
- ☆
We are extremely grateful to B. Peleg, who suggested to us a version of Axiom WD used in this paper, and to S. Barbera and R. Holzman for several helpful comments. Much of the work on this paper was done when both of us were Fellows of the Institute for Advanced Studies, the Hebrew University, Jerusalem, and a part of the work was done when one of us was at the Southern Methodist University. We are grateful to both of these institutions for a very congenial environment for work.