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Generalizing the Gibbard-Satterthwaite theorem: partial preferences, the degree of manipulation, and multi-valuedness

Reffgen, Alexander LU (2011) In Social Choice and Welfare 37. p.39-59
Abstract
The Gibbard–Satterthwaite (GS) theorem is generalized in three ways: First, it is proved that the theorem is still valid when individual preferences belong to a convenient class of partial preferences; second, it is shown that every non-dictatorial surjective social choice function (SCF) is not only manipulable, but it can be manipulated in such a way that some individual obtains either his best or second best alternative; third, we prove a variant of the theorem where the outcomes of the SCF are subsets of the set of alternatives of an a priori fixed size. In addition, all results are proved not only for finite, but also for countably infinite sets of alternatives.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Social Choice and Welfare
volume
37
pages
39 - 59
publisher
Springer
external identifiers
  • wos:000291391100002
  • scopus:79958136915
ISSN
0176-1714
DOI
10.1007/s00355-010-0479-0
language
English
LU publication?
yes
id
4e27d29b-d4b0-4768-a300-f480e6a45eec (old id 1714329)
date added to LUP
2010-11-16 13:58:51
date last changed
2017-11-19 03:50:21
@article{4e27d29b-d4b0-4768-a300-f480e6a45eec,
  abstract     = {The Gibbard–Satterthwaite (GS) theorem is generalized in three ways: First, it is proved that the theorem is still valid when individual preferences belong to a convenient class of partial preferences; second, it is shown that every non-dictatorial surjective social choice function (SCF) is not only manipulable, but it can be manipulated in such a way that some individual obtains either his best or second best alternative; third, we prove a variant of the theorem where the outcomes of the SCF are subsets of the set of alternatives of an a priori fixed size. In addition, all results are proved not only for finite, but also for countably infinite sets of alternatives.},
  author       = {Reffgen, Alexander},
  issn         = {0176-1714},
  language     = {eng},
  pages        = {39--59},
  publisher    = {Springer},
  series       = {Social Choice and Welfare},
  title        = {Generalizing the Gibbard-Satterthwaite theorem: partial preferences, the degree of manipulation, and multi-valuedness},
  url          = {http://dx.doi.org/10.1007/s00355-010-0479-0},
  volume       = {37},
  year         = {2011},
}