On the leximin and utilitarian overtaking criteria with extended anonymity

Kohei Kamaga, Takashi Kojima

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

We present an extension of the overtaking criterion, called fixed-step overtaking social welfare relation (SWR), and its leximin counterpart, called fixed-step W-leximin SWR, for the evaluation of infinite utility streams. Our SWRs satisfy Fixed-step Anonymity. First, we characterize them by using the consistency, called Weak Fixed-step Indifference Consistency, which links indifference for infinite utility streams to indifference for their truncated vectors that are taken periodically. Second, we characterize another utilitarian extension, called S-overtaking SWR, by replacing the consistency with Fixed-step Anonymity. The S-overtaking SWR is a subrelation of the fixed-step overtaking SWR. Meanwhile, the leximin counterpart of the S-overtaking SWR coincides with the fixed-step W-leximin SWR, and we obtain its alternative characterization using Fixed-step Anonymity. Finally, we generalize the impossibility of combining Fixed-step Anonymity with the catching-up SWR by showing the Pareto and strong consistency axioms satisfied by the catching-up SWR come in conflict with Fixed-step Anonymity.

Original languageEnglish
Pages (from-to)377-392
Number of pages16
JournalSocial Choice and Welfare
Volume35
Issue number3
DOIs
Publication statusPublished - 2010

Fingerprint

anonymity
social welfare
Südwestrundfunk
Anonymity
Leximin
Social welfare
Overtaking criterion

ASJC Scopus subject areas

  • Economics and Econometrics
  • Social Sciences (miscellaneous)

Cite this

On the leximin and utilitarian overtaking criteria with extended anonymity. / Kamaga, Kohei; Kojima, Takashi.

In: Social Choice and Welfare, Vol. 35, No. 3, 2010, p. 377-392.

Research output: Contribution to journalArticle

Kamaga, Kohei ; Kojima, Takashi. / On the leximin and utilitarian overtaking criteria with extended anonymity. In: Social Choice and Welfare. 2010 ; Vol. 35, No. 3. pp. 377-392.
@article{b39fb88f8d3d462c937bbd7803d2c7ca,
title = "On the leximin and utilitarian overtaking criteria with extended anonymity",
abstract = "We present an extension of the overtaking criterion, called fixed-step overtaking social welfare relation (SWR), and its leximin counterpart, called fixed-step W-leximin SWR, for the evaluation of infinite utility streams. Our SWRs satisfy Fixed-step Anonymity. First, we characterize them by using the consistency, called Weak Fixed-step Indifference Consistency, which links indifference for infinite utility streams to indifference for their truncated vectors that are taken periodically. Second, we characterize another utilitarian extension, called S-overtaking SWR, by replacing the consistency with Fixed-step Anonymity. The S-overtaking SWR is a subrelation of the fixed-step overtaking SWR. Meanwhile, the leximin counterpart of the S-overtaking SWR coincides with the fixed-step W-leximin SWR, and we obtain its alternative characterization using Fixed-step Anonymity. Finally, we generalize the impossibility of combining Fixed-step Anonymity with the catching-up SWR by showing the Pareto and strong consistency axioms satisfied by the catching-up SWR come in conflict with Fixed-step Anonymity.",
author = "Kohei Kamaga and Takashi Kojima",
year = "2010",
doi = "10.1007/s00355-010-0445-x",
language = "English",
volume = "35",
pages = "377--392",
journal = "Social Choice and Welfare",
issn = "0176-1714",
publisher = "Springer New York",
number = "3",

}

TY - JOUR

T1 - On the leximin and utilitarian overtaking criteria with extended anonymity

AU - Kamaga, Kohei

AU - Kojima, Takashi

PY - 2010

Y1 - 2010

N2 - We present an extension of the overtaking criterion, called fixed-step overtaking social welfare relation (SWR), and its leximin counterpart, called fixed-step W-leximin SWR, for the evaluation of infinite utility streams. Our SWRs satisfy Fixed-step Anonymity. First, we characterize them by using the consistency, called Weak Fixed-step Indifference Consistency, which links indifference for infinite utility streams to indifference for their truncated vectors that are taken periodically. Second, we characterize another utilitarian extension, called S-overtaking SWR, by replacing the consistency with Fixed-step Anonymity. The S-overtaking SWR is a subrelation of the fixed-step overtaking SWR. Meanwhile, the leximin counterpart of the S-overtaking SWR coincides with the fixed-step W-leximin SWR, and we obtain its alternative characterization using Fixed-step Anonymity. Finally, we generalize the impossibility of combining Fixed-step Anonymity with the catching-up SWR by showing the Pareto and strong consistency axioms satisfied by the catching-up SWR come in conflict with Fixed-step Anonymity.

AB - We present an extension of the overtaking criterion, called fixed-step overtaking social welfare relation (SWR), and its leximin counterpart, called fixed-step W-leximin SWR, for the evaluation of infinite utility streams. Our SWRs satisfy Fixed-step Anonymity. First, we characterize them by using the consistency, called Weak Fixed-step Indifference Consistency, which links indifference for infinite utility streams to indifference for their truncated vectors that are taken periodically. Second, we characterize another utilitarian extension, called S-overtaking SWR, by replacing the consistency with Fixed-step Anonymity. The S-overtaking SWR is a subrelation of the fixed-step overtaking SWR. Meanwhile, the leximin counterpart of the S-overtaking SWR coincides with the fixed-step W-leximin SWR, and we obtain its alternative characterization using Fixed-step Anonymity. Finally, we generalize the impossibility of combining Fixed-step Anonymity with the catching-up SWR by showing the Pareto and strong consistency axioms satisfied by the catching-up SWR come in conflict with Fixed-step Anonymity.

UR - http://www.scopus.com/inward/record.url?scp=77955570071&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77955570071&partnerID=8YFLogxK

U2 - 10.1007/s00355-010-0445-x

DO - 10.1007/s00355-010-0445-x

M3 - Article

VL - 35

SP - 377

EP - 392

JO - Social Choice and Welfare

JF - Social Choice and Welfare

SN - 0176-1714

IS - 3

ER -