Generalizing the Gibbard-Satterthwaite theorem: partial preferences, the degree of manipulation, and multi-valuedness
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1714329
- author
- Reffgen, Alexander LU
- organization
- publishing date
- 2011
- 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
- 2016-04-01 13:49:49
- date last changed
- 2022-01-27 21:21:37
@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}}, doi = {{10.1007/s00355-010-0479-0}}, volume = {{37}}, year = {{2011}}, }