An axiomatic characterization of the lexicographic maximin extension of an ordering over a set to the power set

@article{Pattanaik1984AnAC,
  title={An axiomatic characterization of the lexicographic maximin extension of an ordering over a set to the power set},
  author={P. Pattanaik and B. Peleg},
  journal={Social Choice and Welfare},
  year={1984},
  volume={1},
  pages={113-122}
}
The lexicographic maximin extension of an ordering is an important and widely used tool in social choice theory. We provide an axiomatization of it by means of five axioms. When the basic ordering is linear the following four (independent) axioms are sufficient: (1) Gärdenfors principle; (2) Neutrality; (3) Strong Fishburn monotonicity; and (4) Extension. Our result may also have applications in the theory of individual choice under uncertainty. 
Choosers as extension axioms
Set comparisons in a general domain: the Indirect Utility Criterion
Continuous Extensions of an Order on a Set to the Power Set
Extending an order to the power set: The Leximax Criterion
Freedom of choice: the leximax criterion in the infinite case
Automated Search for Impossibility Theorems in Social Choice Theory: Ranking Sets of Objects
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