On Some Axioms for Ranking Sets of Alternatives

S. Barbera; C. R. Barrett; Prasanta K. Pattanaik

doi:10.1016/0022-0531(84)90092-9

On Some Axioms for Ranking Sets of Alternatives

S. Barbera^*, C. R. Barrett, Prasanta K. Pattanaik

^*Autor correspondiente de este trabajo

Producción científica: Contribución a una revista › Artículo › Investigación › revisión exhaustiva

49 Citas (Scopus)

2 Descargas (Pure)

Resumen

The problem of extending an ordering on a finite set of alternatives to its power set is considered. It is shown that two fairly mild axioms imply the restrictive condition that every set is equivalent to the set consisting only of its least and greatest elements. A characterisation of all extensions of a linear ordering, which satisfy our two axioms, is made by means of a class of real valued functions defined on integer pairs. The induced orderings are interpreted in terms of choice under uncertainty and an application made to welfare economics.

Idioma original	Inglés
Páginas (desde-hasta)	301-308
Publicación	Journal of economic theory
Volumen	33
N.º	2
DOI	https://doi.org/10.1016/0022-0531(84)90092-9
Estado	Publicada - ago 1984

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title = "On Some Axioms for Ranking Sets of Alternatives",

abstract = "The problem of extending an ordering on a finite set of alternatives to its power set is considered. It is shown that two fairly mild axioms imply the restrictive condition that every set is equivalent to the set consisting only of its least and greatest elements. A characterisation of all extensions of a linear ordering, which satisfy our two axioms, is made by means of a class of real valued functions defined on integer pairs. The induced orderings are interpreted in terms of choice under uncertainty and an application made to welfare economics.",

author = "S. Barbera and Barrett, \{C. R.\} and Pattanaik, \{Prasanta K.\}",

note = "Funding Information: * We are grateful to the British Academy for financial support which made this collaboration possible. A part of P. K. Pattanaik{\textquoteright}s work was done at the Institute for Advanced Studies, the Hebrew University, Jerusalem. {\textquoteright} Among others see Kannai and Peleg [S], Fishburn 141, Packard [ 121, Heiner and Packard 171, and Barbera and Pattanaik 121.",

year = "1984",

month = aug,

doi = "10.1016/0022-0531(84)90092-9",

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AU - Barrett, C. R.

AU - Pattanaik, Prasanta K.

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PY - 1984/8

Y1 - 1984/8

N2 - The problem of extending an ordering on a finite set of alternatives to its power set is considered. It is shown that two fairly mild axioms imply the restrictive condition that every set is equivalent to the set consisting only of its least and greatest elements. A characterisation of all extensions of a linear ordering, which satisfy our two axioms, is made by means of a class of real valued functions defined on integer pairs. The induced orderings are interpreted in terms of choice under uncertainty and an application made to welfare economics.

AB - The problem of extending an ordering on a finite set of alternatives to its power set is considered. It is shown that two fairly mild axioms imply the restrictive condition that every set is equivalent to the set consisting only of its least and greatest elements. A characterisation of all extensions of a linear ordering, which satisfy our two axioms, is made by means of a class of real valued functions defined on integer pairs. The induced orderings are interpreted in terms of choice under uncertainty and an application made to welfare economics.

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DO - 10.1016/0022-0531(84)90092-9

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JO - Journal of economic theory

JF - Journal of economic theory

IS - 2

ER -

On Some Axioms for Ranking Sets of Alternatives

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